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

^ f A 



REPORT 



OP THE 



SIXTY-THIKD MEETING 



OF THE 



BRITISH ASSOCIATION 



FOR THE 



ADVANCEMENT OF SCIENCE 



HELD AT 



NOTTINGHAM IN SEPTEMBER 1893. 




LONDON : 
JOHN MURRAY, ALBEMARLE STREET. 

1894. 

Office of the Association -. Burlington House, London, W. 



PRINTED BV 

SPOTTISWOODE AXD CO., NEW-STREET SQUARE 

LONDON 



CONTENTS. 



rage 
Objects and Rules of the Association ; xxv 

Places and Times of Meeting and Officers from commencement xxxv 

Presidents and Secretaries of the Sections of the Association fi-om com- 
mencement xlv 

List of Evening Lectures Ixiii 

Lectures to the Operative Classes Ixvi 

Officers of Sectional Committees present at the Nottingham Meeting Ixvii 

Officers and Council, 1893-94 Ixix 

Treasurer's Account Ixx 

Table showing the Attendance and Receipts at the Animal Meetings Ixxii 

Report of the Council to the General Committee Ixxiv 

Committees appointed hy the General Committee at the Nottingham Meet- 
ing in September 1893 Ixxviii 

Other Resolutions adopted by the General Committee Ixxxvii 

Resolutions, &c., referred to the Council for consideration, and action if 

desirable Ixxxvii 

Synopsis of Grants of Money Ixxxviii 

Places of Meeting in 1894 and 1895 Ixxxix 

General Statement of Sums which have been paid on account of Grants 

for Scientific Purposes xc 

General Meetings civ 

Address by the President, Dr. J. S. Rurdon Saxdekson, M.A., M.D., 
LL.D., "d.C.L., F.R.S., F.R.S.E., Professor of Physiology in the 

University of Oxford 3 

A 2 



IV CONTENTS. 



REPORTS ON THE STATE OF SCIENCE. 



[J?» asterisk * indicates that the title only is given. The marh f indicates the same, 
hut a reference is given to the journal or neKSj)a]per wliere it is published in extenso.] 



Page 

Correspouding Societies. — Report of the Committee, consisting of Professor R. 
Meldola (Chairman), Mr. T. V. Holmes (Secretary), Mj. Francis Galton, 
Sir Douglas Galton, Sir Rawson Rawson, Mr. G. J. Stkons, Dr. J. G. 
Gakson, Sir John Evans, Mr. J. Hopkinson, Professor T. G. Bonnet, Mr. 
VV. Whitaker, Mr. W. Topley, Professor E. B. Poulton, Mr. Cuthbeet 
Peek, and Rev. Canon H. B. Tristram 35 

Tables connected with the Pellian Equation from the point where the work 
was left by Degen in 1817. — Report of the Committee, consisting of Pro- 
fessor A. Cayley, Dr. A. R. Forsyth, Professor A. Lodge, and Professor 
J. J. Sylvester. (Drawn up by Professor Cayley) 73 

On the Establishment of a National Physical Laboratory. — Report of the 
Committee, consisting of Professor Olivee J. Lodge (Chairman), Mr. R. T. 
Glazebrooe (Secretary), Lord Kelvin, Lord Rayleigh, Sir 11. E. Roscoe, 
Professors J. J. Thomson, A. W. Ruceer, R. B. Clifton, G. F. FitzGeeald, 
G. Carey Foster, J. Viriami; Jones, A. Schuster, and W. E. Ayrton 120 

The Best Means of Comparing and Reducing Magnetic Observations. — In- 
terim Report of the Committee, consisting of Professor W. Grylls Adams 
(Chairman and Secretary), Lord Kelvin, Professors G. H. Darwin and 
G. Chrystal, Mr. C. H. Carpmael, Professor A. Schuster, Mr. G. M. 
Whipple, Captain Creak, The Astronomer Royal, Mr. William Ellis, 
and Profes.sor A. W. Rucker 120 

On Electro-optics. — Report of the Committee, consisting of Dr. John Kere 
(Chairman), Mr. R. T. Glazebrook (Secretary), Lord Kelvin, and Professor 
A. W. Rucker 121 

Magnetic Work at the Falmouth Observatory. — Report of the Committee, 
consisting of Mr. Howard Fox, Professor A. W. Rucker, and Professor W. 
G.Adams 121 

Experiments for Improving the Construction of Practical Standards for Elec- 
trical Measurements. — Report of the Committee, consisting of Professor 
Carey Foster (Chairman), Lord Kelvin, Professors Ayrton, J. Perry, 
W. G. Adams, and Lord Rayleigh, Drs. 0. J. Lodge, John Hopkinson, 
and A. Muirhead, Messrs. W. H. Preece and Herbert Taylor, Professor 
J. D. Everett, Professor A. Schuster, Dr. J. A. Fleming, Professors 
G. F. FitzGerald, G. Chrystal, and J. J. Thomson, Messrs. R. T. Glaze- 
brook (Secretary), W. N. Shaw, and T. C. Fitzpatrick, Dr. J. T. Bottom- 
ley, Professor J. Viriamu Jones, Dr. G. Johnstone Stoney, Professor 
S. P. Thompson, and Mr. G. Forbes 127 

Appendix L— Supplementary Report of the Electrical Standards 
Committee of the Board of Trade 129 



CONTENTS. V 

Page 

Appendix II. — Experiments on the Effects of the Heating produced 
in the Coils by the Currents used in Testing. By R. T. Glazebrook 1.36 

Appendix III. — On Standards of Low Electrical Eesistance. By 
Professor J. ViRiAMU Jones 137 

The Application of Photography to the Elucidation of Meteorological Pheno- 
mena.— Third Report of the Committee, consisting of Mr. G. J. Stmons 
(Chairman), Professor R. Meldola, Mr. J. Hopkinson, and Mr. A. W. 
CiiATDEN (Secretary). (Drawn up by the Secretary) 140 

The best methods of recording the Direct Intensity of Solar Radiation. — Ninth 
Report of the Committee, consisting of Sir G. G. Stokbs (Chairman), 
Professor A. Schuster, Mr. G. Johnstone Stonet, Sir H. E. Roscoe, 
Captain W. de W. Abnet, Professor H. McLeod, and Mr. G. J. Stmons. 
(Drawn up by Professor McLeod) 144 

The Present State of our Knowledge of Electrolysis and Electro-chemistry. — 
Reportby W. N. Shaw and T. 0. Fitzpateick 146 

Table of Electro-chemical Properties of Aqueous Solutions, compiled 
by T. C. Fitzpateick 146 

Investigation of the Earthquake and Volcanic Phenomena of Japan.— Thir- 
teenth Report of the Committee, consisting of the Rt. Hon. Lord Kelvin, 
Professor \V. G. Adams, Mr. J. T. Bottomlet, Professor A. H. Green, 
Professor C. G. Knott, and Professor John Milne (Secretary). (Drawn 
up by the Secretary) : 214 

Bibliography of Spectroscopy. — Interim Report of the Committee, consisting 
of Professor H. McLeod (Chairman), Professor W. C. Robeets-Austen 
(Secretary), Mr. H. G. Madan, and Dr. D. H. Nagel 227 

Bessel's Functions. — Report of the Committee, consisting of Lord Ratleigh 
(Chairman), Lord Kelvin, Professor Catley, Professor B. Price, Mr. J. 
W. L. Glaishee, Professor A. G. Greenhill, Profes.sor W. M. Hicks, and 
Professor A. Lodge (Secretary), appointed for the purpose of calculating 
Tables of certain Mathematical Functions, and, if necessary, of taking steps 
to carry out the Calculations, and to publish the results in an accessible form 227 

Meteorological Observations on Ben Nevis. — Report of the Committee, consist- 
ing of Lord McLaren (Chairman), Professor A. Crum Brown (Secretaiy), 
Dr. John Murray, Dr. Alexander Buchan, Hon. Ralph Abercromby, 
and Professor R. Copel and. (Drawn up by Dr. Buchan) 280 

Earth Tremors.— Report of the Committee, consisting of Mr. G. J. Symons, 
Mr. C. Davison (Secretary), Sir F. J. Bramwell, Professor G. H. Darwin, 
Professor J. A. Ewing, Dr. Isaac Roberts, Mr. Thomas Gray, Sir John 
Evans, Professors J. Peestwich, E. Hull, G. A. Lebour, R. Meldola, 
and J. W. JuDD, Mr. M. Walton Beown, Mr. J. Glaishee, Professor C. 
G. Knott, Professor J. H. Poynting, and Mr. Horace Daewin. (Drawn 
up by the Secretary) 287 

Appendix. — Account of Observations made with the Horizontal Pen- 
duliun. By Dr. E. von Rebeur-Paschwitz 309 

The Action of Magnetism on Light ; with a critical correlation of the various 
theories of Light-propagation. By Joseph Larmor, M.A., D.Sc, F.R.S., 
Fellow of St John's College, Cambridge 335 

I. Magnetic Action on Light 335 

II. Correlation of General Optical Theories 360 



VI • COJIXENTS. 

Page 

The Bibliography of Solution. — Interim Report ot the Committee, consisting 
01' Professor W. A. Tilden (Chairman), Dr. W. W. J NicoL (Secretary), 
Professor H. McLeod, Mr. S. U. Pjckeeing, Professor W. Ramsay, and 
Professor Sydney Young 372 

The Action of Light upon Dyed Colours. — Report of the Committee, consisting 
of Professor T. E. Thorpe (Chaii'man), Professor J. J. PIummel (Secretary), 
Dr. W. H. Perkin, Professor W. J. Russell, Captain Abney, Professor 
W. STROtrn, and Professor L. Meldola. (Drawn up by the Secretary) ... 373 

The Action of Light on the JHydracids of tlie Halogens in presence of 
Oxygen. — Report of the Committee, consisting of Dr. W. J. Russell, 
Captain W. de W. Abney, Professor W. N. Hartley, Professor W. Ramsay, 
and Dr A Richaedeon (Secretary) 381 

The Investigation of Isomeric Naphthalene Derivatives. — Seventh Report of 
the Committee, consisting of Professor W. A. Tilden and Professor H. E. 
Armstrong (Secretary). (Drawn up by Professor Armstrong) 381 

Wave-length Tables of the Spectra of the Elements and Compounds. — Report 
of the Committee, consisting of Sir H. E. RoscoE, Dr. Marshall Watts, 
Mr. J. N. LocKYER, Professors Dewar, Liveing, Schuster, W. N. Hart- 
ley, and Wolcott Gibes, and Captain Abney. (Drawn up by Dr. Mae- 
shall Watts) 387 

An International Standard for the Analysis of Iron and Steel. — Fifth Report 
of the Committee,consisting of Professor W.C.Roberts- Austen (Chairman), 
Sir F. Abel, Mr. E. Riley, Mr. J. Spillee, Professor J. W. Langley, Mr. 
G. J. Snelus, Professor Tilden, and Mr. Thomas Turner (Secretary). 
(Drawn up by the Secretary) 437 

On Solution. — Report of the Committee, consisting of Professor Tilden 
(Chairman), Dr. W. W. J. NicoL (Secretary), and Professor W.Ramsay ... 438 

The Influence of the Silent Discharge of Electricity on Oxygen and other 
Gases. — Report of a Committee, consisting of Professor H. McLeod (Chair- 
man), Mr. W. A. Shenstone (Secretary), Professor W. Ramsay, and Mr. 
J. Tudoe CuND.vLL. (Drawn up by the Secretary) 439 

I. The Preparation and Storage of Oxygen 439 

II. Ozone from Pure Oxygen. Its Action on Mercury, with a Note on 
the Silent Discharge of Electricity. By W. A. Shenstone and J. 

TuDOE OUNDALL ' 439 

III. Studies on the Formation of Ozone from Oxygen. By W. A. 

Shenstone and Martin Priest 440 

Bacteriology in its relations to Chemical Science. By Percy Frankland, 
Ph.D., B.Sc. (Lond.),F.R.S., Professor of Chemistry in University College, 
Dundee, St. Andrews University 441 

The Circulation of Underground Waters.— Nineteenth Report of the Com- 
mittee, consisting of Professor E. Hull (Chairman), Rev. Dr. H, W. 
Crosskey, Sir D. Galton, Messrs. J. Glaishbr and Percy Kendall, 
Professor G. A. Lebour, Messrs. E, B. Marten, G. H. Morton, and 
W. Pengelly, Professor J. Peestwich, and Messrs. I. Roberts, Thos. S. 
Stooke, G. J. Symons, W. Topley, C. Tylden- Weight, E. Wetheebd, 
W. AVhitakee, and C. E. De Range (Secretarv). (Drawn up by C. E. 
De Rance) " 463 

The Fossil Phyllopoda of the Palfeozoic Rocks.— Tenth Report of the Com- 
mittee, consi,<5tiDg of Profe.'^sor T. Wiltshiee (Chairman), Dr. H. Wood- 
WAED, and Professor T. Rupert Jones (Secretary). (Drawn up by Pro- 
fessor T. Rupert Jones) 465 



CONTENTS. Vii 

Page 
The Eurypterid-bearing Deposits of the Pentland Hills. — Report of the Com- 
mittee, consisting of Dr. R. H. Teaquair (Chairman^, Professor T. Rttpeet 
Jones, and Mr. Malcolm Laxtbie (Secretary). (Drawn up by Mr. M. 
Laueie) ." 470 

The Volcanic Phenomena of Vesuvius and its Neighbourhood. — Report of the 
Committee, consisting of Mr. H. Bauerman, Mr. F. W. Rtjdleb, Mr. 
J. J. H. Teall, and Professor H. J. Johnston-Lavis. (Drawn up by 
Professor H. J. Johnston-Lavis) 471 

The Collection, Preservation, and Systematic Registration of Photogi-aphs 
of Geological Interest in the United Kingdom. — Fourth Report of the 
Committee, consisting of Professor James Geikie (Chairman), Professor 
T. G. Bonnet, Dr. Tempest Anderson, Dr. Valentine Ball, Mr. James 
E. Bedford, Professor W. Boyd Dawkins, Mr. James W. Davis, Mr. 
Edmund J. Gaewood, Mr. William Gray, Mr. Robert Kidston, Mr. 
Aethfe S. Reid, Mr. R. H. Tiddeman, Mr. W. W. Watts, Mr. Hoeace 
B. WooDWAED,aud Mr. Osmund W. Jeffs (Secretary). (Drawn up by the 
Secretary) 473 

The Registration of the Type Specimens of British Fossils. — Fourth Report 
of the Committee, consisting of Dr. Heney Woodavaed (Chairman), Rev. 
G. F. Whidborne, Mr. R. Kidston, Mr. J. E. Maee, and Mr. A. S. 
Woodwaed (Secretary) 482 

The Character of the High-level SheU-bearing Deposits at Clava, Chapelhall, 
and other Localities. — Report of the Committee, consisting of Mr. J. Hoene 
(Chairman), Mr. David Robeetson, Mr. T. F. Jamieson, Mr. James 
Feasee, Mr. P. F. Kendall, and Mr. Dugald Bell (Secretary). (Drawn 
up by Mr. Hoene, Mr. Feasee, and Mr. Bell ; with Special Reports on 
the Organic Remains, by Mr. Robeetson) 483 

Erratic Blocks of England, Wales, and Ireland. — Twenty-first Report of the 
Committee, consisting of Professor E. Hull (Chairman), Professor J. 
Peestwich, Dr. H. W. Ceossket, Professor W. Boyd Dawkins, Professor 
T. McK. Hushes, Professor T. G. Bonnet, Mi-. C. E. De Range, Mr. P. F. 
Kendall (Secretary), Mr. R. H. Tiddeman, Mr. J. W. Woodall, and 
Professor L. C. Miall. (Drawn up by Mr. P. F. Kendall, Secretary) 614 

The present state of our Knowledge of the Zoology of the Sandwich Islands. — 
Third Report of the Committee, consisting of Professor A. Newton (Chair- 
man), Dr. W. T. Blanfoed, Dr. S. J. Hickson, Professor C. V. Riley, 
Mr. 0. Salvin, Dr. P. L. Sclater, Mr. E. A. Smith, and Mr. D. Sharp 
(Secretary) 523 

A Digest of the Observations on the Migration of Birds at Lighthouses and 
Light-vessels. — Interim Report of a Committee, consisting of Professor 
A. Newton (Chairman), Mr. John Cohdeaux (Secretary), Messrs. R. M. 
Baeeington, J. A. Harvie-Brown, W, Eagle Clarke, and the Rev. E. P. 
Knubley 524 

The present state of our Knowledge of the Zoology and Botany of the West 
India Islands, and on taking steps to investigate ascertained deficiencies in 
the Fauna and Flora.— Sixth Report of the Committee, consisting of Dr. 
P. L. Sclatee (Chairman), Mr. George Mueeay (Secretary), Mr. W. 
Caeeuthees, Dr. A. C. L. G. Gunthee, Dr. D. Shaep, Mr. F. DuCane 
Godman, Professor A. Newton, and Dr. D. II. Scott 524 

The Marine Zoology of the Irish Sea —Report of the Committee, consisting of 
Mr. Geoege Beook, Professor A. C. Haddon, Mr. W. E. Hotle, Mr. I. C. 
Thompson (Secretary), Mr. A. 0. Walkee, and Professor W. A. Heedman 
(Chairman) 526 



Vlll CONTENTS. 

Page 

Occupation of a Table at the Zoological Station at T*J^aples. — Report of the 
Committee, consisting of Dr. P. L. Sclater, Professor E. Ray Lankestee, 
Professor J.Cossak Ewart, Professor M. Foster, Mr. A. Sedgwick, Professor 
A. M. Marshall, and Mr. Percy Slaben (Secretary) 537 

I. On the Action of Coloured Light on Assimilation. By Cecil C. 
Duncan 638 

II. On the Function and Correlation of the Pallial Organs of the 
Opisthobranchiata. By John D. F. Gilchrist 540 

Investigations made at the Laboratory of the Marine Biological Association at 
Plymouth. — Report of the Committee, consisting of Professor E. Ray 
Lankester (Chairman), Professor M. Foster, Professor S. H. Vines, and 
Mr. S. F. Harmer (Secretary) 546 

I. The Turbellaria of Plymouth Sound. By F. W. Gamble, B.Sc... 546 

II. The Larvae of Decapod Crustacea. By Edgar J, Allen, B.Sc... 547 

III. Notes on How Fish find Food. By Gregg Wilson, M.A., B.Sc. 548 

The Physiological Action of the Inhalation of Oxygen in Asphyxia, more 
especially in Coal Mines. — Report of the Committee, consistuig of Professor 
J. G. M'cKendeick, F.R.S. (Chairman), Dr. J. T. Bottomley, F.R.S., and 
Mr. W. Ernest F. Thomson, M.A., M.D. (Secretary). (Drawn up by the 
Secretary) 551 

The Legislative Protection of Wild Birds' Eggs. — Report of the Committee, 
consisting of Mr. Thomas Henry Thomas, RCA. (Chairman), Rev. Canon 
Tristram, D.D., LL.D., F.R.S., Professor Alfred Newton, F.R.S., Pro- 
fessor Adolph Leipner, F.Z.S., Professor Newton Parker, Ph.D., F.Z.S., 
and Dr Charles Tanfield Vachell (Secretary). (Drawn up by the 
Secretary) 552 

Index Generum et Specierum Animalium. — Report of the Committee, con- 
sisting of Sir W. II. Flower, Dr. P. L. Sclater, Dr. II. Woodward, and 
Mr. G. Brook (Secretary), for supervising its compilation by Mr. C. Da vies 
Sherborn 553 

Scottish Place-names. — Report of the Committee, consisting of Sir C. W. 
Wilson, F.R.S. (Chairman), Dr. J. Burgess (Secretary), and Mr. Coutts 
Trotter. (Drawn up by the Secretary) 554 

Exploration of Ancient Remains in Abyssinia. — Report of the Committee, 
consisting of Dr. J. G. Garson (Chairman), Mr. J. Theodore Bent (Secre- 
tary), Mr. F. W. RuDLEE, Mr. E. W. Beabeook, and Mr. G. W. Bloxam. 
(Drawn up by Mr. J. Theodore Bent) 557 

Appendix. — On the Morphological Characters of the Abyssinians. By 
J. G. Garson, M.D 563 

The Exploration of the Glacial Region of the Karakoram Mountains. — Report 
of the Committee, consisting of Colonel Godwin-Austen (Chairman), Pro- 
fessor T. G. BoNNEY (Secretary), and Colonel H. C. B. Tanner 564 

The Teaching of Science in Elementary Schools. — Report of the Committee, 
consisting of Dr. J. H. Gladstone (Chairman), Professor II. E. Aemstrong 
(Secretary), Mr. S. Bouene, Dr. Oeosskey, Mr. G. Gladstone, Mr. J. 
Heywood, Sir John Lubbock, Sir Philip Magnus, Professor N. Stoey 
Maskelyne, Sir H. E. Roscoe, Sir R. Temple, and Professor S. P. Thompson 566 

The Methods of Economic Training adopted in this and other Countries. — 
Report of the Committee, consisting of Professor W. Cunningham (Chair- 
man), Professor E. C. K. Conner (Secretary), Professor F. Y. Edgeworth, 
Professor H. S. Foxwell, Dr. J. N. Keynes, and Mr. H. Higgs 571 



CONTENTS. IX 

Page 

The Climatological and Hydrograpliical Conditions of Tropical Africa. — 
Second Report of the Committee, consisting of Mr. E. G. Ravenstein 
(Chairman), Mr. Baldwin Latham, Mr. G. J. Stmons, F.R.S., and Dr. 
H. R. Mill (Secretary). (Drawn up by Mr. E. G. Ravenstein) 572 

The Dryness of Steam in Boiler Trials. — Interim Report of the Committee, 
consisting of Sir F. Beamm-ell (Chairman), Professor W. C. Unwin (Secre- 
tary), Professor A. B. W. Kennedy, Mr. Maik Rtjmley, Mr. Jeremiah 
Head, and Professor Osborne Reynolds 572 

The Development of Graphic Methods in Mechanical Science. — Third Report 
by Professor H. S. Helb Shaw, M.Inst.C.E 573 

On the Physical Deviations from the Normal among Children in Elementary 
and other Schools. — Report of the Committee, consisting of Sir Douglas 
Galton (Chairman), Dr. F. Warner (Secretary), Mr. G. W. Bloxam, Mr. 
E. W. Beabrook, and Dr. J. G. Garson. (Drawn up by Dr. Francis 
Warner) 614 

Ethnographical Survey of the United Kingdom. — First Report of the Com- 
mittee, consisting of Mr. Feancis Galton (Chairman), Dr. J. G. Garson, 
Professor A. C. Haddon, Dr. Joseph Anderson, Mr. E. W. Brabeoob: 
(Secretary), Mr. J. Romillx Allen, Professor D. J. Cunningham, Pro- 
fessor Boyd Dawkins, Professor R. Meldola, General Pitt-Rivers, and 
Mr. E. G. Ravenstein. (Drawn up by the Secretary) 621 

The North- Western Tribes of Canada. — Interim Report of the Committee, 
consisting of Dr. E. B. Tylor, Mr. G. W". Bloxam (Secretary), Dr. G. M. 
Dawson, Mr. R. G. Haliburton, and Mr. H. Hale, appointed to investi- 
gate the physical characters, languages, and industrial and social condition 
of the North-Western Tribes of the Dominion of Canada 653 

Anthropometric Laboratory. — Report of the Committee, consisting of Sir 
W. H. Flowee (Chairman), Dr. J. G. Garson (Secretary), Mr. G. W. 
Bloxam, Professor A. C. Haddon, and Dr. Wilbeeforce Smith. (Drawn 
up by the Secretary 654 

Uniformity in the Spelling of Barbaric and Savage Languages and Race 
Names. — Report of the Committee, consisting of Mr. Francis Galton 
(Chairman), Dr. E. B. Ttlor, Professor A. C. Haddon, Mr. G. W. Bloxam, 
Mr. Ling Roth, and Mr. C. E. Peek (Secretary) 662 

The Automatic Balance of Reciprocating Mechanism. By W. Worbt Beau- 
mont, MInst.C.E 665 



CONTENTS. 



TRANSACTIONS OF THE SECTIONS. 



Section A.— MATHEMATICAL AND PHYSICAL SCIENCE. 

THURSDAY, SEPTEMBER li. 

Pa^e 
A.ddress by R. T. Glazebeook, MA., F.R.S., President of the Section 671 

L Interim Report of the Committee on a National Physical Laboratory ... 681 

2. Interim Report of the Committee on Electro-optics 681 

3. Report of the Committee on Solar Radiation 681 

4. Report of the Committee for Comparing and Reducing Magnetic 
Observations 681 

5. Report of the Committee in connection with the Magnetic Work of the 
Falmouth Observatory 681 

6. On the Period of Vibration of Electrical Disturbances upon the Earth. 

By Professor G. F. FitzGerald, Sc.D., M.A., F.R.S., F.T.C.D 682 

7. The Moon's Atmosphere and the Kinetic Theory of Gases. By G. H. 

Bryan, M.A 682 

8. *0n Grinding and Polishing. By Lord Ratleigh, Sec.R.S 685 

9. Simple Apparatus for Observing and Photographing Interference and 
Diffraction Phenomena. By W. B. Croft, M.A 685 

10. On Wilson's Theory respecting the asserted foreshortening of the inner 
side of the Penumbrse of the Solar Spots when near the Sun's Ijiuib, and 
of the probable thickness of the Photospheric and also Penumbral 
Strata of the Solar Envelopes. By Rev. Fredekice; Howlett 686 

FRIDAY, SEPTEMBER 15. 

1. Report on the Present State of our Knowledge ot Electrolysis and 
Electro-chemistry. By W. N. Shaav, F.R.S., and the Rev. T. C. 
Fitzpateice; 688 

2. On the Connection between Ether and Matter. By Professor Oliver J. 
Lodge, F.R.S. 688 

3. On a Mechanical Analogue of Anomalous Dispersion. By R. T. Glaze- 
brook, M.A., F.R.S 688 

4. Note on Professor Ebert's Estimate of the Radiating Power of an Atom, 
with Remarks on Vibrating Systems giving Special Series of Overtones 
like those given out bv some Molecules. By Professor G. F. FitzGerald, 
M.A., F.R.S .". 689 

5. On the Reflection of Sound or Light from a Corrugated Surface. By 
Lord Raxleigh 690 

6. fOn the Piezo-electric Property of Quartz. By Lord Kelvin, Pres.R.S. . 691 

7. On a Piezo-electric Pile. By Lord Kelvin, Pres.R.S 691 

8. Electrical Interference Phenomena somewhat Analogous to Newton's 

Rings, but exhibited by Waves in Wires. By Edwin H. Baeton, B.Sc. 692 



CONTENTS. XI 

Page 

9. On Interference Phenomena exhibited by the Passage of Electric Waves 
through Layers of Electrolyte. By G. Qdny Yule 694 

10. On a Familiar Type of Caustic Curves. By J. Laemor, F.R.S 695 

SATURDAY, SEPTEMBER 16. 

1. Report of the Committee on Mathematical Tables (Bessel's Functions) ... 696 

2. Report of the Committee on the Pellian Equation 696 

3. On a Spherical Vortex. By M. J. M. Hill, M.A., D.Sc, Professor of 
Mathematics at University College, London 696 

4. On the Magnetic Shielding of Two Concentric Spherical Shells. By 

Professor A. W. Rijckee, F.R.S 698 

5. On the Equations for Calculating the Shielding of a Long Iron Tube on 

an Internal Magnetic Pole. By Professor G. F. FitzGeeald, M.A., 
F.R.S 698 

6. On the Equations for Calculating the Effect of a Hertzian Oscillator on 

Points in its Neighbourhood. By Professor G. F. FitzGeeald, M.A., 
r.R.S 698 

7. Magnetic Action on Light. By J. Larmoe, F.R.S 699 

8. *0n a Special Class of Generating Functions in the Theory of Numbers. 

By Major P. A. MacMahon, R.A., F.R.S 699 

9. On Agreeable Numbers. By Lieut.-Col. Allan Cunningham, R.E., 
Fellow of King's College, London 699 



MONDAY, SEPTEMBER 18. 

1. Report of the Committee on Earth Tremors 699 

2. Report of the Committee on the Volcanic and Seismological Phenomena 

of Japan 700 

*Discussion on the Teaching of Elementary Physics introduced by the three 
following Papers : — • 

'6. Apparatus for Class-work in Elementary Practical Physics. By Professor 
G. Caeet Foster, F.R.S 700 

4. On Physics Teaching in Schools. By W. B. Croft, M.A 700 

5. Notes on Science Teaching in Public Schools. By A. E. Hawkins, B.Sc. 701 

6. Report of the Committee on the Application of Photography to Meteoro- 
logical Phenomena 701 

7. Report of the Ben Nevis Committee 701 

TUESDAY, SEPTEMBER 19. 

1. Report of the Electrical Standards Committee 702 

2. On Standards of Low Electrical Resistance. By Professor J. Viriamu 
Jones 702 

3. An Apparatus for Comparing nearly Equal Resistances. By F. H. 
Nalder : 702 

4. Note on a Galvanometer suited to Physiological Use. By Dr. Oliver J. 

Lodge, F.R.S., and F. H. Nalder 703 



Xii CONTENTS. 

Page 

5. On a Simple Interference Arrangement. By Lord Ratleigh, Sec.R.S.... 703 

6. fOn the Construction of Specula for Reflecting Telescopes upon New 

Principles. By Dr. A. Shafaeik 704 

7. Supplementary Note on the Ether. By Dr. Oliver J. Lodge, F.R.S. ... 704 

8. On the Publication of Scientific Papers. By A. B. Basset, M.A., F.R.S. 704 

9. *0n a new Form of Air-pump. By Professor J. J. Thomson, F.R.S. ... 70.5 

1 0. *A Peculiar Motion assumed by Oil Bubbles in ascending Tubes containing 
Caustic Solutions. By F. T. Trotiton 705 

11. On Electro-magnetic Trails of Images in Plane, Spherical, and Cylindrical 
Current Sheets. By G. H. Bryan, M.A 706 

12. On Thermal Relations between Air and Water. By Hugh Robert Mill, 

D.Sc, F.R.S.E 7C6 

13. *0n a new Artificial Horizon. By W. P. Shadbolt 707 

14. *Investigations as to what would be the Laws which would Regulate the 

Transplacement of a Liquid by a Moving Body ; and Reasons why Ether 
eludes our Senses. By E. Major 707 



Section B.— CHEMICAL SCIENCE. 

THURSBAT, SEPTEMBER 14. 

Addi-ess by Professor J. Emerson Reynolds, M.D., Sc.D., F.R.S., President 

of the Section 708 

1. On Tools and Ornaments of Copper and other Metals from Egypt and 

Palestine. By Dr. J. H. Gladstone, F.R.S 715 

2. Report on International Standards for the Analysis of Iron and Steel ... 716 

3. *0n Native Iron Slanufacture in Bengal. By H. Harris and T. Turner 716 

4. On Nitride of Iron. By G. J. Fowler, M.Sc 716 

5. Report on the Silent Discharge of Electricity in Oxygen and other 
Gases 717 



FBI BAT, SEPTEMBER 15. 

1. Report on the Action of Light upon Dyed Colours 717 

2. *Demonstration of the Preparation and Properties of Fluorine by Moissan's 
Method. By Dr. M. Meslans 717 

3. *Interim Report on the Formation of Haloids 717 

4. Report on the Action of Light on the Hydracids of the Halogens in the 
Presence of Oxygen 718 

•6. On the Iodine Value of Sunlight in the High Alps. By Dr. S. Rideal . 718 

6. On a Modified Form of Bunsen and Roscoe's Pendulum Actinometer. By 

Dr. Arthur Richardson and J. Quick 719 

7. On the Expansion of Chlorine Gas and Bromine Vapour under the 
Influence of Light. By Dr. Arthur Richardson 719 

8. On the Cause of the Red Colouration of Phenol. By Charles A. Kohn, 

Ph.D., B.Sc 720 



CONTENTS. Xni 

Page 

9. On the Rate of Evaporation of Bodies in Atmospheres of Different 
Densities. By Dr. R. D. Phookan 721 

10 On the Occurrence of Cyano-nitride of Titanium in Ferro-manganese. 
ByT. W.Hogg 721 

3I0NDAY, SEPTEMBER 18. 

1. *Interim Report on the History of Chemistry 722 

2. Report on the Wave-length Tables of the Spectra of the Elements 722 

3. *Interim Report on the Bibliography of Spectroscopy 722 

4. Report on the Bibliography of Solution 722 

5. Report on Solution 723 

6. Discussion on the Present Position of Bacteriology, more especially in its 
relation to Chemical Science, opened by Professor Percy F. Fkankland, 
F.R.S 723 

7. 'Remarks on the Chemistry of Bacteria. By R. Wakington, F.R.S. 723 

8. On Fermentation in the Leather Industry. By J. T. Wood 723 

9. On some Ferments derived from Diseased Pears. By Geoege Tate, Ph.D., 
F.C.S 724 

10. *0n the Action of Permanganate of Potassium on Sodium Thiosulphate 
and Sulphate. By G. E. Brown and Dr. W. W. J. Nicol 725 

11. On the Application of Sodium Peroxide to Water Analysis. By Dr. S. 
RiDEAL and A. J. Boult 725 



TUESDAY, SEPTEMBER 19. 

1. Report on Isomeric Naphthalene Derivatives 726 

2. On the Application of Electrolysis to Qualitative Analysis. By Charles 

A. KoHN, Ph.D., B.Sc 726 

3. 'Interim Report on the Proximate Constituents of Coal 727 

4. Apparatus for Extraction for Analysis of Gases Dissolved in Water. By 
Edgar B. Truman, M.D., F.C.S 727 

5. *A Discussion on Explosions in Coal Mines, with special reference to the 
Dust Theory, was introduced by Professor H. B. Dixon, F.R.S 728 

6. The Application of the Hydrogen Flame in an Ordinary Miner's Safety 
Lamp to Accurate and Delicate Gas Testing. By Professor Frank 
Clovfes, D.Sc. Lond 728 

7. *0n the Gases enclosed in Coal Dust. By Professor P. P. Bedson 729 

8. *A Note on the Temperature and Luminosity of Gases. By Profe.ssor 

A. Smithells 729 

9. On Ethyl Butanetetracarboxylic Acid and its Derivatives. By Bevan 
Lean, kA., B.Sc 729 

10. On the Salts of a new Platinum-sulphurea Base. By W. J. Sell, M.A., 
F.C.S., F.I.C., and T. H. Easteeeield, M.A 731 

11. On Citrazinic Acid. By W. J. Sell, M.A., F.C.S., F.I.C., and T. H. 
Easterfield, M.A 731 

12. On a Nottingham Sandstone containing Barium Sulphate as a Cementing 

Material. By Professor Frank Clowes, D.Sc 732 



XIV CONTENTS. 

Section C— GEOLOGY. 

THURSDAY, SEPTEMBER 14. 

Page 
Address by J. J. H. Teall, M.A., F.R.S., F.G.S., President of the Section ... 733 

1. Notes of the Water-bearingr Capacity of the New Red Sandstone of 
Nottingham. By Professor Edwaed Hull, LL.D., F.R.S., F.G.S 748 

2. On a Nottingham Sandstone containing Barium Sulphate as a Cementing 
Material. By Professor Frank Clowes, D.Sc 745 

3. On the Discovery of a Concealed Ridge of pre-Carbnniferous Rocks under 
the Trias of Netherseal, Leicestershire. By Professor Edward Hull, 
LL.D., F.R.S., F.G.S 745 

4. On the Geology of the Coastland of Caria. By John L. Myres 746 

5. Report on the Fossil Phyllopoda of the Palfeozoic Rocks 747 

6. On the Discovery of Cephalaspis in the Caithness Flags. By Dr. R H. 
Traquair, F.R.S 747 

7. Report on the Eurypterid-bearing Deposits of the Pentland Hills 747 

8. On some Vertebrate Remains not hitherto recorded from the Rhtetic Beds 

of Britain. By Montagu Browne, F.G.S., F.Z.S 748 

9. Note on a Fault at Cinder Hill. By George Fowler, M.Iust.C.E., 
F.G.S •: '. .'749 

10. On the Base of the Cambrian in Wales. By H. Hicks, M.D., F.R S 

F.G.S : : : .'750 

IL On the Reptilia of the British Trias. By E. T. Newton, F.R.S 752 



FRIDAY, SEPTEMBER 15. 

L t Joint Discussion with Section E on the Limits of Geology and Geo- 
g™P"y t8-3.5, *7o3 

2. The Dissected Volcano of Crandall Basin, Wyoming. By Professor 

Joseph Paxson Iddings 753 

3. On Structures in Eruptive Bosses which resemble those of Ancient 

Gneisses. By Sir Archibald Geikie, F.R.S 754 

4. On the Fittings in Pebbles from the Trias. By Professor W. J. Sollas, 
D.Sc, F.R.S :. ; 755 

5. On Bones and Antlers of Cervus f/iffanfem incised and marked by Mutual 

Attrition while buried in bogs or Marl. By V. Ball, C.B., LL.D., 
F.R.S 756 

6. 'On a Mass of Cemented Shells dredged from the Sea Bed. By Professor 

W. A. Herdman, F.R.S 75(3 

7. Note to accompany the Exhibition of a Geological Map of India. By 

R. D. Oldham, A.R.S.M., F.G.S., of the Geological Survey of India 756 

8. Geological Sketch of Central East Africa. By Walcot Gibson, F.G.S. 758 

9. Report on the Volcanic Phenomena of Vesuvius 759 

10. On Quartz Enclosures in Lavas of Stromboli and StromboUcchio, and their 
Eflect on the Composition of the Rock. By Professor H. J. Johnston- 
Latis, M.D., M.R.C.S., B.-es-Sc, F.G.S 759 



CONTENTS. XV 

Page 

11. On the Gypsum Deposits of Nottinghamshire and Derhyshire. By A. T. 
Metcalfe, F.G.S 760 

12. Report on Photographs of Geological Interest 760 

13. On a Bed of Oolitic Iron-ore in the Lias of Raasay. By Horace B. Wood- 

ward, F.G.S 760 

14. Note on a Transported Mass of Chalk iu the Boulder Clay at Catworth in 
Huntingdon.shire. By A. C. G. Cameron, Geological Survey 760 

15. Augen Structure in Relation to the Origin of Eruptive Rocks and Gneiss. 

By J. G. GooDCHiLD, F.G.S 761 



SATURDAY, SEPTEMBER 16. 

1. The Genetic Relations of the Basic Eruptive Rocks of Gran (Kristiania 
Region). By Professor W. C. Brosger, of the University of Kristiania 762 

2. Petrological Features of the Dissected Volcano of Crandall Basin, 
"Wyoming. By Professor Joseph Paxson Iddings 763 

3. Berthelot's Principle applied to Magmatic Concentration. By Alfred 
Haeker, M.A., F.G.S 765 

4. On the Origin of Intermediate Varieties of Igneous Rocks by Intrusion 
and Admixture, as observed at Barnavave, Carlingford. Bv Professor 

W. J. SoLLAS, D.Sc, F.R.S ". 765 

5. On the Transformation of an Amphibolite into Quartz-mica-diorite. By 
Professor W. J. Sollas, D.Sc, F.R.S 765 

6. On some Igneous Rocks of South Pembrokeshire, with a Note on the 
Rocks of the Isle of Grassholme. By F. T. Howard, B.A., and E. W. 
Small, M.A., B.Sc 766 

7. Notes on a Hornblende Pikrite from Greystones, Co. Wicklow. By 

W. W. Watts, M.A., F.G.S 767 

8. Report on the Registration of Type Specimens of Fossils 767 



MONDAY, SEPTEMBER 18. 

1. *Discussion on Coral Reefs, Fossil and Recent. Opened by Professor 
W. J. Sollas, F.R.S 768 

Twenty Years' Work on the Younger Red Rocks. By Rev. A. Irving, 
D.Sc, B.A., F.G.S 768 



o 



3. ♦On the Trias of the Midlands. By Professor C. Lapwoeth, F.R.S 768 

4. On the Occurrence of Fossils in the Magnesian Limestone of Bulwell, near 

Nottiagham. By Baron A. voN Rbinach and W. A. E Ussher 768 

5. Note on the ' Himlack ' Stone near Nottingham. By Professor E. Hull, 
F.R.S., F.G.S 769 

6. On the Junction of the Permian and Triassic Rocks at Stockport. By 

J. AV. Gray, F.G.S., and Percy F. Kendall, F.G.S 769 

7. Note on some Molluscan Remains lately di.'icovered in the English 

Keuper. By R. Bullen Newton, F.G!S., British Museum (Natural 
History) 770 



Xvi CONTENTS. 

Page 

8. Observations on the Skiddaw Slates of the North of the Isle of Man. By 

Herbert Bolton, Assistant Keeper, the Manchester Museum, Owens 
OoUege 770 

9. *0n the Volcanic Phenomena of Japan. By Professor J. Milne, F.R.S. 771 
10. On the Radiolarian Cherts of Cornwall. By Howaed Fox, F.G.S 771 



TUESDAY, SEPTEMBER 19. 

1. *Discussion on Geological Education. Opened by the Reading of the 

following Papers 772 

Geology in Secondary Education. By Professor Geenville A. J. 
Cole, M.R.I.A., F.G.S 772 

On Geology in Professional Education. By Professor G. A. Lebotjr, 
M.A., F.G.S 773 

2. The Glaciation of Asia. By Prince Keopotkin 774 

3. On some Assumptions in Glacial Geology. By Professor T. G. Bonne r, 

D.Sc, F.R.S 775 

4. On the Glacial Period, its Origin and Effects, and the Possibility of its 

Recurrence. By C. A. Lindvall, of Stockholm 776 

5. Report on the High-level Shell-bearing Deposits at Clava, Chapelhall, and 

other Localities 776 

6. Report on Erratic Blocks 776 

7. On some Shell-middens in North Wales. By P. W. Abbott and P. F. 
Kendall, F.G.S 776 

8. A Map of the Esker Systems of Ireland. By Professor W. J. Sollas, 
D.Sc, F.R.S 777 

9. On some Shelly Clay and Gravel in North-east Aberdeenshire. By 
Dugald Bell, F.G.S 778 

10. On the pre-Glacial Form of the Ground in Lancashire and Cheshire. By 

C. E. De Rance, F.G.S .". 779 

WEDNESDAY, SEPTEMBER 20. 

1. On the Distribution of Granite Boulders in the Clyde Valley. By 
DuGALB Bell, F.G.S 780 

2. On the Derbyshire Toadstoue. By H. Arnold-Bbmeose, M.A., F.G.S. ... 780 

3. Note on the Perlitic Quartz Grains in Rhyolite. By W. W. Watts, 
M.A., F.G.S 781 

4. On the Minute Structure of the Skeleton of Monograptus Priodon. By 
Professor W. J. Sollas, D.Sc, F.R.S 781 

5. Report on the Circulation of Underground Waters 782 



Section D.— BIOLOGY. 

THURSDAY, SEPTEMBER 14. 

Address by Rev. H. B. Teisteam, M.A., LL.D., D.D., F.R.S., President 'of 

the Section 784 

1. Report on the Zoology of the Sandwich Islands 783 



CONTENTS. XVii 

Page 
2. On the Zoology of the Sandwich Islands. By D. Sharp, F.R.S 783 

a. Interim Keport on a Digest of Observations on the Migration of Birds at 
Lighthouses 784 

4. Report on the Zoology and Botany of the West India Islands 784 

6. *Note on the Discovery of Diprotodon Hemains in Australia. By 
Professor W. Stirling 784 



FRIDAY, SEPTEMBER 15. 

1. *0n the Physico-chemical and Vitalistic Theories of Life. By J. S. 
IIaxdane 798 

2. *0n the Effect of the Stimulation of the Vagus Nerve on the Disengage- 
ment of Gases in the Swimming-bladder of Fishes. By Dr. Christian 
Bohr 798 

3. On Malformation from Pre-natal Influence on the Mother. By Alfred 

R, Wallace, D.O.L., F.R.S 798 

4. On f 'alorimetry by Surface Thermometry and Hygrometry. Bv AuGTrsTUS 

D. Waller, M.D., F.R.S '. 799 

5. 'On a Method of Recording the Heart Sounds. By Professor W. 

EiNTHOVEN 801 

0. *0n Nerve Stimulation. By F. Gotch, F.R.S 801 

7. On the Digestive Ferments of a large Protozoon. By Marcus Hartog 

and Augustus E. Dixon 801 

8. Report on the Physiological Action of the Inhalation of Oxygen 802 



Department of Zoology. 

1. On the Luminous Organs of Cephalopoda. By William E. Hotle 802 

2. Report on the Marine Zoology of the Irish Sea 803 

3. *Interim Report on a Deep-sea Tow-net 803 

4. The Origin of Organic Colour. By F. T. Mott, F.R.G.S 803 

6. Remarks on the Roots of the Lemna and the Reversing of the Fronds in 
Lemna trimlca. By Miss Nina F. Latard 803 



SATURDAY, SEPTEMBER 16. 

1 . *Interim Report on the Botanical Laboratory at Peradeniya, Ceylon 804 

2. Interim Report on the Legislative Protection of Wild Birds' Eggs 805 

3. On the Etiology and Life-history of some Vegetal Galls and their 

Inhabitants. By G. B. Rothera 805 

4. On some New Features in Nuclear Division in Lilium Martagon. By 
Professor J. B. Farmer 806 



MONDAY, SEPTEMBER 18. 

1. *Discus3ion on Coral Reefs. Opened by Professor W. J. Sollas, M.A., 
F.R.S : 807 

2. Report on W^ork carried on at the Zoological Station, Naples 807 

1893. a 



XVlll CONTENTS. 

Page 

3. Report on Work carried on at the Biological Station, Plymouth 807 

4. Interim Eeport on the Index Generum et Specierum Animalium 807 

6. A few Notes on Seals and Whales seen during the Voyage to the Antarctic 
Ocean, 1892-93. By Wm. S. Bruce 807 

6. On the Penguins of the Antarctic Ocean. By C. W. Donald, M.B 808 

7. On the Development of the Molar Teeth of the Elephant, with Remarks 

on Dental Series. By Professor J. Cleland, F.R.S 808 



TUESDAY, SEPTEMBER 19, 

1. On certain Gregarinidse, and the possible connection of Allied Forms with 
Tissue Changes in Man. By Charles II. Cattle, M.D., M.R.C.P., and 
James Millar, M.D 809 

2. On the Wings of Archesopteryx and of other Birds. By C. Herbert 
Hurst 810 

3. On the Sensory Canal System of Fishes. By Walter E. Collinge 810 

4. On the Starch of the Chlorophyll-granule, and the Chemical Processes 
involved in its Dissolution and Translocation. By Horace T. Brown, 
F.R.S 811 

5. On Cytological Differences in Homologous Organs. By Professor G. 

GiLSON, of Louvain , 813 

6. On Karyokinesis in the Fungi. By Harold Wager, F.L.S 816 

7. On Variation of Fecundity in Trifolium pratense and its varieties and 

Trifolium medium. By William Wilson 817 

8. On the Cortex of Tmesipteris tannensis, Bernh. By R. J, Harybt 
Gibson, M.A., F.L.S 817 

9. On Lime Salts in relation to some Physiological Processes in the Plant. 

By Dr. J. Clark 818 

10. On the Development of the ' Ovipositor ' in the Cockroach (Periplaneta 

orientalis). By Professor A. Denny 818 



Section E.— GEOGRAPHY. 

THURSDAY, SEPTEMBER 14. 

Address by Henry Sbebohm Sec.R.G.S., F.L.S., F.Z.S., President of the 

Section 819 

1. A Journey across Australia. By Guy Boothby 832 

2. On the Islands of Chiloe. By Mrs. Lilly Grove, F.R.G.S 833 

3. On Recent Explorations in Katanga. By E. G. Ravenstein 83-'? 

4. *Pictures of Japan. By Professor J. Milne, F.R.S 833 



FRIDAY, SEPTEMBER 15. 

1. tOn the Limits between Physical Geography and Geology, By Clements 
R. Markham, C.B., F.R.S ^. .;....... 834 

2."0n the Relations of Geology to Physical Geography, By W. Toplby, 
F.R.S 834 



CONTENTS. XIX 

Page 

tA Discussion on tho limits between Physical Geograpty and Geology 
followed the reading of these Papers 835 

3. Report on Scottish Place Names 835 

4. Report of the Karakoram Expedition 835 

5. *0n the Influence of Land and Water on tlie Temperature of the Air. 

By J. Y. Buchanan, F.R.S 835 

6. The Temperature and Density of Sea Water between the Atlantic Ocean 
and North Sea. By H. N. Dickson, F.R.S.E 835 

7. The Clyde Sea Area : a Study in Physical Geography. By Hugh Robert 

Mill, D.Sc, F.RS.E 836 

8. Confio-uration of the English Lakes. By Hugh Robert Mill, D.Sc, 
P.R.S.E 836 

MONDAY, SEPTEMBER 18. 

1. Report of the Committee on the Exploration of Ancient Remains in 
Abyssinia 836 

2. Report of the Committee on the Climatological and Hydrographical 
Conditions of Tropical Africa 836 

3. On Uganda and its People. By Captain Williams, R.A 837 

4. On Hausa Pilgrimages from the Western Sudan. By Rev. Chakles H. 

Robinson, M.A 837 

5. *0n the Relation of Lake Tanganyika and the Congo. By J. Howard 
Reid 837 

6. On Environment in relation to the Native Tribes of the Congo Basin. By 
Herbert Waed 837 

7. On the Vertical Rehef of Africa. By Dr. H. G. Schlichter 837 

8. The Distribution of Disease in Africa. By R. W. Felken, M.D., 
F.R.S.E 839 

9. Middle Egypt from Ptolemaic Maps and Recent Surveys. By Cope 
Whitehouse, M.A., F.R.A.S 839 

TUESDAY, SEPTEMBER 19, 

1. Notes of an Antarctic Voyage. By Wm. S. Bruce | 840 

2. On the Antarctic Expedition of 1892-93. By C. W. Donald, M.B 841 

3. *0n the Importance of Antarctic Exploration. By Admiral Sir Erasmus 
Ommanney 841 

4. Recent Exploration in Tibet. By E. Delmar Morgan 841 

6. On the Bengal Duars. By Edward Heawood, M. A., F.R.G.S 841 

6. The Use of the Lantern in Geographical Teaching. By B. Bentham 

Dickenson, M.A 842 

Section F.— ECONOMIC SCIENCE AND STATISTICS. 

THURSDAY, SEPTEMBER 14. 

Address by Professor J. Shield Nicholson, M.A., President of the Section... 843 

1. Report on the Teaching of Science in Elementary Schools 850 

a2 



XX CONTENTS. 

Page 

2. Report on the Methods of Economic Traininj^ adopted in this and other 
Countries 850 

3. The Improvement of Labourers' Cottages. By Rev. J. 0. Bevan, M.A., 
F.G.S Bol 

4. 'Index Numbers. By Stephen Bouenb 851 



FRIDAY, SEPTEMBER 15. 

1. On Agricultural Depression. By H.H.Scott 851 

2. The Diminution of the Net Immigration from the rest of the country into 
the great towns of England and Wales, 1871-91. By Edwin Cannan, 
M.A 851 

3. *0n Poor Law and Old Age. By Rev. J. Frome Wilkinson 852 

4. On Statistical Correlation between Social Phenomena. By Professor F. 

Y. Edgeworth 852 

5. On the Lessons of the Australian Banking Collapse. By C. Gairdner... 853 

6. On Bishop Hugh Latimer as an Economist. By the Rev. W. Cunning- 
ham, D.D 853 

MOXDAY, SEPTEMBER 18. 

1. On Nottingham Lace and Fashion. By J. B. Firth 854 

2. *0n Agricultural Depression. By W. J. Allsebeook 855 

3. On Home Work — The Share of the Woman in Family Maintenance. By 
Mifjs Ada Heather-Big g 855 

4. On the Progress of the Newspaper Press, and the Need of Reform and 

Consolidation of the I^aws affecting it. By Professor J. A. Strahan, 
M.A., LL.B 856 

6. *0n the Census of Foreigners in France. By M. A. de Liegeard 85G 

6. On Social and Economical Heredity. By W. B. Grant 856 

TUESDAY, SEPTEMBER 19. 

1. *0n the Currency Problem. By Professor H. S. Foxwell, M.A 857 

2. On the Currency Question practically considered from a Commercial and 
Financial Point of View. By W. E. Dorrington 857 

3. On some Objections to Bimetallism viewed in connection with the Report 

of the Indian Currency Committee. By L. L. Price 858 

4. On India and the Currency. By F. C. Harrison 859 

Section G.— MECHANICAL SCIENCE. 
THURSDAY, SEPTEMBER \i:. 

Address by Jeremiah Head, M.Inst.C.E., F.C.S., President of the Section ... 860 

1, On the Automatic Balance of Reciprocating Mechanism. By W. AVorbt 
Beaumont, M.Inst.C.E 873 



CONTENTS. XXI 

Page 

2. On Lace Machinery. By E. Doxtghtt 873 

S. Oa Knitting Machinery. By Csas. R. Woodward 874 

4. *0n Lace and Hosiery Machinery. By Professor W. RoBiNSOiir 874 



FRIDAY, SEPTEMBER 15. 

1. Third Report on the Development of Graphic Methods in Mechanical 
Science. By Professor IL S. Hele Shaw, M.Inst.C.E 874 

2. Report on Determining the Dryness of Steam in Boiler Trials 874 

3. *0n Thermal Storage by Utilisation of Town Refuse. By C. C. Keep... 874 

4. On the Disposal of Refuse. By William Waenee, A.M.List.C.E 874 

6. On Warming and Ventilation. By Frank Ashwell, M.Inst.M.E 875 

•6. 'On Modern Watchmaking. By T. P. Hewitt 877 

7. On Patent Percussive Tool for Calking, Chipping, Mining. By J. Mac- 
EwAN Ross 877 



MONDAY, SEPTEMBER 18. 

1. On the Relative Cost of Conductors with Different Systems of Electric 
Power Transmission. By Gisbert Kapp 878 

2. On the Utilisation of Waste AVater-power for Generating Electricity. By 
Albion T. Snell 878 

3. On a new Form of VariaWe Power-gear for Electric Railways and Tram- 

ways. By W. WoEBT Beaumont, M.Inst.C.E 880 

4. *0n Self-exciting Armatures and Compensators for Loss of Pressure. By 
W. B. Satees 881 

•6. On a Mechanical System of Electrical Conductors. By E. Payne 881 



TUESDAY, SEPTEMBER 19. 

1 . On Flashing Lights for Lighthouses. By O. T. Olsen 882 

2. On an Automatic Gem-separator. By William S. Lockiiakt, 
M.Inst.C.E., M.Inst.M.E '. 883 

3. On some Experiments with Ventilating Fans or Air- propellers. By 

William George Walker, M.InstM.E. 884 

4. *0n the Testing Machine and Experimental Steam Engine in the 
Engineering Laboratories of University College, Nottingham. By Prof. 

W. Robinson 884 



Section H.— ANTHROPOLOGY. 

THURSDAY, SEPTEMBER 14. 
Address by R. Mttneo, M.A., M.D., F.R.S.E., President of the Section 885 

1. On the Ethnographic Aspect of Dancing. By Mrs. Lillt Grove, 
F.R.G.S 895 

2. Report on the Anthropometric Laboratory 895 



Xxii CONTENTS. 

Page 

3. Report on the PhyBical Deviations from the Normal among Children in 

Elementary and other Schools 895 

4. On Anthropometric Work in large Schools. By Beeteam C. A. Wiudle, 
D.Sc.,M.D., M.A 895 

5. Notes on Anthropometric Weighing. By W. Wixbekfoece Smith, 
M.D., M.R.C.P 89& 

FRIDAY, SEPTEMBER 15. 

1. Report on the Ethnographical Survey of the United Kingdom 896. 

2. *0n Anglo-Saxon Remains and Coeval Relics from Scandinavia. By 
Professor Hans Hildebeand 896- 

y. On the Origin and Development of Early Christian Art in Great Britain 
and Ireland. By J. Romilly Allen, F.S. A.Scot 896. 

4. *0n an Implement of Hafted Bone, with a Hippopotamus Tooth inserted, 
from Calf Hole, near Grassington. By Rev. E.Jones 897 

5. The Prehistoric Evolution of Theories of Punishment, Revenge, and 

Atonement. By Rev. G. Haetwell Jones 89? 

6. ' Four ' as a Sacred Number. By Miss A. AV. Bcckland 898- 

SATURDAY, SEPTEMBER IC. 

1. On Ancient Metal Implements from Egypt and Lachish. By Dr. J. H. 
Gladstone 899" 

2. Notes on Flint Saws and Sickles. By Robeet Muneo, M.D 899 

3. On Prehistoric Remains in Crete. By John L. Mtees 899' 

4. *Funeral Rites and Ceremonies among the Tshinyai, or Tshinyangwe. By 
Lionel Decle 90O 

6. *The Arungo and Marombo Ceremonies among the Tshinyangwe. By 
Lionel Deole 90O 

6. *TheMa-Goa. By Lionel Decle 90O 



MONDAY, SEPTEMBER 18. 

1. Report on the Exploration of Ancient Remains in Abyssinia 900' 

2. On the External Characters of the Abyssinians examined by Mr. Bent. 

By J. G. Gaeson, M.D 900 

3. Ethnographical Notes relating to the Congo Tribes. By Heebeet 

Waed, F.R.G.S 900' 

4. On the Mad Head, By Ceocelet Clapham, M.D 900- 

5. *0n the Dards and Siah-Posh Kafirs. By J. Beddoe, M.D., F.R.S., and 

Dr. Leitnee 001' 

G. Pin-wells and Rag-bushes. By E. Sidney Haetland, F.S.A 901 

7 . *0n the Primitive Americans. By Miss J . M. Welch 901 

8. On the Indians of the Mackenzie and Yukon Rivers, Canada. By the 
Right Rev. Dr. Bompas, Bishop of Selkirk 901 

9. *Dn the Australian Natives. By Miss J. A. Fowlee 902 



CONTENTS. xxiii 

Page 

10. •On a Modification of the Australian Aboriginal Weapon termed the 
Leonile, Langeel, Bendi, or Buccan, By E. Eiheeidge, Jun 902 

11. *0n an Unusual Form of Rush-hasket from the Northern Territory of 
South Austraha. By R, Ethebidge, Jun 902 



TUESDAY, SEPTEMBER 19. 

1. Recent Introduction into the Indian Army of the Method of Finger Prints 

for the Identification of Recruits. By Francis Galton, F.R.S 902 

2. On the Excavation of the Stone Circle of Lag-ny-Boiragh on the Meayll 
Hill at Port Erin, Isle of Man, By P. M. 0. Keemode, F.S.A.Scot, 
and Professor "VV. A. Keedman, F.R.S 902 

3. On the Structure of Lake Dwellings. By Robert Muneo, M.D 903 

4. A British Village of Marsh Dwellings at Glastonbury. By Arthtje 

BuLLEiD, F.S.A 903 

6. *0n the Place of the Lake Dwellings at Glastonbury in British Archaeo- 
logy. By Professor W. BoTD Da WKINS, F.R.S 903 

6. On Early Uses of Flint in Polishing. By H. Stopes 904 

7. On Palaeolithic Anchors, Anvils, Hammers, and Drills. By H. Sxopes . . . 904 

8. Report on Uniformity in the SpeUing of Barbaric and Savage Languages 

and Race-names 904 

9. Interim Report on the North-Western Tribes of the Dominion of Canada 904 
Index 906 



sxiv 



LIST OF PLATES. 



PLATE I. 

Illustrating the Tenth Report on the Fossil Phyllopoda of the Palaeozoic Rocks. 

PLATES II., IIL 

Illustrating the Report on the Character of the High-level Shell-bearing Deposits 
at Clava, Chapelhall, and other Localities. 

PLATE IV. 
Illustrating the Report on the Marine Zoology of the Irish Sea. 

PLATE V. 

Illustrating Mr, Seebohm's Address to the Geographical Section. 



ERRATA. 

In ]88i) (Newcastle) Report. 
Page 28. In equation (2) for + (.i- + «»)?<, read - (.i- + n")u. 



In 1893 (Nottingham) Report. 
Page 308, fig. 10. The Scale should be transferred to fig. 4, p. 295. 



OBJECTS AND EULES 

OP 

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 Officers and Members of the Councils, or Managing Committees, 
of Philosophical Institutious shall be entitled, in like manner, to become 
Members of the Association. 

All Members of a Philosophical Institution recommended by its Coun- 
cil or Managing Committee shall be entitled, in like manner, to become 
Members of the Association. 

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

Com,pnsitions, Subscriptions, and Privileges. 

Life Members shall pay, on admission, the sum of Ten Pounds. They 
shall receive gratuitously the Keports of the Association which may be 
published after the date of such payment. They are eligible to all the 
offices of the Association. 

AinjUAL Subscribers shall pay, on admission, the sum of Two Pounds, 
and in each following year the sum of One Pound. They shall receive 



XXVI KULES OF THE ASSOCIATION. 

gratvitoushj the Reports of the Association for the year of their admLssion 
and for the years in which they continue to pay without intermission their 
Annnal Subscription. By omitting to pay this subscription in any par- 
ticular year, Members of this class (Annual Subscribers) lose for that and 
all future years the privilege of receiving the volumes of the Association 
gratis ; but they may resume their Membership and 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 Association. 
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 Five 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 furcliase it at reduced (or Members') 
price, according to the following specification, viz. : — 

1. Gratis. — Old Life Members who have paid Five Pounds as a compo- 

sition for Annual Payments, and previous to 1845 a further 
sum of Two Pounds as a Book Subscription, or, since 1845, 
a farther sum of Five Pounds. 

New Life Members who have paid Ten Pounds as a composition. 

Annual Members who have not intermitted their Annual Sub- 
scription. 

2. At reduced or Members' Price, viz., two-thirds of the Publication Price. 

— Old Life Members who have paid Five Pounds as a compo- 
sition for Annual Payments, but no further sum as a Book 
Subscription. 

AnnualMembers who have intermitted their Annual Subscription. 

Associates for the year. [Privilege confined to the volume for 
that year only.] 

3. Members may purchase (for the purpose of completing their sets) any 

of the volumes of the Reports of the Association up to 1874, 
of which more than 15 copies remain, at 2s. Qd. per volume.* 

Application to be made at the Office of the Association. 
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 1874, are on sale, at £10 the set. 



RULES OF THE ASSOCIATION. XXVIl 



Meetings. 

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

General Committee. 

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. Peemanent Members. 

1. Members of the Council, Presidents of the Association, and Presi- 
dents of Sections for the present 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 sub- 
mitting new claims under this Bide to the decision of the Council, they must 
be sent to the Secretary at least one month before the Meeting of the Associa- 
tion. The decision of the Council on the claims of any Member of the Associa- 
Hon to be placed on the list of the General Committee to be final. 

Class B, Tempokary Members.^ 

1. Delegates nominated by the Corresponding Societies under the 
conditions hereinafter explained. Claims under 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 under this Rule 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. Yice-Presidents and Secretaries of Sections. 

Organising 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 for election. 

From the time of their nomination they constitute Organising Com- 
mittees for the purpose of obtaining information upon the Memoirs and 
Reports likely to be submitted to the Sections,^ and of preparing Reports 

' Eevised by the General Committee, 1884. 

^ Passed by the General Committee, Edinburgh, 1871 . 

' Notice to Contributors of Memoirs. — Authors are reminded that, under an 
arrangement dating from 1871, the acceptance of Memoirs, and the days on which 
they are to be read, are now as far as possible determined by Organising Committees 
for the several Sections lefore the beginning of the Meeting. It has therefore become 



3XV1H BULES OF THE ASSOCIATION. 

thereon, and on the order in which it is desirable that they should be 
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 Organising Sectional Committees.' 

An Organising 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 Sectional Committee, after which their functions as an 
Organising Committee shall cease.^ 

Constitution of the Sectional Committees.^ 

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 Members (not Associates) present 
.at the Meeting whose assistance they may particularly desire. The Sec- 
tional Committees thus constituted shall have power to add to their 
aiumber from day to day. 

The List thus formed is to be entered daily in the Sectional Minute- 
Book, and a copy forwarded without delay to the Printei', who is charged 
with publishing the same before 8 A.M. on the next day in the Journal of 
ithe Sectional Proceedings. 

Business of the Sectional Committees. 

Committee Meetings are to be held on the Wednesday, and on the 
following Thursday, Friday, Saturday,* Monday, and Tuesday, for the 
•objects stated in the Rules of the Association, and specified below. The 
Organising Committee of a Section is empowered to arrange the hours of 
aneeting of the Section and the Sectional Committee. 

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



o 



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 

necessary, in order to give an opportunity to the Committees of doing justice to the 
several Communications, that eacli author sliould prepare an Abstract of his Memoir 
of a length suitable for insertion in the published Transactions of the Association, 
and that he should send it, together with the original Memoir, by book-post, on or 

before , addressed to the General Secretaries, at the office of 

the Association. 'For Section ' If it should be inconvenient to the Author 

that his paper should be read on any particular days, he is requested to send in- 
formation 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 inserted in the Annual Volume 
unless it is handed either to the Recorder of the Section or to the Assistant General 
Secretary before the conclusion of the Meeting. 

' Sheffield, 1879. ^ Swansea, 1880. » Edinburgh, 1871. 

* The meeting on Saturday is optional, Southport, 1883. 



RULES OF THE ASSOCIATION. XXIS 

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

3. Papers which have been reported on unfavourably by the Organ- 
ising Committees shall not be brought before the Sectional 
Committees.' 

At the first meeting, one of the Secretaries will read the Minutes of 
last year's proceedings, as recorded in the Minute-Book, and the Synopsis 
of Recommendations adopted at the last Meeting of the Association 
and printed in the last volume of the Report. He will next proceed to 
read the Report of the Organising Committee.^ The list of Communi- 
cations to be read on Thursday shall be 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. Tha 
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 ly Authors, are to he forwarded, at the close of the 
Sectional Meetings, to the Secretary. 

The Vice-Presidents and Secretaries of Sections become ex officio 
temporary Members of the General Committee (vide p. xxvii), 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 ofi'ered 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 
Committees for the execution of such Reports or researches ; and to state 
whether, 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 Memhers of the Committee should he named, and 

These rules were adopted by the General Committee, Plyirouth, 1877. 
* This and the following sentence were added by the General Committee, Edin- 
burgh, 1871. 



XXX EPLES OF THE ASSOCIATION. 

one of them appointed to act as Chairman, who shall have notified per- 
sotially or in writing his willingness to accept the office, the Chairman to have 
the responsibility of receiving and disbursing the grant (if any has been made) 
and securing the presentation of the Report in due time ; and, further, it is 
expedient that one of the members should be appointed to act as Secretary, for 
ensuring attention to business. 

That it is desirable that the number of Members appointed to serve on a 
Committee should be as small as is consistent with its efficient ivorking. 

That a tabular list of the Committees appointed on the recommendation 
of each Section should be sent each year to the Recorders of the several Sec- 
tions, to enable them to fill in the statement whether the several Committees 
appointed on the recommendation of their respective Sections had presented 
their reports. 

Tliat on the proposal to recommend the appointment of a Committee for a 
special object of science having been adopted by the Sectional Committee, the 
number of Members of such Committee be then fixed, but that the Members to 
serve on such Co^nmittee be nominated and selected by the Sectional Com' 
mittee at a subsequent meeting.^ 

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 Assistant General Secretary 
for presentation to the Committee of Recommendations. Unless this be 
done, the Recommendations cannot receive the sanction of the Association. 

N.B. — Recommendations which may originate in any one of the Sections 
must first be sanctioned by the Committee of that Section before they can 
be referred to the Committee 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 Committee 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 are required to present to each following Meeting of the 
Association a Report of the progress which has been made ; and the 
Chairman of a Committee to whom a money grant has been made must 
forward to the General Officers, before July 1, a statement of the sums 
which have been expended, with vouchers, and the balance which 
remains disposable on each grant. 

Grants of money sanctioned at any one Meeting of the Association 
expire on June 30 following ; nor is the Treasurer authorised, 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 

' Eevised by the General Committee, Bath, 1888. 

' Passed by the General Committee at Sheffield, 1879. 



BULBS OF THE ASSOCIATION. XXXI 

Committee to do so ; and no money so raised shall be expended except in 
accordance with the rules of tbe Association. 

In each Committee, the Chairman is the only person entitled 
to call on the Treasurer, Professor A. W. Riicker, F.R.S., Burlington 
House, London, W., 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, when not 
employed in carrying on scientific inquiries for the Association. 

Business of the Sections. 

The Meeting Room of each Section is opened for conversation shortly 
before the meeting commences. T/ie Section Rooms and approaches thereto 
can he tised for no notices, exhibitions, or other purposes than those of the 
Association. 

At the time appointed the Chair will be taken,' and the reading of 
communications, in the order previously made public commenced. 

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. 

A Report presented to the Association, and read to the Section which 
originally 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 they are engaged, except when employed on 
messages by one of the Officers directing these Rooms. 

' The Organising Committee of a Section is empowered to arrange the hours of 
meeting of the Section and Sectional Committee. Passed by the General Committee 
at Edinburgh, 1892. 



XXXll RULES OF THE ASSOCIATION. 



Committee of Recommendations. 

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. 

Presidents of the Association in former years are ex officio members of 
the Committee of Recommendations.^ 

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

All proposals for establishing new Sections, or altering the titles of 
Sections, or for any other change in the constitutional forms and funda- 
mental rules of the Association, shall be referred to the Committee of 
Recommendations for a report.^ 

If the President of a Section is unable to attend a meeting of the 
Committee of Recommendations, the Sectional Committee shall be 
authorised to appoint a Vice-President, or, failing a Vice-President, 
some other member of the Committee, to attend in his place, due notice 
of the appointment being sent to the Assistant General Secretary.^ 

Corresponding Societies} 

1. Any Society is eligible to be placed on the List of Corresponding 
Societies of the Association which undertakes local scientific investiga- 
tions, and publishes notices of the results. 

2. Application may be made by any Society to be placed on the 
List of Corresponding Societies. Applications must be addressed to the 
Secretary on or before the 1st of June preceding the Annual Meeting at 
which it is intended they should be considered, and must be accompanied 
by specimens of the publications of the results of the local scientifia 
investigations recently undertaken by the Society. 

3. A Corresponding Societies Committee shall be annually nomi- 
nated by the Council and appointed by the General Committee for the 
purpose of considering these applications, as well as for that of keeping 
themselves generally informed of the annual work of the Corresponding 
Societies, and of superintending the preparation of a list of the papers, 
published by them. This Committee shall make an annual report to the 
General Committee, and shall suggest such additions or changes in the 
List of Corresponding Societies as they may think desirable. 

4. Every Corresponding Society shall return each year, on or before the 
1st of June, to the Secretary of the Association, a schedule, properly filled 
up, which will be issued by the Secretary of the Association, and which will 
contain a request for such particulars with regard to the Society as may 
be required for the information of the Corresponding Societies Committee. 

6. There shall be inserted in the Annual Report of the Association 

> Passed by the General Committee at Newcastle, 1863. 

* Passed by the General Committee at Birmingham, 1865, 
' Passed by the General Committee at Leeds, 1890. 

* Passed by the General Committee, 1884. 



RDLES OF THE ASSOCIATION. XXxiii 

a list, in an abbreviated form, of the papers published hj the Corre- 
sponding Societies during the past twelve months which contain the 
results of the local scientific work conducted by them ; those papers only 
being included which refer to subjects coming under the cognisance of 
one or other of the various Sections of the Association. 

6. A Corresponding Society shall have the right to nominate any 
one of its members, who is also a Member of the Association, as its dele- 
gate to the Annual Meeting of the Association, who shall be for the time 
a Member of the General Committee. 

Conference of Delegates of Corresponding Societies. 

7. The Conference of Delegates of Corresponding Societies is em- 
powered to send recommendations to the Committee of Recommen- 
dations for their consideration, and for report to the General Committee. 

8. The Delegates of the various Corresponding Societies shall con- 
stitute a Conference, of which the Chairman, Vice- Chairmen, and Secre- 
taries shall be annually nominated by the Council, and appointed by the 
General Committee, and of which the members of the Corresponding 
Societies Committee shall be ex officio members. 

9. The Conference of Delegates shall be summoned by the Secretaries 
to hold one or more meetings during each Annual Meeting of the Associa- 
tion, and shall be empowered to invite any Member or Associate to take 
part in the meetings. 

10. The Secretaries of each Section shall be instructed to transmit to 
the Secretaries of the Conference of Delegates copies of any recommen- 
dations forwarded by the Presidents of Sections to the Committee of 
Hecommendations bearing upon matters in which the co-operation of 
Corresponding Societies is desired ; and the Secretaries of the Conference 
of Delegates shall invite the authors of these recommendations to attend 
the meetings of the Conference and give verbal explanations of their 
objects and of the precise way in which they would desire to have them 
carried into effect. 

11. It will be the duty of the Delegates to make themselves familiar 
with the purport of the several recommendations brought before the Confer- 
ence, in order that they and others who take part in the meetings may be 
able to bring those recommendations clearly and favourably before their 
respective Societies. The Conference may also discuss propositions bear- 
ing on the promotion of more systematic observation and plans of opera- 
tion, and of greater uniformity in the mode of publishing i-esults. 

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 
1893. y if ^ ^ 



XXxiv RULES OF THE ASSOCIATION. 



Council. 

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

(1) The Council shall consist of ^ 

1. The Trustees. 

2. The past Presidents. 

3. The President and Vice-Presidents for the time being. 

4. The President and Vice-Presidents elect. 

5. The past and present General Treasurers, General and 

Assistant General Secretaries. 

6. The Local Treasurer and Secretaries for the ensuing 

Meeting. 

7. Ordinary Members. 

(2) The Ordinary Members shall be elected annually from the 

General Committee. 

(3) There shall be not more than twenty-five Ordinary Members, of 

whom not more than twenty shall have served on the Council, 
as Ordinary Members, in the previous year. 

(4) In order to carry out the foregoing rule, the following Ordinary 

Members of the outgoing Council shall at each annual election 
be ineligible for nomination : — 1st, those who have served on 
the Council for the greatest number of consecutive years ; and, 
2nd, those who, being resident in or near London, have 
attended the fewest number of Meetings during the year 
— observing (as nearly as possible) the proportion of three by 
seniority to two by least attendance. 

(5) The Council shall submit to the General Committee in their 

Annual Report the names of the Members of the General 
Committee whom they recommend for election as Members of 
Council. 

(6) The Election shall take place at the same time as that of the 

Officers of the Association. 

Papers and Cominunications. 

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. 

' Passed by the General Committee at Belfast, 1874, 



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xlv 



Presidents and Secretaries of the Sections of the Association. 



Date and Place 



Presidents 



Secretaries 



MATHEMATICAL AND PHYSICAL SCIENCES. 

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



1882. Oxford 

1833. Cambridge 

1834. Edinburgh 



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

Sir D. Brewster, F.R.S 

Rev. W. Whewell, F.R.S. 



Rev. H. Coddington. 

Prof. Forbes. 

Prof. Forbes, Prof. Lloyd. 



SECTION A. — MATHEMATICS AND PHYSICS. 



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 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 

1853. Hull 



Rev. Dr. Robinson 

Rev. William Whewell, F.R.S. 

Sir D. Brewster, F.R.S 

Sir J. F. W. 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'CuUoch, M.R.LA. ... 
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. Whewell, D.D., 

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

F.B.S., F.R.S.E. 
The Very Rev. the Dean of 

Ely, F.R.S. 



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.MacquornRankine,Prof.Smyth, 

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

Prof. Stevelly, Prof . G. G. Stokes. 
Prof. Dixon, W. J. Macquorn Ran- 
kine, Prof. Stevelly, J. Tyndall. 
B. Blaydes Haworth, J. D. SoUitt, 

Prof. Stevelly, J. Welsh. 



xlvi 



EEPORT 1893. 



Date and Place 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 

1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton... 

1873. Bradford... 

1874. Belfast 

1875. Bristol 

1876. Glasgow ... 

1877. Plymouth... 

1878. Dublin 

1879. Sheffield ... 



Presidents 



Prof. G. G. Stokes, M.A., Sec 

K.S. 
Kev. Prof. Kelland, M.A., 

F.E.S., F.E.S.E. 
Rev. R. Walker, M.A., P.R.S 

Rev. T. R. Robinson, D.D., 
F.R.S., M.R.I.A. 

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

The Earl of Rosse, M.A., K.P., 

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

G. B. Airy, M.A., D.C.L., 

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

F.R.S. 
Prof .W. J. Macquorn Rankine, 

C.E., F.R.S. 

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

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

F.R.A.S. 

Prof. Wlieatstone, D.C.L., 

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

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

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

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

LL.D., F.R.S, 

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



W. De La Rue, D.C.L., F.R.S. 

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

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

Prof. Balfour Stewart, M.A., 

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

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

Prof. G. C. Foster, B.A., F.R.S., 

Pres. Physical Soc. 
Rev. Prof. Salmon, D.D., 

D.C.L., F.R.S. 
George Johnstone Stoney, 

M.A., F.R.S, 



Secretaries 



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, 
J. P. Hennessy, Prof. Maxwell, H. 

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

Prof. Stevelly. 
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. 

Jenkin, Prof. Stevelly, Rev. C. T. 

Whitley. 
Prof. Fuller, F. Jenkin, 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 

WhitworUi. 
Prof. W. G. Adams, J. T. Bottomley, 

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.Rodweli. 
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. Barrett, J. T. Bottomley, 

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

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

J. W. L. Glaisher, F. G. Landon. 
Prof. J. Casey, G. F. Fitzgerald, J. 

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

0. J. Lodge, D. MacAlister. 



PEESIDENTS AND SECKETARIES OF THE SECTIONS. 



xlvii 



Date and Place 


1880. 


Swansea ... 


1881. 


York 


1882. 


Southamp- 
ton. 


1883. 


Southport 


1884. 


Montreal ... 


1885. 


Aberdeen. . . 


1886. Birmingham 


1887. 


Manchester 


1888. 


Bath 


1889. 


Newcastle- 
npon-Tyne 


1890. 


Leeds 


1891. 


Cardiff 


1892. 


Edinburgh 


1893. 


Nottingham 



Presidents 



Prof. W. Grylls Adams, M.A., 

F.R.S. 
Prof. Sir W. Thomson, M.A., 

LL.D., D.C.L., F.R.S. 
Et. Hon. Prof. Lord Rayleigh, 

M.A., F.R.S. 

Prof.O.Henrici, Ph.D., F.R.S. 

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

Prof. G. Chrystal, M.A., 

F.R.S.E. 
Prof. G. H. Darwin, M.A., 

LL.D., F.R.S. 
Prof. Sir R. S. Ball, M.A., 

LL.D., F.R.S. 
Prof. G. F. Fitzgerald, M.A., 

F.R.S. 
Capt. W. de W. Abney, C.B., 

E.E., F.R.S. 

J. W. L. Glaisher, Sc.D., 

F.R.S., V.P.R.A.S. 
Prof. 0. J. Lodge, D.Sc, 

LL.D., F.R.S. 
Prof. A. Schuster, Ph.D., 

F.R.S., F.R.A.S. 
R. T. Glazebrook, M.A., F.R.S. 



Secretaries 



W. E. Ayrton, J. W. L. Glaisher, 

Dr. O. J. Lodge, D. MacAlister. 
Prof.W. E. Ayrton, Prof. 0. J. Lodge, 

D. MacAlister, Rev. "W. Routh. 
W. M. Hicks, Prof. O. J. Lodge, 

D. MacAlister, Rev. G. Richard- 
son. 
W. M. Hicks, Prof. O. J. Lodge, 

D. MacAlister, Prof. R. C. Rowe. 
C. Carpmael, W. M. Hicks, Prof. A. 

Johnson, Prof. O. J. Lodge, Dr. D, 

MacAlister. 
R. E. Baynes, R. T. Glazebrook, Prof. 

W. M. Hicks, Prof. W. Ingram. 
R. E. Baynes, R. T. Glazebrook, Prof. 

J. H. Poynting, W. N. Shaw. 
R. E. Baynes, R. T. Glazebrook, Prof. 

H. Lamb, W. N. Shaw. 
R. E. Baynes, R. T. Glazebrook, A. 

Lodge, W. N. Shaw. 
R. E. Baynes, R. T. Glazebrook, Prof. 

A. Lodge, W. N. Shaw, Prof. H. 

Stroud. 
R. T. Glazebrook, Prof. A. Lodge, 

W. N. Shaw, Prof. W. Stroud. 
R. E. Baynes, J. Larmor, Prof. A. 

Lodge, Prof. A. L. Selby. 
R. E. Baynes, J. Larmor, Prof. A. 

Lodge, Dr. W. Peddle. 
W. T. A. Emtage, J. Larmor, Prof. 

A. Lodge, Dr. W, Peddle. 



CHEMICAL SCIENCE. 

COMMITTEE OF SCIENCES, II. — CHEMTSTET, MINEEALOGT. 



1832. Oxford 

1833. Cambridge 

1834. Edinburgh 



.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. Christison. 



SECTION B. — CHEMISTRY AND MINEEALOGT. 



1835. Dublin. 

1836. Bristol. 



1837. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 

1843. Cork 

1844. York 

1845. Cambridge 



Dr. T. Thomson, F.R.S. .. 
Rev. Prof. Cumminsr 



Michael Faraday, F.R.S 

Rev. William Whewell,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.LA 

Prof. T. Graham, F.R.S 

Rev. Prof. Cummina: 



Dr. Apjohn, Prof. Johnston. 

Dr. Apjohn, Dr. C. Henry, W. Hera- 
path. 

Prof. Johnston, Prof. Miller, Dr. 
Reynolds. 

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. Prideaus, Robert Hunt, W. M. 
Tweedy. 

Dr. L. Playfair, E. Hunt, J. Graham. 

R. Hunt, Dr. Sweeny. 

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

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



xlviii 



REPOKT — 1893. 



Date and Place 



Presidents 



1846. Southamp- 

ton. 

1847. Oxford 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 



1853. Hull 

1854. Liverpool 

1855. Glasgow ... 

1856. Cheltenham 



1857. Dublin.... 

1858. Leeds .... 

1859. Aberdeen. 

1860. Oxford.... 



1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton ... 

1873. Bradford... 

1874. Belfast 

1875. Bristol 

1876. Glasgow ... 

1877. Plymouth... 

1878. Dublin 



Secretaries 



Michael Faraday, D.C.L., 

F.R.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. 
Thomas Andrews,M.D.,F.R.S. 

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

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

Dr. LyonPlayfair,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.C.L. 
Dr. Lyon Playf air, C.B., F.R.S. 

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

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

Dr. Alex. W. Williamson, 

W. Odiing, M.B., F.R.S., 

1? P 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. 

Prof. H. E. Roscoe, B.A., 

F.R.S., F.C.S. 
Prof. T. Andrews, M.D., F.R.S. 

Dr. J. H. Gladstone, F.R.S.... 

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

Prof. A. Crum Brown, M.D., 

F.R.S.B., F.C.S. 
A. G. Vernon Harcourt, M.A., 

F.R.S., F.C.S. 
W. H. Perkin, F.R.S 

F. A. Abel, F.R.S., F.C.S. ... 
I 

I Prof. Maxwell Simpson, M.D., 
I F.R.S., F.C.S. 



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

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

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. Edwards, Dr. Gladstone, Dr. 
Price. 

Prof. Frankland, Dr. H. E. Roscoe. 

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

Dr. Davj', Dr. Gladstone, Prof. Sul- 
livan. 

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

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

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

A. Vernon Harcourt, G. D. Liveing. 

H. W. Elphinstone, W. Odiing, Prof. 
Roscoe. 

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

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

A. V. Harcourt, H. 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. A. Crum Brown. A. E. Fletcher, 
Dr. W. J. Russell. 

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

Dr. Mills, W. Chandler Roberts, Dr. 
W. J. Russell, Dr. T. Wood. 

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

Dr. T. Cranstoun Charles, W. Chand- 
ler Roberts, Prof. Thorpe. 

Dr. H. E. Armstrong, W. Chandler 
Roberts, W. A. Tilden. 

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

Dr. Oxland, W. Chandler Roberts, 
J. M. Thomson. 

W. Chandler Roberts, J. M. Thom- 
son, Dr. C. R. Tichborne, T. Wills. 



PRESIDENTS AND SECRETAEIES OF THE SECTIONS. 



xlix 



Date and Place 



1879. Sheffield ... 

1880. Swansea ... 



1881. York. 



1882. Southamp- 

ton. 

1883. Southport 

1884. Montreal ... 
188.5. Aberdeen... 

1886. Birmingham 

1887. Manchester 

1888. Bath 

1889. Newcastle- 

upon-Tyne 

1890. Leeds 

1891. Cardiff 

1892. Edinburgh 

1893. Nottingham 



Presidents 



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

Joseph Henry Gilbert, Ph.D., 
F.K.S. 

Prof. A. W. Williamson, Ph.D., 

F.E.S. 
Prof. G. D. Liveing, M.A., 

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

Prof. Sir H. E. Eoscoe, Ph.D., 

LL.D., F.E.S. 
Prof. H. E. Armstrong, Ph.D., 

F.E.S., Sec. C.S. 
W. Crookes, F.E.S., V.P.C.S. 



Dr. E. Schunck, F.E.S., F.C.S. 

Prof. W. A, Tilden, D.Sc, 
F.E.S., V.P.C.S. 

Sir T. Lowthian Bell, Bart., 
D.C.L., F.E.S., F.C.S. 

Prof. T. E. ThoqDe, B.Sc, 
Ph.D., F.E.S., Treas. C.S. 

Prof. W. C. Eoberts-Austen, 
C.B., F.E.S., F.C.S. 

Prof. H.McLeod,F.E.S.,F. C.S. 

Prof. J. Emerson Eeynolds, 
M.D., D.Sc, F.E.S. 



Secretaries 



H. S. Bell, W. Chandler Eoberts, J. 

M. Thomson. 
P. Phillips Bedson, H. B. Dixon, Dr. 

"W. E. Eaton Hodgkinson, J. M. 

Thomson. 
P. Phillips Bedson, H. B. Dixon, 

T. Gough. 
P. Phillips Bedson, H. B. Dixon, 

J. L. Notter. 
Prof. P. Phillips Bedson, H. B. 

Dixon, H. Forster Morley. 
Prof. P. Phillips Bedson, H. B. Dixon, 

T. McFarlane, Prof. W. H. Pike. 
Prof. P. Phillips Bedson, H. B. Dixon, 

H.ForsterMorley.Dr. W.J. Simpson. 
Prof. P. Phillips Bedson, H. B. 

Dixon, H. Forster Morley, W. W. 

J. Nicol, C. J. Woodward. 
Prof. P. Phillips Bedson, H. Forster 

Morley, W. Thomson. 
Prof. H. B. Dixon, Dr. H. Forster 

Morley, E. E. Moyle, Dr. W. W. 

J. Nicol. 
Dr. H. Forster Morley, D. H. Nagel, 

Dr. W. W. J. Nicol, H. L. Pattin- 

son, jun. 
C. H. Bothamley, Dr. H. Forster 

Morley, D. H. Nagel, Dr. W. W. 

J. Nicol. 
C. H. Bothamley, Dr. H. Forster 

Morley, Dr. W. W. J. Nicol, Dr. 

G. S. Turpin. 
Dr. J. Gibson, Dr. H. Forster Morlev, 

D. H. Nagel, Dr. W. W. J. Nicol". 
J. B. Coleman, M. J. E. Dunstan, 

D. H. Nagel, Dr. W. W. J. Nicol. 



GEOLOGICAL (and, until 1851, GEOGRAPHICAL) SCIENCE. 

COMMITTEE OP SCIENCES, III. — GEOtOGY AND GEOGRAPHY. 



1832. Oxford 

1833. Cambridge. 

1834. Edinburgh. 



1835. Dublin. 

1836. Bristol. 



E. I. Murchison, F.E.S 

G. B. Greenough, F.E.S 

Prof. Jameson 



John Taylor. 

W. Lonsdale, John Phillips. 
Prof. Phillips, T. Jameson Torrie, 
Eev. J. Yates. 



SECTION C. — GEOLOGY AND GEOGRAPHY. 



1837. Liverpool... 

1838. Newcastle. . 

1839. Birmingham 

1893. 



E. J. Griffith 

Eev. Dr. Buckland, F.E.S.— 

Geography, E. I. Murchison, 

F.E.S. 
Eev. Prof. Sedgwick, F.E.S.— 

<T<;o;7raj?Ay,G.B.Greenough, 

C. Lyeli, F.E.S., V.P.G.S.— 
Geography, Lord Prudhoe. 

Eev. Dr. Buckland, F.E.S.— 
Geography, G.B.Greenough, 
F.E.S. 



I Captain Portlock, T. J. Torrie. 
William Sanders, S. Stutchbury, 
T. J. Torrie. 

Captain Portlock, E. Hunter. — Geo- 
graphy, Captain H. M. Denham, 
E.N. 

W. C. Trevelyan, Capt. Portlock.— 
Geography, Capt. Washington. 

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



REPORT — 1893. 



Date and Place 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 

1843. Cork 

1844. York 

1845. Camhridge. 

1846. Soiithamp- 
ton. 

1847. Oxford 

1848. Swansea ... 
1 849.Birmingham 
1850.Edinhurgh> 



Presidents 



Charles Lyell, F.E.S.— Geo- 
graphy, G. B. Greenough, 
F.R.S. 

H. T. De la Beche, F.E.S. ... 

R. I. Murchison, F.E.S 

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

Henry Warburton, M.P.,Pres. 
Geol. See. 

Rev. Prof. Sedgwick, M.A., 
F.R.S. 

Leonard Horner,F.R.S. — Geo- 
graphy, G. B. Greenough, 
F.R.S. 

Very Rev.Dr.Buckland,F.R.S. 

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

F.R.S. 
Sir Charles Lyell, F.R.S., 

F.G.S. 
Sir Roderick I. Murchison, 

F.R.S. 



Secretaries 



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

W. J. Hamilton,EdwardMoore, M.D., 
R. Hutton. 

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

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

Prof. Ansted, E. H. Bunbury. 

Rev. J. C. Cumming, A. C. Ramsay, 

Rev. W. Thorp. 
Robert A. Austen, Dr. J. H. Norton, 

Prof. Oldham. — Geography, Dr. C. 

T. Beke. 
Prof. Ansted, Prof. Oldham, A. C. 

Ramsay, J. Ruskin. 
Starling Benson, Prof. Oldham, 

Prof. Ramsay. 
J. Beete Jukes, Prof. Oldham, Prof. 

A. C. Ramsay. 
A. Keith Johnston, Hugh Miller, 

Prof. Nicol. 



185L 

1852. 

1853. 
1854. 

1855. 

1856. 

1857. 
1858. 
1859. 
1860. 
1861. 
1862. 
1863. 



Ipswich ... 

Belfast 

Hull 

Liverpool . . 

Glasgow ... 

Cheltenham 

Dublin 

Leeds 

Aberdeen... 

Oxford 

Manchester 
Cambridge 
Newcastle 



SECTION c {continued). — geologt, 
WilliamHopkins, M, A.,F. R. S 



Lieut.-Col. Portlock, R.E., 
F.R.S. 

Prof. Sedgwick, F.R.S 

Prof. Edward Forbes, F.R.S. 

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

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

The Lord Talbot de Malahide 

William Hopkins,M.A.,LL.D., 

F.R.S. 
Sir Charles Lyell, LL.D., 

D.C.L., F.R.S. 
Rev. Prof. Sedgwick, LL.D., 

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

LL.D., F.R.S. 
J. Beete Jukes, M.A., F.R.S. 

Prof. Warington W. Smyth, 
F.R.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. W. Woodall. 
James Bryce, Prof. Harkness, Prof. 

Nicol. 
Rev. P. B. Brodie, Rev. R. Hep- 
worth, Edward Hull, J. Scougall, 

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 Da^lish, H. C. 

Sorby, Thomas Sopwith. 



' 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 Ivi. 



PEESIDENTS AND SECRETARIES OF THE SECTIONS. 



u 



Date and Place 



1864. 

1865. 

1866. 

1867. 

1868. 

1869, 

1870. 

1871. 

1872. 

1873. 

1874. 

1875. 

1876. 
1877. 

1878. 

1879. 

1880. 

1881. 

1882. 

1883. 

1884. 

1885. 

1886. 

1887. 

1888. 

1889. 

1890. 

1891. 

1892. 

1893. 



Bath 

Birmingham 
Nottingham 
Dundee ... 
Norwich ... 

Exeter 

Liverpool... 
Edinburgh 
Brighton ... 
Bradford ... 

Belfast 

Bristol 



Presidents 



Glasgow .. 
Plymouth.. 



Dublin 

Sheffield ... 

Swansea ... 

York 

Southamp- 
ton. 
Southport 

Montreal ... 

Aberdeen . . . 

Birmingham 

Manchester 

Bath 



Prof. J. Phillips, LL.D., 

F.R.S., F.G.S. 
Sir R. I. Murchison, Bart., 

K.C.B. 
Prof. A. C. Eamsay, LL.D., 

F.E.S. 
Archibald Geikie, F.R.S., 

F.G.S. 
E. A. C. Godwin-Austen, 

F.E.S., F.G.S. 
Prof. R. Harkness, F.R.S., 

F.G.S. 
Sir Philip de M.Grey Egerton, 

Bart., M.P., F.R.S. 
Prof. A. Geikie, F.R.S., F.G.S. 

R. A. C. Godwin-Austen, 

F.R.S., F.G.S. 
Prof. J. Phillips, D.C.L., 

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

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

F.G.S. 

Prof. John Young, M.D 

W. Pengelly, F.R.S., F.G.S. 



Secretaries 



Newcastle- 
upon-Tyne 
Leeds 



Cardiff 

Edinburgh 
Nottingham 



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

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

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

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

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

Prof. W. C. WUliamson, 

LL.D., F.R.S. 
W. T. Blanford, F.R S., Sec. 

G.S. 
Prof. J. W. Judd, F.R.S., Sec. 

G.S. 
Prof. T. G. Bonney, D.Sc, 

LL.D., F.R.S., F.G.S. 
Henry Woodward, LL.D., 

F.R.S,, F.G.S. 
Prof. W. Boyd Dawkins, M.A., 

F.R.S., F.G.S. 
Prof. J. Geikie, LL.D., D.C.L., 

F.R.S., F.G.S. 
Prof. A. H. Green, M.A., 

F.R.S., F.G.S. 
Prof. T. Rupert Jones, F.R.S., 

F.G.S. 
Prof. C. Lapworth, LL.D., 

F.R.S., F.G.S. 
J. J. H. Teall, M.A., F.R.S., 

F.G.S. 



W. B. Dawkins, J. Johnston, H. C. 
Sorby, 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, 

Rev. O. Fisher, Rev. J. Gunn, W, 
Pengelly, Rev, H. H. Winwood. 

W, Pengelly, W, Boyd Dawkins, 
Rev. H. H. Winwood. 

W. Pengelly, Rev. H. H. Winwood, 
W. Boyd Dawkins, G. H. Morton. 

R. Etheridge, J. Geikie, T. McKenny 
Hughes, L. C. Miall. 

L. C. Miall, George Scott, William 
Topley, Henry Woodward. 

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

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

L. C, Miall, E, B, Tawney, W. Top- 
ley, 

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

Dr. Le Neve Foster, E, H. Tidde- 
man, W, Topley, 

E, T. Hardman, Prof, J, O'Eeilly, 
E, H. Tiddeman. 

W, Topley, G, Blake Walker. 

W. Topley, W. Whitaker. 

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

T. W. Shore, W. Topley, E. West- 
lake, W. Whitaker. 

E. Betley, C. E. De Eance, W. Top- 
ley, W. Whitaker. 

F. Adams, Prof. E. W. Claypole, W. 
Topley, W. Whitaker. 

C. E. De Ranee, J. Home, J. J. H, 

Teall, W. Topley. 
W. J. Harrison, J. J. H. Teall, W. 

Topley, W. W. Watts. 
J. E. Marr, J. J. H. Teall, W. Top- 
ley, W. W. Watts. 
Prof. G. A, Lebour, W. Topley, W, 

W. Watts, H. B. Woodward. 
Prof. G. A. Lebour, J. E. Marr, W. 

W. Watts, H. B. Woodward. 
J. E. Bedford, Dr. F. H. Hatch, J. 

E. Marr, W. W. Watts. 
W. Galloway, J. E. Marr, Clement 

Reid, W. W, Watts. 
H. M. Cadell, J. E. Marr, Clement 

Reid, W. W, Watts. 
J. W. Carr, J. E. Marr, Clement 

Reid, W. W. Watts. 



c 2 



lii 



KEPOKT 1893. 



Date and Place 



Presidents 



Secretaries 



BIOLOGICAL SCIENCES. 

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

1832. Oxford I Rev, P. B. Duncan, F.G.S. ...I Rev. Prof. J. S. Henslow. 

1833. Cambridge ' Rev. W. L. P. Garnons, F.L.S.I C. C. Babington, D. Don. 

1834. Edinburgh . I Prof . Graham |W. Yarrell, Prof. Burnett. 



1835. Dublin, 

1836. Bristol, 



1837. Liverpool... 

1838. Newcastle 

1 839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 



1843. Cork. 

1844. York. 



1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford 



SECTION r». — ZOOLOGY AND BOTANY. 

Dr. Allman J. Curtis, Dr. Litton. 

Rev. Prof. Henslow [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. 

John Richardson, M.D., F.R.S. J. Couch, Dr. Lankester, R. Patterson. 
Hon. and Very Rev. W. Her- ' Dr. r,,ankester, R. Patterson, J. A. 



W. S. MacLeay 

Sir W. Jardine, Bart. 



Prof. Owen, F.R.S 

Sir W. J. Hooker, LL.D. 



bert, LL.D., F.L.S. 
William Thompson, F.L.S. ... 

Very Rev. the Dean of Man- 
chester. 
Rev. Prof. Henslow, F.L.S... 



Turner. 
G. J. Allman, Dr. Lankester, R. 

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

Dr. Lankester. 
Dr. Lankester, T. V. Wollaston. 
Sir J. Richardson, M.D., Dr. Lankester, T. V. Wollaston, H. 

F.R.S. i Wooldridge. 

H. E. Strickland, M.A., F.R.S. Dr. Lankester, Dr. Melville, T, V. 

I Wollaston. 



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

[For the Presidents and Secretaries of the Anatomical and Physiological Sub- 
sections and the temporary Section E of Anatomy and Medicine, see p. Iv.] 



1848. Swansea ... 

1 849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 



1853. Hull 

1854. Liverpool.. 

1855. Glasgow .. 

1856. Cheltenham 



1857. Dublin. 



L. W. Dillwyn, F.R.S. 



William Spence, F.R.S 

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

Rev. Prof. Henslow, M.A., 

F.R.S. 
W. Ogilby 



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

Prof. W. H. Harvey, M.D., 
F.R.S. 



Dr. R. Wilbraham Falconer, A. Hen- 
frey, Dr. Lankester. 

Dr. Lankester, Dr. Russell. 

Prof. J. H. Bennett, M.D., Dr. Lan- 
kester, Dr. Douglas 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. 



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



PRESIDENTS AND SECRETABIES OF THE SECTIONS. 



liii 



Date and Place 

1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 




Secretaries 



C. C. Babii.gton, M.A., F.E.S. 

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

Kev. Prof. Henslow, F.L.S.... 

Prof. C. C. Babington, F.E.S. 

Prof. Huxley, F.E.S 

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

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

T. Thomson, M.D., F.E.S. ... 



Henry Denny, 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. Brady, C. E. Broom, H. T. 

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

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



SECTION D (continued), BIOLOGT.' 



1866. Nottingham 



1867. 
1868. 



Dundee ... 
Norwich .., 



1869. Exeter. 



1870. Liverpool... 



1871. Edinburgh 



1872. Brighton .., 



1873. Bradford ... 



Prof. Huxley, LL.D., F.E.S. 

— Phydological Dep., Prof. 

Humphry, M.D., F.E.S.— 

Anthropological Dep., Alf. 

E. Wallace, F.R.G.S. 
Prof. Sharper, M.D., Sec. R.S. 

— Btp. of Zool. and Bot., 

George Busk, M.D., F.E.S. 
Rev. M. J. Berkeley, F.L.S. 

— Bep. of Physiology, W. 

H. Flower, F.R.S. 

George Busk, F.R.S., F.L.S. 
— Bcp. of Bot. and Zool., 
C. Spence Bate, F.R.S.— 
Bep. of Ethno., E. B. Tylor. 

Prof. G. Rolleston, M. A., M.D., 
P.E.S., ¥.lj.Q. — Bip. of 
Anat. and PAyswZ.,Prof. M. 
Poster, M.D., ¥.!,.'&.— Bep. 
of Ethno., J. Evans, F.R.S. 

Prof. Allen Thomson, M.D., 
Y.U.^.—BLp. of Bot. and 
.21joZ.,Prof.WyvilleThomson, 
F.E.S.— !>«/>. of Anthrojwl., 
Prof. W. Turner, M.D. 

Sir J. Lubbock, Bart., F.E.S.— 
Bep. of Anat. and Physiol., 
Dr. Burdon Sanderson, 
F.E.S.— i>f7;. of Anthropol., 
Col. A. Lane Fox, F.G.S. 

Prof. Allman, Y.^.^.—Bep. of 
Anat.and Phymul.,'Pi:ot. Ru- 
therford, M.D. — Bep. of An- 
thropol., Dr. Beddoe, 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, Eev. 
H. B. Tristram, Prof. W. Turner. 

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

Dr. T. S. Cobbold, Prof. M. Foster, 
E. Bay Lankester, Prof. Lawson, 
H. T. Stainton, Eev. 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. Fraser, Dr. Arthur- Gamgee, 
E. Ray Lankester, Prof. Lawson, 
H. T. Stainton, C. Staniland Wake, 
Dr. W. Rutherford, Dr. Kelbui-ne 
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. Eudler, J. 
H. Lamprey. 



' At a meeting of the General Committee in 1865, it was resolved: — 'That the 
title of Section D be changed to Biology;' and 'That for the word "Subsection," 
in the rules for conducting the business of the Sections, the word "Department" 
be substituted.' 



liv 



BEPOET — 1893. 



Date and Place 



1874. Belfast . 



1875. Bristol , 



1876. Glasgow ... 



1877. Plymouth.. 



1878. Dublin 



1879. Sheffield ... 



1880, Swansea 



1881. York. 



1882. Southamp- 
ton. 



1883. Southport' 



1884. Montreal 2. 



Presidents 



Prof. Kedfem, M.B.—Bep. of 
Zool. and Bot., Dr. Hooker, 
C.B.jPres.K.S.— i>f^. ofAn- 
throp., Sir W.R.Wilde, M.D. 

P. L. Sclater, F.E.S.— ZJep.o/ 
Anat.and Physiol.,'PToi.Cle- 
land, M.D., F.R.S.— Z>ep. of 
AnthropoL, Prof. Rolleston. 
M.D., F.R.S. 

A. Russel Wallace, F.R.G.S., 
F.L.S. — Dep. of Zool. and 
Bot., Prof. A. Newton, M.A., 
F.R.S.— i)?^. of Anat. and 
Physiol, Dr. J. G. McKen- 
drick, F.E.S.E. 

J.Gwyn JefiEreys,LL. D.,F.R.S. , 
F.L.S. — Dep. of Anat. and 
Physiol., I^of. Macalister, 
M.D. — Bep. of AnthropoL, 
Francis Galton, M.A.,F.R.S. 

Prof. W. H. Flower, F.R.S.— 
Dep. of AnthropoL, Prof. 
Huxley, Sec. B..^.—Dep. 
of Anat. and PhysioL, R. 
McDonnell, M.D., F.R.S. 

Prof. St. George Mivart, 
V.^.^.—Dep. of AnthropoL, 

E. B. Tylor, D.C.L., F.R.S. 
— Dep. of Anat. and Phy- 
sioL, Dr. Pye-Smith. 

A. C. L. Giinther, M.D., F.R.S. 
— Dep. of Anat. and Phy- 
sioL, F. M. Balfour, M.A., 
F.B,.S.— Dep. of AnthropoL, 

F. W. Rudler, F.G.S. 
Richard Owen, C.B., M.D., 

F.B,.S.— Dep. of AnthropoL, 
Prof. W. H. Flower, LL.D., 
F.R.S.— Dep. of Anat. and 
Physiol., 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.lj.S.—Dep. of AnthropoL, 
Prof. W. Boyd Dawkins, 
M.A., F.R.S. 

Prof. E. RayLankester,M.A., 
F.R.S. — Dep. of AnthropoL, 
W. Pengelly, F.R.S. 



Prof. H. 
F.R.S. 



N. Moseley, M.A., 



Secretaries 



W. T. Thiselton-Dyer, R. O. 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. Hingston, 
Prof. W. R. M'Nab, J. B. Rowe, 
F. W. Rudler. 

Dr. R. J. Harvey, Dr. T. Hayden, 
Prof. W. 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 Priestley, 
Howard Saunders, Adam Sedg- 
wick. 



G. W. Bloxam, W. A. Forbes, Rev. 
W. 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. 



G. W. Bloxam, Dr. G. J. Haslam, 

W. Heape, W. Hurst, Prof. A. M. 

Marshall, Howard Saunders, Dr. 

G. A. Woods. 
Prof. W. Osier, Howard Saunders, A, 

Sedgwick, Prof. R. R. Wright. 



' By direction of the General Committee at Southampton (1882) the Departments 
of Zoology and Botany and of Anatomy and Physiology were amalgamated. 

- By authority of the General Committee, Anthropology was made a separate 
Section, for Presidents and Secretaries of which see p. Ixii. 



PBESIDBiNTS AND SECRETARIES OP THE SECTIONS. 



Iv 



Date and Place 

1885. Aberdeen... 

1886. Birmingham 

1887. Manchester 

1888. Bath 



1889. Newcastle- 

upon-Tyne 

1890. Leeds 



1891. Cardiff. 



1892. Edinburgh 



1893. Nottingham 



Presidents 



Prof. "W. C. Mcintosh, M.D., 
LL.D., F.K.S. F.R.S.E. 

W. Carruthers, Pres. L.S., 
F.R.S., F.G.S. 

Prof. A. Newton, M. A., F.R.S., 
F.L.S., V.P.Z.S. 

W. T. Thiselton-Dyer, C.M.G., 
F.R.S., F.L.S. 

Prof. J. S. Burdon Sanderson, 
M.A., M.D., F.R.S. 

Prof. A. MUnes Marshall, 
M.A., M.D,, D.Sc, F.R.S. 



Francis Darwin, M.A., M.B., 
F.R.S., F.L.S. 

Prof. W. Rutherford, M.D., 
F.R.S., F.R.S.E. 

Rev. Canon H. B. Tristram, 
M.A., LL.D., F.R.S. 



Secretaries 



W. Heape, J. McGregor-Robertson, 
J. Duncan Matthews, Howard 
Saunders, H. Marshall Ward. 

Prof. T. W. Bridge, W. Heape, Prof. 
W. Hillhouse, W. L. Sclater, Prof. 
H. Marshall Ward. 

C. Bailey, F. E. Beddard, S. F. Har- 
mer, W. Heape, W. L. Sclater, 
Prof. H. Marshall Ward. 

F. E. Beddard, S. F. Harmer, Prof. 
H. Marshall Ward, W. Gardiner, 
Prof. W. D. Halliburton. 

C. Bailey, F. E. Beddard, S. F. Har- 
mer, Prof. T. Oliver, Prof. H. Mar- 
shaU Ward. 

S. F. Harmer, Prof. W. A. Herdman, 
Dr. S. J. Hickson, Prof. F. W. 
Oliver, H. Wager, Prof. H. Mar- 
shall Ward. 

F. E. Beddard, Prof. W. A. Herdman, 
Dr. S. J. Hickson, G. Murray, Prof. 
W. N. Parker, H. Wager. 

G. Brook, Prof. W. A. Herdman, G. 
Murray, Prof. W. Stirling, H. 
Wager. 

G. C. Bourne, Prof. J. B. Farmer, 
Prof. W. A. Herdman, Dr. S. J. 
Hickson, Dr. W. B. Ransom, W. 
L. Sclater. 



ANATOMICAL AND PHYSIOLOGICAL SCIENCES. 

COMMITTEE OF SCIENCES, V. — ANATOMY AND PHTSIOLOGT. 



1833. Cambridge IDr. Haviland 

1834. Edinburgh I Dr. Abercrombie 



Dr. Bond, Mr. Paget. 

Dr. Roget, Dr. William Thomson. 



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



1835. Dublin.... 

1836. Bristol .... 

1837. Liverpool. 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow 



Dr. Pritchard 

Dr. Roget, F.R.S 

Prof. W. Clark, M.D 

T. E. Headlam, M.D 

John Yelloly, M.D., F.R.S. 
jj tt^mes Watson, 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. O. Rees, F. Ryland. 
Dr. J. Brown, Prof. Couper, Prof. 

Reid. 



SECTION E. — PHYSIOLOGY. 



1841. Plymouth... 

1842. Manchester 

1843. Cork 

1844. York 

1845. Cambridge 



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

Edward Holme, M.D., F.L.S. 
Sir James Pitcairn, M.D. ... 

J. C. Pritchard, M.D 

Prof. J. Haviland, M.D 



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

Sargent. 
Dr. Chaytor, Dr. R. S. Sargent. 
Dr. John Popham, Dr. R. S. Sargent. 
I. Erichsen, Dr. R. S. Sargent. 
Dr. R. S. Sargent, Dr. Webster. 



Ivi 



REPORT — 1893. 



Date and Place 



1846. Southamp- 
ton. 
18i7. Oxford' .. 



Presidents 



Secretaries 



Prof. Owen, M.D., F.R.S. 
Prof. Ogle, M.D., F.R.S, . 



C. P. Keele, Dr. Laycock, Dr. Sar- 
I gent. 

jDr. Thomas K. Chambers, W. P. 
I Ormerod. 



PHYSIOLOGICAL SUBSECTIONS OF SECTION D. 



1850. 
1855. 
1857. 


Edinburgh 
Glasgow ... 
Dublin 


1858. 


Leeds 


1859. 


Aberdeen... 


1860. 


Oxford 


1861. 


Manchester 


1862. 
1863. 


Cambridge 
Newcastle 


1864. 


Bath 


1865. 


Birming- 
ham.- 



Prof. Bennett, M.D., F.R.S.E. 
Prof. Allen Thomson, F.R.S. 

Prof. R. Harrison, M.D 

Sir Benjamin Brodie, Bart., 

F.R.S. 
Prof. Sharpey, M.D., Sec.R.S. 
Prof.G.Bol]eston,M.D.,F.L.S. 
Dr. John Davy, F.R.S. L.& E. 

G. E. Paget, M.D 

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

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

F.R.S, 



Prof. J. H. Corbett.Dr. J. Struthers. 
Dr. R. D. Lyons, Prof. Redfern. 
C. G. Wheelhouse. 

Prof. Bennett, Prof. Redfern, 
Dr. R. M'Donnell, Dr. Edward Smitii, 
Dr. W. Roberts, Dr. Edward Smitli. 
G. F. Helm, Dr. Edward Smith. 
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 1851, see Section C, 
p. xiix.] 

ETHNOLOGICAL SUBSECTIONS OF SECTION D. 



1846. Southampton 

1847. Oxford 

1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 



Dr. Pri t cliard 

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



Vice-Admiral Sir A. Malcolm 



Dr. King. 
Prof. Buckley. 
G. Grant Francis. 
Dr. R. G. Latham. 
Daniel Wilson. 



SECTION E. — GEOGEAPHT AND ETHNOLOGY. 



1851, Ipswich ... 

1852, Belfast 

1853, Hull 

1854, Liverpool... 

1855, Glasgow ... 

1856, Cheltenham 

1857, Dublin 



Sir R. I. 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. I. 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.LA. 



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. 



> 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. lii.). Section E, being then vacant, was assigned in 1851 tc 
Geography. 

" Vide note on page liii. 



to 



PBESIDENTS AND SECEETARIES OF THE SECTIONS. 



Ivii 



Date and Place 

1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 



Presidents 



Sir E. I. 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. I. 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, R.N., 
F.R.S. 



Secretaries 



R. Cull, Francis Galton, P. O'Cal- 
laghan. Dr. Norton Shaw, Thomas 
Wright. 

Richard Cull, Prof.Geddes, Dr. Nor- 
ton Shaw. 

Capt. Bvirrows, 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. Bates, 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, R. 
Sturrock. 

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



SECTION E (continued). — geogeapht. 



1869 


Exeter 


1870 


Liverpool.. 


1871. 


Edinburgh 


1872. 


Brighton .. 


1873. 


Bradford ... 


1874. 


Belfast 


1875. 


Bristol 


1876. 


Glasgow ... 


1877. 


Plymouth... 


1878. 


Dublin 


1879. 


Sheffield ... 


1880. 


Swansea ... 


1881. 


York 


1882. 
1883. 


Southamp- 
ton. 
Southport 



I Sir Bartle Frere, K.C.B., 
LL.D., F.R.G.S. 

SirR.LMurchison,Bt.,K.C.B., 
I LL.D.,D.C.L.,F.R.S.,F.G.S. 

Colonel Yule, C.B., F.R.G.S. 



H. W. Bates, Clements R. Markham, 

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

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

Rev. J. Newton, J. H. Thomas. 
H. W. Bates, A. Keith Johnston, 
I Clements R. Markham. 
Maior Wilson, R.E., F.R.S., I E.G. Ravenstein, E. C. Rye, J. H. 

F.R.G.S. Thomas. 

Lieut. - General Strachey, iH. W. Bates, E. C. Rye, F. F. 



Francis Galton, F.R.S 

Sir Rutherford Alcock, K.C.B. i 



R.E.,C.S.I.,F.R.S.,F.R.G.S., 
F.L.S., F.G.S. 
! Capt. Evans, C.B., F.R.S, 



Tuckett. 

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

Wood. 
H. W. Bates, F. E. Fox, E. C. Rye. 



Adm. Sir E. Ommanney, C.B., 
F.R.S., F.R.G.S., F.R.A.S. 

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

Clements R. Markham, C.B.,'h. W. Bates, C. E. D. Black, E. C 



John Coles, E. C. Eye. 



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

Lieut.-Gen. Sir J. H. Lefroy, 
C.B.,K.C.M.G.,R.A., F.R.S, 
F.R.G.S. 

Sir J. D. Hooker, K.C.S.L, 
C.B., F.R.S. 

Sir R. Temple, Bart., G.C.S.I., 
F.R.G.S. 

Lieut.-Col. H. H. Godwin- 
Austen, F.E.S. 



Eye. 
H. W. Bates, E. C. Eye. 



J. W. Barry, H. W. Bates. 

E. G. Eavenstein, E. C. Eye. 

John Coles, E. G. Eavenstein, E. C, 
Eye. 



Iviii 



KEPORT — 1893. 



Date and Place ' 



1884. 


Montreal ... 


1885. 


Aberdeen... 


1886. 


BinniBgham 


1887. 


Manchester 


1888. 


Bath 


1889. 
1890. 


Newcastle- 
upon-Tyne 
Leeds 


1891. 


CardiflE 


1892. 


Edinburgh 


1893. 


Nottingham 



Presidents 



Gen. Sir J. H. Lefroy, C.B., 

K.C.M.G., F.R.S.jV.P.K.G.S. 
Gen. J. T. Walker, C.B., R.E., 

LL.D., F.E.S. 
Maj.-Gen. Sir. F. J. Goldsmid, 

K.C.S.I., C.B., F.R.G.S. 
Col. Sir C. Warren, E.E., 

G.C.M.G., F.R.S., F.R.G.S. 
Col. Sii- C. W. Wilson, R.E., 

K.C.B., F.R.S., F.R.G.S. 
Col. Sir F. de Winton, 

K.C.M.G., C.B., F.R.G.S. 
Lieut.-Col. Sir R. Lambert 

Playfau-, K.C.M.G., F.R.G.S. 
E. G. Ravenstein, F.R.G.S., 

"P s s 
Prof. J. Geikie, D.C.L.,F.R.S., 

V.P.R.Scot.G.S. 
H. Seebohm, Sec. R.S., F.L.S., 

F.Z.S. 



Secretaries 



Rev. AbbSLaflamme, J. S. O'HaUoran, 

E. G. Ravenstein, J. F. Torrance. 
J. S. Keltie, J. S. O'HaUoran, E. G. 

Ravenstein, Rev. G. A. Smith. 
F. T. S. Houghton, J. S. Keltie, 

E. G. Ravenstein. 
Rev. L. C. Casartelli, J. S. Keltie, 

H. J. Mackinder, E. G. Ravenstein. 
J. S. Keltie, H. J. Mackinder, E. G. 

Ravenstein. 
J. S. Keltie, H. J. Mackinder, R. 

Sulivan, A. Silva White. 
A. Barker, John Coles, J. S. Keltie, 

A. Silva White. 
John Coles, J. S. Keltie, H. J. Mac- 
kinder, A. Silva White, Dr. Yeats. 
J. G. Bartholomew, John Coles, J. S. 

Keltie, A. Silva White. 
Col. F. Bailey, John Coles, H. O. 

Forbes, Dr. H. R. Mill. 



STATISTICAL SCIENCE. 

COMMITTEE OF SCIENCES, TI. — STATISTICS. 

1833. Cambridge! Prof. Babbage, F.E.S i J. E. Drinkwater. 

1834. Edinburgh I Sir Charles Lemon, Bart 1 Dr. Cleland, C. Hope Maclean. 



SECTION F. — STATISTICS. 



1835. Dublm. 

1836. Bristol. 



1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 



Charles Babbage, F.E.S 

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

Rt. Hon. Lord Sandou 

Colonel Sykes, F.E.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. ... 



1837. Livei-pool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 

1843. Cork Sir C. Lemon, Bart., M.P. 

1844. York Lieut.-Col. Sykes, F.R.S., 

F.L.S. 

Rt.Hon. the Earl Fitzwilliam 
G. E. Porter, F.R.S 



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

J. H. Vivian, M.P., F.R.S. ... 
Rt. Hon. Lord Lyttelton 



Very Rev. Dr. John Lee, 
V.P.R.S.E. 



W. Greg, Prof. Longfield. 

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. Luney, G. W. Ormerod, Dr. 

W. C. Tayler. 
Dr. D. BuUen, Dr. W. Cooke Tayler. 
J. Fletcher, J. Heywobd, Dr. Lay- 
cock. 
J. Fletcher, Dr. W. Cooke Tayler. 
J. Fletcher, F. G. P. Nelson, Dr. W. 

C. Tayler, 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. 
Prof. Hancock, J. Fletcher, Dr. J. 

Stark. 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



lix 



Date and Place 



1851. Ipswich 

1852. Belfast.. 



1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 



Presidents 



Sir John P. Boileau, Bart. ... 
His Grace the Archbishop of 

Dublin. 
James Heywood, M.P., F.K.S. 
Thomas Tooke, F.K.S 

K. Monckton Milnes, M.P. ... 



Secretaries 



J. Fletcher, Prof. Hancock. 

Prof. Hancock, Prof. Ingram, James 
MacAdam, jun. 

Edward Cheshire, W. Newmarch. 

E. Cheshire, J. T. Danson, Dr. W. H. 
Duncan, W. Newmarch. 

J. A. Campbell, E. Cheshire, W. New- 
march, Prof. R. H. Walsh, 



SECTION F (continued). — ECONOMIC SCIENCE AND STATISTICS. 



1856. Cheltenham 



1857 
1858, 
1859 
1860. 
1861. 

1862. 
1863. 

1864. 

1865. 

1866. 

1867. 

1868. 

1869. 

1870. 

1871. 
1872. 
1873. 
1874, 

1875. 

1876. 

1877. 
1878. 



Dublin 

Leeds 

Aberdeen... 

Oxford 

Manchester 



Rt. Hon. Lord Stanley, M.P. 



His Grace the Archbishop of 

Dublin, M.R.LA. 
Edwaid Baines 



Col. Sykes, M.P., F.E.S 

Nassau W. Senior, M.A 

William Newmarch, F.E.S.... 



Cambridge Edwin Chadwick, C.B 



Newcastle 



Bath 

Birmingham 
Nottingham 
Dundee 

Norwich.... 

Exeter 

Liverpool... 

, Edinburgh 
. Brighton... 
Bradford ... 
, Belfast 



Bristol... 
Glasgow 



Plymouth... 
Dublin 



William Tite, M.P., F.E.S. ... 

William Farr, M.D., D.C.L., 

F.E.S. 
Et. Hon. Lord Stanley, LL.D., 

M.P. 
Prof. J. E. T. Eogers 



M. E. Grant-Duff, M.P 

Samuel Brown, Pres. Instit. 
Actuaries. 

Et. Hon. Sir Stafford H. North- 
cote, Bart., C.B., M.P. 

Prof. W. Stanley Jevons, M.A. 

Et. Hon. Lord Neaves 

Prof. Henry Fawcett, M.P. ... 
Et. Hon. W. E. Forster, M.P. 
Lord O'Hagan 



1879. Sheffield 



1880. 
1881. 



Swansea 
York 



James Heywood, M.A., F.E.S., 

Pres. S.S. 
Sir George Campbell, K.C.S.I., 

M.P. 
Et. Hon. the Earl Fortescue 
Prof. J. K. Ingram, LL.D., 

M.E.LA. 
G. Shaw Lefevre, M.P., Pres. 

S.S. 

G. W. Hastings, M.P 

Et. Hon. M. E. Grant-Duff, 

M.A., F.E.S. 



Eev. 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, 

Capt. Fishbourne, Dr. J. Strang. 
Prof. Cairns, Edmund Macrory, A. M, 

Smith, Dr. John Strang. 
Edmund Macrory, W. Newmarch, 

Eev. Prof. J. E. T. Eogers. 
David Chadwick, Prof. E. C. Christie, 

E. Macrory, Eev. Prof. J. E. T. 

Eogers 
H. D. Macleod, Edmund Macrory. 
T. Doubleday, Edmund Macrory, 

Frederick Purdy, James Potts. 
E. Macrory, E. T. Payne, F. Purdy. 

G. J. D. Goodman, G. J. Johnston, 

E. Macrory. 
E. Birkin, jun.. Prof. Leone Levi, E. 

Macrory. 
Prof. Leone Levi, E. Macrory, A. J. 

Warden. 
Rev. W. C. Davie, Prof. Leone Levi. 

E. Macrory, F. Purdy, C. T. D. 
Acland. 

Chas. E. Dudley Baxter, E. Macrory, 

J. Miles Moss. 
J. G. Fitch, James Meikle. 
J. G. Fitch, Barclay Phillips. 
J. G. Fitch, Swire Smith. 
Prof. Donnell, F. 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. 

W. F. Collier, P. Hallett, J. T. Pim. 

W. J. Hancock, C. Molloy, J. T. Pim. 



Prof. Adamson, E. E. Leader, C. 

Molloy. 
N. A. Humphreys, C. Molloy. 
C. Molloy, W. W. Morrell, J. F. 

Moss. 



Jx 



KEPORT 1893. 



Date and Place 



1882. 
1883. 
1884. 
1885. 
1886. 
1887. 



Southamp- 
ton. 
Southport 

Montreal ... 

Aberdeen... 

Birmingham 

Manchester 



1888. Bath. 



1889. 
1890. 

1891. 

1892. 

1893. 



Newcastle- 
upon-Tyne 
Leeds 



Cardiff 

Edinburgh 
Nottingham 



Presidents 



Rt. Hon. G. Sclater-Booth, 

M.P., F.R.S. 
R. H. Inglis Palgrave, F.R.S. 

Sir Richard Temple, Bart., 
G.C.S.I., CLE., F.R.G.S. 

Prof. H. Sidgwick, LL.D., 
Litt.D. 

J. B. Martin, M.A., F.S.S. 

Robert Giffen, LL.D.,V.P.S.S. 



Rt. Hon. Lord Bramwell, 
LL.D., F.R.S. 

Prof. F. Y. Edgeworth, M.A., 

Prof. A.MarshaU, M.A., F.S.S. 



Prof. AV. Cunningham, D.D., 
D.Sc, F S.S. 

Hon. Sir C. AV. Fremantle. 
K.C.B. 

Prof. J. S. Nicholson, D.Sc, 
F.S.S. 



Secretaries 



G. Baden- Powell, Prof. H. S. Fox- 
well, A. Milnes, C. Molloy. 
Rev. W. Cunningham, Prof. H. S. 

Foxwell, J. N. kejTies, C. MoUoy. 
Prof. H. S. Foxwell, J. S. McLennan, 

Prof. J. Watson. 
Rev. W. Cunningham, Prof. H. S. 

Foxwell, C. McCombie, J. F. Moss. 
F. F. Barham, Rev. W. Cunningham, 

Prof. H. S. Foxwell, J. F. Moss. 
Rev. AV. Cunningham, F. Y. Edge- 
worth, T. H. EUiott, C. Hughes, 

Prof. J. E. C. Munro, G. H. Sar- 

gant. 
Prof. F. Y. Edgeworth, T.H.Elliott, 

Prof. H. S. Foxwell, L. L. F. R. 

Price. 
Rev. Dr. Cunningham, T. H. Elliott, 

F. B. Jevons, L. L. F. R. Price. 
W. A. Brigg, Rev. Dr. Cunningham, 

T. H. EUiott, Prof. J. E. C. Munro, 

L. L. F. R. Price. 
Prof. J. Brough, E. Cannan, Prof. 

E. C. K. Conner, H. LI. Smith, 

Prof. W. R. Sorley. 
Prof. J. Brough, J. R. Findlay, Prof. 

E. C. K. Gonner, H. Higgs, 

L. L. F. R. Price. 
Prof. E. C. K. Gonner, H. de B. 

Gibbins, J. A. H. Green, H. Higgs, 

L. L. F. R. Price. 



MECHANICAL SCIENCE. 



SECTION G. — MECHANICAL SCIENCE. 



1836. Bristol 

1837. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow .... 

1841. Plymouth 

1842. Manchester 

1843. Cork 

1844. York 

1845. Cambridge 
1846.Southampton 

1847. Oxford 

1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich 



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

Rev. Dr. Robinson 

Charles Babbage, F.R.S 

Prof. Willis, F.R.S., and Robt. 

Stephenson. 
Sir John Robinson 



John Taylor, F.R.S 

Rev. Prof. Willis, F.R.S 

Prof. J. Macneill, M.R.I. A.... 

John Taylor, F.R.S 

George Rennie, F.R.S 

Rev. Prof. Willis, M.A., F.R.S. 
Rev. Prof .Walker, M.A.,F.R.S. 
Rev. Prof .Walker, M.A..F.R.S. 
Robt. Stephenson, M.P., F.R.S. 

Rev. R. Robinson 

William Cubitt, F.R.S 



T. G. Bunt, G. T. Clark, W. West. 
Charles Vignoles, Thomas Webster. 
R. Hawthorn, C. Vignoles, T. 

Webster. 
W. Carpmael, 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, Charles Vignoles. 
James Thomson, Robert Mallet. 
Charles Vignoles, 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. 
John Head, Charles Manby. 



PRESIDENTS AND SECRETAKIES OF THE SECTIONS. 



Ixi 



Date and Place 

1852. Belfast 

1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 

1838. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 
1863. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingh am 

1866. Nottingham 

1867. Dundee 

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 ... 

1881. York 

1882. Southamp- 

ton 



Presidents 



Secretaries 



John "Walker, C.E., LL.D., 

F.R.S. 
William Fairbairn, C.E., 

F.E.S. 
John Scott Russell, F.E.S. ... 

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. Macqiwrn Rankine, 

LL.D., F.R.S. 
J. F. Bateman, C.E., F.R.S.... 

William Fairbairn, LL.D., 

F R S 
Rev. Prof. Willis, M.A.,F.R.S. 

J. Hawkshaw, F.R.S 

Sir W. G. Armstrong, LL.D., 

F.R.S. 
Thomas Hawksley, V.P. Inst. 

C.E., F.G.S. 
Prof .W. J. Macquorn Rankine, 

LL.D., F.R.S. 
G. P. Bidder, C.E., F.R.G.S. 

C. W. Siemens, F.R.S 

Chas. B. Vignoles, C.E., F.R.S. 

Prof. Fleeming Jenkin, F.R. S. 

F. J. Bramwell, C.E 

W. H. Barlow, F.R.S 



Prof. James Thomson, LL.D., 

C.E., F.R.S.E. 
W. Froude, C.E., M.A., F.R.S. 

C. W. Merrifield, F.R.S 

Edward AVoods, C.E 

Edward Easton, C.E 

J. Robinson, Pros. Inst. Mech. 

Eng. 
James Abernethy, V.P. Inst. 

C.E., F.R.S.E. 
Sir W. G. Armstrong, C.B., 

LL.D., D.C.L., F.R.S. 
John Fowler, C.E., F.G.S. ... 



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. 

Jeffery. 
Prof. Downing, W.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. M. Fawcett, P. Le Neve Foster. 

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. 

O. Tarbotton. 
P. Le Neve Foster, John P. Smith, 

W. W. Urquhart. 
P. Le Neve Foster, J. F. Iselin, C. 

Manbj', 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. Bottomley, jun., W. J. Millar, 

J. N. Shoolbred, J. P. Smith. 
A. T. Atchison, Dr. Merrifield, J. N. 

Shoolbred. 
A. T. Atchison, R. G, Symes, H. T. 

Wood. 
A. T. Atchison, Emerson Bainbridge, 

H. T. Wood. 
A. T. Atchison, H. T. Wood. 

A. T. Atchison, J. F. Stephenson, 

H. T. Wood. 
A. T. Atchison, F. Churton, H. T. 

Wood. 



Ixii 



REPORT 1893. 



Date and Place 

1883. SouthpoTt 

1884. Montreal ... 

1885. Aberdeen... 

1886. Birmingham 

1887. Manchester 

1888. Bath 

1889. Newcastle- 

upon-Tyne 

1890. Leeds 

1891. Cardiff 

1892. Edinburgh 

1893. Nottingham 



Presidents 



James Brunlees, F.Pi.S.E., 

Pres.Inst.C.E. 
Sir F. J. Bramwell, F.E.S., 

V.P. Inst.C.E. 
B. Baker, M.Inst.C.E 

Sir J. N. Douglass, M.Inst. 

C.E. 
Prof. Osborne Reynolds, M.A., 

LL.D., F.R.S. 
W. H. Preece, F.R.S., 

M.Inst.C.E. 
W. Anderson, M.Inst.C.E. ... 

Capt. A. Noble, C.B., F.E.S. 

F.R.A.S. 
T. Forster Brown, M.Inst.C.E., 

Prof. W, C. Dnwin, F.R.S., 

M.Inst.C.E. 
Jeremiah Head, M.Inst.C.E., 

F.C.S. 



Secretaries 



A. T. Atchison, E. Rigg.H. T.Wood. 

A. T. Atchison, W. B. Dawson, J. 

Kennedy, H. T. Wood. 
A. T. Atchison, F. G. Ogilvie, E. 

Rigg, J. N. Shoolbred. 
C. W. Cooke, J. Kenward, W. B. 

Marshall, E. Rigg. 
C. F. Budenberg, W. B. Marshall, 

E. Rigg. 
C. W. Cooke, W. B. Marshall, E. 

Rigg, P. K. Stothert. 
C. W. Cooke, W. B. Marshall, Hon. 

C. A. Parsons, E. Rigg. 
E. K. Clark, C. W. Cooke, W. B. 

Marshall, E. Rigg. 
C. W. Cooke, Prof. A. C. Elliott, 

W. B. Marshall, E. Rigg. 
C. W. Cooke, W. B. Marshall, W. C. 

Popplewell, E. Rigg. 
C. W. Cooke, W. B. Marshall, E. 

Rigg, H. Talbot. 



ANTHROPOLOGICAL SCIENCE. 



SECTION H. — ANTHROPOLOGY. 



1884. 
1885. 

1886. 

1887. 

1888. 

1889. 

1890. 

1891. 

1892. 

1893. 



Montreal . . . 
Aberdeen... 

Birmingham 

Manchester 

Bath 



Newcastle- 
upon-Tyne 
Leeds 

Cardiff 

Edinburgh 

Nottingham 



E. B. Tylor, D.C.L., F.R.S. ... 
Francis Galton, M.A., F.R.S. 

Sir G. Campbell, K.C.S.L, 

M.P., D.C.L., F.R.G.S. 
Prof. A. H. Sayce, M.A 

Lieut. -General Pitt-Rivers, 

D.C.L., F.R.S. 
Prof. Sir W. Turner, M.B., 

LL.D., F.R.S. 
Dr. J. Evans, Treas.R.S,, 

F.S.A., F.L.S., F.G.S. 
Prof. F. Max Miiller, M.A. ... 

Prof. A. Macalister, M.A., 

M.D., F.R.S. 
Dr. R. Munro, M.A., F.R.S.E. 



G. W. Bloxam, W. Hurst. 

G. W. Bloxam, Dr. J. G. Garson. W. 

Hurst, Dr. A. Macgregor. 
G. W. Bloxam, Dr. J. G. Garson, W. 

Hurst, Dr. R. Sauodby. 
G. W. Bloxam, Dr. J. G. Garson, Dr. 

A. M. Paterson. 

G. W. Bloxam, Dr. J. G. Garson, J. 

Harris Stone. 
G. W. Bloxam, Dr. J. G. Garson, Dr. 

R. Morison, Dr. R. Howden. 
G. W. Bloxam, Dr. C. M. Chadwick, 

Dr. J. G. Garson. 
G. W. Bloxam, Prof. R. Howden, H. 

Ling Roth, E. Seward. 
G. W. Bloxam, Dr. D. Hepburn, Prof. 

B. Howden, H. Ling Roth. 

G. W. Bloxam, Rev. T. W. Davies, 
Prof. R. Howden, F. B. Jevons, 
J. L. Myres. 



LIST OF EVENING LECTURES. 



Ixiii 



LIST OF EVENING LECTURES. 



Date and Place 



1842. Manchester 



1843. Cork . 



1844. York , 



1845. Cambridge 

1846. Southamp- 

ton. 



1847. Oxford. 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 



1853. Hull, 



1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 



Lecturer 



k 



Charles Vignoles, P.E.S 

Sir M.L Brunei 

R. L Murchison 

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

Prof. E. Forbes, F.E.S 

Dr. Robinson 

Charles Lyell, F.R.S 

Dr. Falconer, F.R.S 

G.B.Airy,r.R.S.,Astron.Royal 

R. L Murchison, F.R.S 

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

Charles Lyell, F.R.S 

W. R. 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. Faraday, F.R.S 

Rev. Prof. "Willis, M.A., F.R.S. 

Prof. J. H. Bennett, M.D., 
F.R.S.E. 

Dr. Mantell, F.R.S 

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

G.B.Airy,F.R.S.,Astron. Royal 
Prof. G. G. Stokes, D.C.L., 

F.R.S. 
Colonel Portlock, 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. B. 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... 



Subject of Discourse 



The Principles and Construction of 
Atmospheric Railways. 

The Thames Tunnel. 

The Geology of Russia. 

The Dinornis of New Zealand. 

The Distribution of Animal Life in 
the ^gean Sea. 

The Earl of Rosse's Telescope. 

Geology of North America. 

The Gigantic Tortoise of the Siwalik 
Hills in India. 

Progress of Terrestrial Magnetism. 

Geology of Russia. 

Fossil Mammalia of the British Isles. 

Valley and Delta of the 3Iississippi. 

Properties of the Explosive substance 
discovered by Dr. Schonbein; also 
some Researches of his own on the 
Decomposition of Water by Heat. 

Shooting Stars. 

Magnetic and Diamagnetic Pheno- 
mena. 

The Dodo (^Bidui in£j>tus). 

Metallurgical Operations of Swansea 
and its Neighbourhood. 

Recent Microscopical Discoveries. 

Mr. Gassiot's Battery. 

Transit of different "Weights with 
varying "Velocities on Railways. 

Passage of the Blood through the 
minute vessels of Animals in con- 
nection with Nutrition. 

Extinct Birds of New Zealand. 

Distinction between Plants and Ani- 
mals, and their changes of Form. 

Total Solar Eclipse of July 28, 1851. 

Recent Discoveries in the properties 
of Light. 

Recent Discov€fry of Rock-salt at 
Carrickfergus, and geological and 
practical considerations connected 
with it. 

Some peculiar Phenomena in the 
Geology and Physical Geography 
of Yorkshire. 

The present state of Photography. 

Anthropomorphous Apes. 

Progress of Researches in Terrestrial 
Magnetism. 

Characters of Species. 

Assyrian and Babylonian Antiquities 
and Ethnology. 

Recent Discoveries in Assyria and 
Babylonia, with the results of 
Cuneiform research up to the 
present time. 

Correlation of Physical Forces. 



Lsiv 



REPOET — 1893. 



Date and Place 



1837 
1858. 
1859. 

1860. 
1861. 

1862 
1863. 

1864. 
1865. 

1866. 
1867. 



Lecturer 



Dublin Prof. W. Thomson, F.R.S. ... 

jEev. Dr. Livingstone, D.C.L. 
Leeds 'Prof. J. PhiIlips,LL.D.,F.R.S. 

jProf. R. Owen, M.D., F.R.S. 
Aberdeen... , Sir R. I. Murchison, D.C.L... . 
Rev. Dr. Robinson, F.R.S. ... 

Oxford |Rev. Prof. Walker, F.R.S. ... 

I Captain Sherard Osborn, R.N. 
Manchester | Prof .W. A. Miller, M.A., F.R.S. 

\g. B. Airy, F.R.S., Astron. 
Royal. 

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

Prof. Odling, F.R.S 

Prof. Williamson, F.R.S 



Cambridge 
Newcastle 



Bath. 



James Glaisher, F.R.S.. 



Prof. Roscoe, F.R.S 

Dr. Livingstone, F.R.S. ... 
Birmingham J. Beete Jukes, F.R.S 



Nottingham 
Dundee 



1868. Norwich . 

1869, 

1870 



Exeter 



1871. 

1872. 

1873. 
1871. 

1875. 
1876. 



Liverpool... 

Edinburgh 

Brighton .., 

Bradford ... 
Belfast 



Bristol 

Glasgow ... 



William Huggins,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. AV. Odling, F.R.S 

Prof. J. Phillips, LL.D.,F.R.S. 
J. Norman Lockyer F.R.S. .. 

Prof. J. Tyndall, 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 



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 

:SirWyville Thomson, F.R.S. 



Subject of Discourse 



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. 
Physical Constitution of the Sun. 
Arctic Discovery. 
Spectrum Analysis. 
The late Eclipse of the Sun. 

The Forms and Ad ion of Water. 

Organic Chemistry. 

The Chemistry of the Galvanic Bat- 
tery considered in relation to 
Dynamics. 

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. 

ArchiBology of the early Buddhist 
Monuments. 

Reverse Chemical Actions. 

Vesuvius. 

The Physical Constitution of the 
Stars and Nebulfe. 

The Scientific Use of the Imagina- 
tion. 

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 
Civilisation. 

Insect Metamorphosis. 

The Aims and Instruments of Scien- 
tific Thought. 

Coal and Coal Plants. 

Molecules. 

Common Wild Flowers considered 
in relation to Insects. 

The H^-pothesis that Animals are 
Automata, and its History. 

The Colours of Polarised Light. 

Railway Safety Appliances, 

Force. 

The Challenger Expedition. 



LIST OF EVENING LECTURES. 



kv 



Date and Place 



Lecturer 



1877. Plymouth. 



1878. Dublin 



1879. Sheffield 

1880. Swansea 

1881. York 



1882. Southamp- 

ton. 

1883. Southport 



1884. Montreal, 



1885. Aberdeen. 



1886. Birmingham 



1887. Manchester 



Subject of Discourse 



1888. Bath. 



1889. Newcastle- 

upon-Tyne 

1890. Leeds 

1891. CardifE 

1892. Edinburgli 

1893. Nottingham 



W. Warington Smyth, M.A., 

F.K.S. 

Prof. Odling, F.R.S 

G. J. Romanes, F.L.S 

Prof. Dewar, F.K.S 

W. Crookes, F.R.S 

Prof. E. Ray Lankester, F.R.S. 
Prof .W.Boyd Dawkins, F.R.S. 

Francis Galton, F.R.S 

Prof. Huxley, Sec. R.S 

W. Spottiswoode, Pres. R.S. 

Prof. Sir Wra. Thomson, F.R.S. 
Prof. H. N. Moseley, F.R.S. 
Prof. R. S. BaU, F.R.S 

Prof. J. G. McKendrick, 
F.R.S.E. 

Prof. O. J. Lodge, D.Sc 

Rev. W. H. Dallinger, F.R.S. 



Prof. W. G. Adams, F.R.S. ... 

John Murray, F.R.S.E 

A. W. Riicker, M.A., F.R.S. 
Prof. W. Rutherford, M.D. ... 
Prof. H. B. Dixon, F.R.S. ... 
Col. Sir F. de Winton, 

K.C.M.G. 
Prof. W. E. Ayrton, F.R.S. ... 

Prof. T. G. Bonney, D.Sc, 

F.R.S. 
Prof. W. C. Roberts-Austen, 

F.R.S. 
Walter Gardiner, M.A 

E. B. Poulton, M.A., F.R.S.... 
Prof. C. Vernon Boys, F.R.S. 

Prof.L. C. Miall,F.L.S.,F.G.S. 

Prof . A. W. Riicker, M. A.,r.R.S. 
Prof. A. Milnes Marshall, 

D.Sc, F.R.S. 
Prof. J. A. Ewing, M. A., F.R.S., 

F.R.S.E. 
Prof. A. Smithells, B.Sc. 
Prof. Victor Horsley, F.R.S. 



The Physical Phenomena connected 
with tlie 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 Functions. 

Tides. 

Pelagic Life. 

Recent Researches on the Distance 
of the Sun. 

Galvanic and Animal Electricity. 

Dust. 

The Modern Microscope in Re- 
searches on the Least and Lowest 
Forms of Life. 
The Electric Light and Atmospheric 
I Absorption. 
, The Great Ocean Basins. 
I Soap Bubbles. 
The Sense of Hearing. 
The Rate of Explosions in Gases. 
Explorations in Central Africa. 

The Electrical Transmission of 

Power. 
The Foundation Stones of the Earth's 

Crust. 
The Hardening and Tempering of 

Steel. 
How Plants maintain themselves in 

the Struggle for Existence. 
Mimicry. 
Quartz " Fibres and their AppUca- 

tions. 
Some Difficulties in the Life of 

Aquatic Insects. 
Electrical Stress. 
Pedigrees. 

Magnetic Induction. 

Flame. 

The Discovery of the Physiology of 
the Nervous System. 



1893. 



Ixvi 



EEPOET — 1893. 



LECTUEES TO THE OPERATIVE CLASSES. 



Date and Place 



1867. 
1868. 
1869. 



Dundee.. 

Norwich 
Exeter .. 



1870. Liverpool , 



1872. 
1873. 
1874. 
1875. 
1876. 

1877. 
1879. 
1880. 
1881. 

1882. 

1883. 
1884. 
1885. 
1886. 

1887. 
1888. 

1889. 

1890. 
1891. 
1892. 
1893. 



Brighton 
Bradford 
Belfast.., 
Bristol .., 
Glasgow- 



Plymouth 
Sheffield 
Swansea 
York 



Southamp- 
ton. 
Southport 
Montreal ... 
Aberdeen... 
Birmingham 

Manchester 
Bath 

Newcastle- 
upon-Tyne 

Leeds 

Cardiff 

Edinburgh 
Nottingham 



Lecturer 



Prof. J. Tyndall, LL.D.,F.R.S. 
Prof. Huxley, LL.D., F.R.S. 
Prof. MiUer, M.D., F.R.S. ... 



Sir John Lubbock, Bart.,M.P., 

F.R.S. 
W.Spottiswoode,LL.D.,F.R.S. 
C.W.Siemens, D.C.L., F.R.S. 

Prof. Odling, F.R.S 

Dr. W. B. Carpenter, F.R.S. 
Commander Cameron, C.B., 

R.N. 

W. H. Preece 

W. E. Ayrton 

H. Seebohm, F.Z.S 

Prof. Osborne Reynolds, 

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



Sir F. J. Bramwell, F.R.S. ... 

Prof. R. S. Ball, F.R.S 

H. B. Dixon, M.A 

Prof. W. C. Roberts-Austen, 

F.R.S. 

Prof. G. Forbes, F.R.S 

Sir John Lubbock, Bart., M.P., 

F.R.S. 
B. Baker, M.Inst.C.E 

Prof. J. Perry, D.Sc, F.R.S. 
Prof. S. P. Thompson, F.R.S. 
Prof. C. Vernon Boys, F.R.S. 
Prof. Vivian B. Lewes 



Subject of Discourse 



Matter and Force. 

A Piece of Chalk. 

Experimental Illustrations of the 
modes of detecting the Composi- 
tion of the Sun and other Heavenly 
Bodies by the Spectrum. 

Savages. 

Sunshine, Sea, and Sky, 

Fuel. 

The Discovery of Oxygen. 

A Piece of Limestone. 

A Journey through Africa. 

Telegraphy and the Telephone. 

Electricity as a Motive Power. 

The North-East Passage. 

Raindrops, Hailstones, and Snow- 
flakes. 

Unwritten History, and how to 
read it. 

Talking by Electricity — Telephones. 

Comets. 

The Nature of Explosions. 

The Colours of Metals and their 
Alloys. 

Electric Lighting. 

The Customs of Savage Races. 

The Forth Bridge. 

Spinning Tops. 
Electricity in Mining. 
Electric Spark Photographs. 
Spontaneous Combustion. 



Ixvii 



I 



OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE 
NOTTINGHAM MEETING. 

SECTION A.— MATHEMATICAL AND PHYSICAL SCIENCE. 

President.— R. T. Glazebrook, M.A., F.R.S. 

Vice-Presidents. — Professor G. Carey Foster, F.R.S. ; Professor W. H. 
Heaton, M.A. ; Lord Rayleigh, Sec.R.S. ; Professor A. W. Reinold, 
F.R.S. 

Secretaries.— J. Larmor, F.R.S.; Dr. W. Peddie, F.R.S.E. ; W. T. A. 
Emtage, M.A. ; Professor A. Lodge, M.A. {Recorder). 

SECTION B. — CHEMICAL SCIENCE. 

President.— Pvoies.s,ov J. Emerson Reynolds, M.D., D.Sc, F.R.S., V.P.C.S. 

Vice-Presidents. — Professor F. Clowes, D.Sc. ; Professor H. B. Dixon, 
F.R.S. ; Dr. J. H. Gladstone, F.R.S. ; Professor H. McLeod, F.R.S.; 
Dr. W. H. Perkin, F.R.S. ; Sir H. E. Roscoe, F.R.S.; Professor T. 
E. Thorpe, F.R.S. ; Professor W. A. Tilden, F.R.S. 

Secretaries.— Z . B. Coleman, F.C.S. ; M. J, R. Dunstan, F.R.S.E. ; D. H. 
Nagel, M.A. ; Dr. W. W. J. Nicol, F.R.S.E. {Becorder). 

SECTION C. — GEOLOGY, 

President.— J. J. H. Teall, M.A., F.R.S. 

Vice-Presidents. — Professor W. C. Brogger ; Sir A. Geikie, F.R.S. ; Pro- 
fessor J. P. Iddings ; Rev. A. Irving, D.Sc. ; Professor T. Rupert 
Jones, F.R.S. ; Professor C. Lapworth, F.R.S. ; Rev. J. Magens 
Mello, M.A. ; Henry Woodward, F.R.S. 

Secretaries.— J. W. Carr, M.A.; J. E. Marr, F.R.S.; Clement Raid, F.G.S. ; 
W. W. Watts, M.A. (Becorder), 

SECTION D. — BIOLOGY. 

President.— Hev. Canon H. B. Tristram, M.A., LL.D., D.D., F.R.S. 

Vice-Presidents. — Professor D. J. Cunningham, F.R.S. ; Sir W. H. Flower, 
K.C.B., F.R.S. ; J. N. Langley, F.R.S. ; Professor A. Newton, F.R.S. ; 
Dr. D. H. Scott, F.L.S. 

Secretaries. — G. C. Bourne, M.A. ; Professor J. B. Farmer, F.L.S. ; Pro- 
fessor W. A. Herdman, F.R.S.; Dr. S. J. Hickson, M.A. (Becorder) ; 
Dr. W. B. Ransom ; W. L. Sclater, F.Z.S. 

d2 



Ixviii REPORT — 1893. 



SECTION E. — GEOQRAPHT. 

President.— Henry Seebohm, Sec.R.G.S., F.L.S., F.Z.S. 

Vice-Presidents. — Professor Bonney, D.Sc, F.R.S. ; J. Y. Buclianan, F.R.S.; 
Colonel Godwin-Ansten, F.R.S. ; J. Scott Keltie, F.R.G.S. ; Clements 
R. Markliam, C.B., F.R.S.; E. Delmar Morgan, F.R.G.S.; E. G. 
Ravenstein, F.R.G.S. 

Secretaries. — Lieut. -Col. Fred. Bailey, Sec.R.S.G.S. ; John Coles, F.R.G.S. ; 
H. 0. Forbes, F.R.G.S.; Dr. H. R. Mill, F.R.S.E. {Becorder). 

SECTION F. — ECONOMIC SCIENCE AND STATISTICS. 

President. — Professor J. S. Nicholson, D.Sc, F.S.S. 

Vice-Presidents. — Professor Bastable, M.A. ; Professor W. Cunningham, 
D.D. ; Professor Edgeworth, D.C.L. ; Hon. Sir C. W. Fremantle, 
K.C.B. ; .J. B. Martin, M.A. ; R. H. Inglis Palgrave, F.R.S. ; Pro- 
fessor H. Sidgwick, D.Litt. ; Professor J. E. Symes, M.A. 

Secretaries. — Professor E. C. K. Gonner, M.A. {Recorder) ; H. de B. Gib- 
bins, M.A. ; J. A. H. Green ; H. Higgs, LL.B. ; L. L. F. R. Price, 
M.A. 

SECTION G. — MECHANICAL SCIENCE. 

President. — Jeremiah Head, M.Inst.C.E. 

Vice-Presidents. — Sir Frederick Bramwell, Bart., F.R.S. ; Gisbert Kapp, 
M.Inst.C.E. ; Professor W. Robinson ; Professor W. C. Unwiu, 
F.R.S. ; Edward Woods, M.Inst.C.E. 

Secretaries. — Conrad "W. Cooke ; W. Bayley Marshall, M.Inst.C.E. ; E. 
Rigg, M.A. (Recorder) ; H. Talbot. 

SECTION n. — ANTHEOPOLOGT. 

President.— Robert Munro, M.A., M.D., F.R.S.E. 

Vice-Presidents. — Professor Boyd Dawkins, F.R.S. ; Professor A. H. 
Sayce, M.A. 

Searetaries. — G. W. Bloxam, M.A, (Recorder) ; Rev. T. Witton Davies, 
B.A. ; Professor R. Howden, M.B. ; F. B. Jevons, M.A. ; J. L. 
Myres, B.A. 



OFFICERS AND COUNCIL, 1893-94. 

PRESIDENT. 

Dr.. J. S. BtTRDON SANDERSON, M.A., M.D., LL.D., D.O.L., F.R.S., F.R.S.E., Professor of 
Physiology in the University of Oxford. 

VICE-PRESIDENTS. 



His Grace the Duke op St. Albans, Lord Lien- 
tenant of NottinghBinshire. 

His Grace the Duke of Devonsbike, K.G., Chan- 
cellor of the University of Cambridge. 

His Grace the Duke of Portland, Lord Lieu- 
tenant of Caithness. 

His Grace the Duke op Newcastle. 

The Eight Hon. Lohd Belper, LLM. 



The Right Worshipful the Mayor of Nottinci- 

HAM. 

The Right Hon. Sir W. R. GnoVE, M.A., D.C.L., 

LL.D., F.R.S.. F.R.S.E. 
Sir John Turkey, J.P. 
Professor Michael Foster, M.A., M.D., LL.D., 

Sec.R.S.. F.L.S., F.C.S. 
W. H. Ransom, Estj., M.D., P.R.S. 



PRESIDENT ELECT. 
Thb Most Hon. the MARQUES3 OP SALISBURY. K.G., D.C.L., P.E.S., ClianceUor of the 

University of Oxford. 



VICE-PRESIDI 

The Right Hon. the Earl op Jersey, G.C.M.G., 
Lord-Lieutenant of the County of Cxford. 

The Right Hon. Lord Wantage, K.C.B., V.C.,Lord- 
-Licutenant of Berkshire. 

The Right Hon. the Earl op Roserery, E.G., P.R.S. 

The Right Rev. the Lord Bishop op Oxford, 
D.D. 

The Right Hon. Lord Rothschild, Lord-Lieu- 
tenant of Bucks. 

The Right Hon. Lord Kelvin, D.C.L., Pres.R.S. 



ENTS ELECT. 

The Rev. the Vice-Chancbllor OF THE TTsrvER- 

sity OP Oxford. 
Sir W. R. Axsox, D.C.L., Warden of All Sonls 

College. 
Sir Bhrniurd Samuelson, Bart., M.P., P.R.S. 
Sir Henry Dyke Acland, Bart., M.D., P.R.S., 

Regius Professor of Medicine. 
The Rev. tlie Master op Pembroke College, 

Sedleian Professor of Natural Philosophy. 
Dr. J. J. Sylvester, F.R.S., Savilian Professor of 

Geometry. 



GENERAL SECRETARIES. 

Capt. Sir Douglas Galton, K.C.B., D.C.L., LL.D., F.R.S., P.G.S., 12 Chester Street, London, S.W. 

A. G. Vernon Harcourt, Esq., M.A., D.C.L., LL.D., P.R.S. , F.C.S., Cowley Grange, Oxford. 

ASSISTANT GENERAL SECRETARY. 
G. Griffith, Esq., M.A., Harrow, Middlesex. 

GENERAL TREASURER. 
Professor Abthuh Ruckkr, M.A., F.R.S., Burlington House, London, W. 

LOCAL SECRETARIES FOR THE MEETING AT OXFORD. 
Gilbert C. Bourne, Esq., M.A. I D. H. Nagel, Esq., M.A. 

G. C. Druce, Esq., M.A. | 

LOCAL TREASURER FOR THE MEETING AT OXFORD. 
F. M. Davis, Esq. 



ORDINARY MEMBERS 
Anderson, Dr. W., P.R.S. 
Atrton, Professor W. E., P.R.S. 
Baker, Sir B., K.C.M.G., P.R.S. 
Ball, Sir R. S., F.R.S. 
Boys, Professor 0. Vernon, F.R.S. 
Edgeworth, Professor, M.A. 
Evans, Sir J., K.C.B., F.R.S. 
Glazebrook. R. T., Esq., F.R.S. 
Green, Professor A. H., F.R.S. 
HoRSLEY, Professor Victor, F.R.S. 
LrvEiNG, Professor G. D., F.R.S. 
Lodge, Professor Oliver J., F.R.S. 
Markham, CLE.MBNTS R., Esq., C.B., F.R.S. 



OF THE COUNCIL. 

Meldola, Professor R., P.R.S. 
Preece, W. H., Esq., F.R.S. 
Rajisay, Professor W., F.R.S. 
Rkixold, Professor A. W., F.E.S. 
Reynolds, Professor J. Emkkson, M.D., 

P.R.S. 
Sedgwick, Professor H., M.A. 
Sy.mons, G. J., Esq., F.R.S. 
Thomson, Professor J. J., M.A., P.R.S. 
Unwix, Professor W. C, F.R.S. 
Ward, Professor Marshall, F.R.S. 
Whitaker, W., Esq., F.R.S. 
Woodward, Dr. H., F.R.S. 



EX-OFFICIO MEMBERS OF THE COUNCIL. 
The Trustees, the President and President Elect, the Presidents of former years, the Vice-Presidents and 
Vice-Presidents Elect, the General and Assistant General Secretaries for the present and former years, 
the Secretary, the General Treasurers for the present and former years, and the Local Treasurer and 
Secretaries for the ensuing Meeting. 

TRUSTEES (PERMANENT). 
The Right Hon. Sir John Lubbock, Bart., M.P., D.C.L., LL.D., P.R.S., P.L.S. 
The Right Hon. Lord Rayleigh, M.A., D.C.L., LL.D., Sec.R.S., F.R.A.S. 
The Eight Hon. Lord Playpair, K.C.B., Ph.D., LL.D., F.R.S. 



PRESIDENTS OF FORMER TEARS. 



The Duke of Argyll, K.G., K.T. 
Lord Armstrong, C.B., LL.D. 
Sir William R. Grove, F.R.S. 
Sir Joseph D. Hooker, K.C.S.I. 
Sir G. G. Stokes, Bart., F.R.S. 
The Rt. Hon. Prof. Huxley. F.R.S. 
Lord Kelvin, LL.D., Pres.R.S. 



Prof. A. W. Williamson, F.R.S. 
Prof. Allman, M.D., F.R.S. 
Sir John Lubbock, Bart., F.R.S. 
Prof. Cayley, LL.D., F.R.S. 
Lord Ravleigh, D.C.L., Sec.R.S. 
Lord Plavfair, K.C.B., F.R.S. 
Sir Wm. Dawson, C.M.G., F.R.S. 



Sir H. E. Roscoe, D.C.L., P.R.S. 
Sir P. J. Bramwell, Bart., F.R.S. 
Sir W. H. Flower, K.C.B., F.R.S. 
Sir Frederick Abel, Bart., F.R.S. 
Dr. Wm. Muggins F.R.S. 
Sir Archibald Geikie, F.R.S. 



GENERAL OFFICERS OP FORMER TEARS. 



P. Galton, Esq., F.R.S. 

Prof. Michael Foster, Sec.R.S. 



[ G. Griffith, Esq., M.A. I Prof. T. G. Bonney, D.Sc, F.R.S. 

I P. L. Sclater, Esq., Ph.D., F.R.S. | Prof. A. W. Williamson, F.R.S. 



AUDITORS. 
J. B. Martin, Esq., M.A., F.S.S. | Prof. W. Cunningham, D.Sc. | Prof. T. E. Thorpe, F.R.S. 



Ixx REPORT 1893. 



THE BEITISH ASSOCIATION FOE 



Br. THE GENERAL TREASURER'S ACCOUNT, 

1892-93. RECEIPTS. 

£ 

Balance brought forward 328 

Life Compositions 170 

New Annual Members' Subscriptions 300 

Annual Subscriptions 669 

Sale of Associates' Tickets 724 

Sale of Ladies' Tickets 439 

Sale of Publications 120 

Interest on Exchequer Bills 11 

Dividends on Consols 227 

Dividends on India 3 per Cents 105 

Unexpended Balance of Grant (made in 1891) for investi- 
gating the Phenomena accompanying the Discharge of 

Electricity from Points 6 15 4 

Unexpended Grant (made in 1891) for improving a Deep-sea 

Tow-net 40 



(. 


d. 


8 


6 
































18 


6 


11 


6 


18 


4 


6 






£3142 18 2 



Investments. 

£, s. d. 

In hands of Trustees : 

2f per cent. Consolidated Annuities 8500 

India 3 per cent. Stock 3600 

In hands of Treasurer : 

Exchequer Bills ■ 500 

£12600 



BALANCE SHEET, 1892-93. Ixxi 



THE ADVANCEMENT OF SCIENCE. 



from July 1,1892, to June 30, 1893. Cr. 

1892-93. PAYMENTS. 

£ s. d. 

Expenses of Edinburgh Meeting, including Trinting, Adver- 
tising, Payment of Clerks, &c 196 15 

Kent and Office Expenses 67 18 7 

Salaries 500 

Messrs. Spottiswoode &; Co., printing, binding, &c 1079 7 4 

Grants. 

£ s. d. 

Electrical Standards 25 

Meteorological Observations on Ben Nevis 150 

Tables of Mathematical Functions 15 

Eecording the Direct Intensity of Solar Radiation 2 8 6 

Magnetic Work at the Falmouth Observatoiy 25 

Isomeric Naphthalene Derivatives 20 

Erratic Blocks ■'^ a a 

Fossil Phyllopoda 5 

■Underground Waters 5 

Shell-bearing Deposits at Olava, Chapelhall, &c 20 

Eurypterids of the Pentland Hills 10 

Table at the Naples Zoological Station 100 

Table at the Plymouth Biological Laboratory 30 

Fauna of Sandwich Islands 100 

Zoology and Botany of West India Islands 50 

Exploration of Irish Sea 30 

Physiological Action of Oxygen in Asphyxia 20 

Index of Genera and Species of Animals 20 

Exploration of Karakoram Mountains 50 

Scottish Place-names (10?., less 3i. returned) 7 

Climatology and Hydrography of Tropical Africa 50 

Methods ot Economic Training (4?., less 13s. returned) 3 7 

Anthropometric Laboratory 5 

Exploration of Ancient Remains in Abj ssinia 25 

North-Westem Tribes of Canada 100 

Corresponding Societies Committee 30 



907 15 6 



Balance at Bank of England, Western Branch 424 8 9 
Less Cheques drawn but not presented 39 



385 8 9 
In hands of General Treasurer 5 13 



391 1 9 
;e3142 IS 2 



Akthub W. KiJCKER, General Treasurer. 

JOHN B. MARTIN, -I ^„^i^„,.,. 

Wm. Cunningham, j 
Jnly 5, 1893 . 



Table showing the Attendance and Receipts 



Date of Meeting 



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, Aug. 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 .. 

1868, Aug. 19 .. 

1869, Aug. 18 .. 

1870, Sept. 14 .. 

1871, Aug. 2 .. 

1872, Aug. 14 .. 

1873, Sept. 17 .. 

1874, Aug. 19 .. 
187.5, Aug. 25 .. 

1876, Sept. 6 .. 

1877, Aug. 15 .. 

1878, Aug. 14 .. 

1879, Aug. 20 .. 

1880, Aug. 25 .. 

1881, Aug. 31 .. 

1882, Aug. 23 .. 

1883, Sept. 19.. 

1884, Aug. 27 .. 

1885, Sept. 9 .. 

1886, Sept. 1 .. 

1887, Aug. 31 ... 

1888, Sept. 5 ... 

1889, Sept. 11... 

1890, Sept. 3 ... 

1891, Aug. 19 ... 

1892, Aug. 3 ... 

1893, Sept. 13... 



Where held 



Presidents 



York 

Oxford 

Cambridge 

Edinburgh 

Dublin 

Bristol 

Liverpool 

Ne wcastle-on- Tyne 

Birmingham 

Glasgow 

Plymouth 

Manchester 

Cork 

York 

Cambridge 

Southampton 

Oxford 

Swansea 

Birmingham 

Edinburgh 

Ipswich 

Belfast 

Hull 

Liverpool 

Glasgow 

Cheltenham 

Dublin 

Leeds 

Aberdeen 

Oxford 

Manchester 

Cambridge 

Newcastle-on-Tyne 

Bath 

Birmingham 

Nottingham 

Dundee 

Norwich 

Exeter 

Liverpool 

Edinbm-gh 

Brighton 

Bradford 

Belfast 

Bristol 

Glasgow 

Plymouth 

Dublin 

Sheffield 

Swansea 

York 

Southampton 

Southport 

Montreal 

Aberdeen 

Birmingham 

Manchester 

Bath 

Newcastle-on-Tyne 

Leeds 

Cardiff 

Edinburgh 

Nottingham 



The Earl Fitzwilliam, D.C.L. 

The Eev. W. Buckland, F.R.S. 

The Eev. 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.R.S 

The Duke of Northumberland 

The Rev. W. Vernon Harcourt 

The Marquis of Breadalbane... 

The Rev. VV. Whewell, F.R.S. 

The Lord Francis Egerton 

The Earl of Rosse, F.R.S 

The Rev. G. Peacock, D.D. ... 

Sir John F. W. Herschel, Bart, 

Sir Roderick I. MurchisoD,Bart, 

Sir Robert H. Inglis, Bart 

The Marquis of Northampton 
^ The Rev. T. R. Robinson, D.D. 

1 Sir David Brewster, K.H 

1 G. B. Airy, Astronomer Royal 
i Lieut.-General Sabine, F.R.S. 

i William Hopkins, F.R.S 

' The Earl of Harrowby, F.R.S. 
i The Duke of Argyll, F.R.S. ... 
I Prof. C. G. B. Daubeny, M.D. 

The Rev.Humphrey Lloyd, D.D. 
I Richard Owen, M.D., D.C.L.... 

H.R.H. the Prince Consort ... 

The Lord Wrottesley, M.A. ... 

WilliamFairbairn,LL.D.,F.R.S. 

The Rev. Professor Willis, M.A. 

Sir William G.Armstrong, C.B. 

Sir Charles Lyell, Bart., M.A. 

Prof. J. Phillips, M.A., LL.D. 

William R. Grove, Q.C., F.R.S. 

The Duke of Buccleuch,K.C.B. 

Dr. Joseph D. Hooker, F.R.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.R.S. ... 

Prof. A. W. Williamson, F.R.S. 

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

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

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

Prof. A. Thomson, M.D., F.R.S. 

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

Prof.G. J. Allman, M.D., F.R.S. 

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

Sir John Lubbock, Bart., F.R.S. 

Dr. C. W. Siemens, F.R.S 

Prof. A. Cavley, D.C.L., F.R.S. 

Prof. Lord Rayleigh, F R.S. ... 

SirLyonPlayfair,K.C.B.,F.E.S. 

Sir J.W. Dawson, C.M.G.,F.R.S. 

Sir H. E. Roscoe. D.C.L.,F.R.S. 

Sir F. J. Bramwell, F.R.S 

Prof. W.H. Flower, C.B., F.R.S. 

Sir F. A. Abel. C.B., F.R.S. ... 

Dr. W. Huggins, F.R.S 

Sir A. Geikie, LL.D., F.R.S. ... 

Prof. J. S. Burden Sanderson... 



Old Life 
Members 



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 
203 
235 
225 
314 
428 
266 
277 
259 
189 
280 
201 



Ladies were not admitted by purchased tickets until 1843. 



t Tickets of Admission to Sections only. 



at Annual Meetings of the Association. 



Attended by 


Amount 

received 

during tlie 

Meeting 


Hums paid on 

Account of 

Grants for Scien 

tifio Purposes 


Year 


OM Annua 
Members 


1 New Annua 
Members 


1 A 

Cl 


Se's ^"i^^ 


Foreigners Total 




... 




... 


•• 


353 






1831 
1832 






















900 






1833 


• 




... 









1298 




£20 

167 


18.54 
1835 




• 




siV 

376 
185 
190 
22 
39 
40 
25 


4( 
2' 
45 
3' 


'.'. 1100* 

'.'. 60* 
J3t 331* 
160 

9t 260 
)7 172 
rO 196 
)5 203 
re 197 


34 

40 

28 

35 

j 36 

j 53 

15 


1350 
1840 
2400 
1438 
1353 
891 
1315 

1079 
857 

1320 
819 




435 

922 12 6 

932 2 2 

1595 11 

1546 16 4 

1235 10 11 

1449 17 8 

1565 10 2 

981 12 8 

831 9 9 

685 16 

208 5 4 

275 1 8 


1836 
1837 
1838 
1839 
1840 
1841 
1842 
1843 
1844 
1845 
1846 
1847 
1848 










46 
75 
71 
45 










94 




65 




197 




64 


£707 o"o 


93 


33 


4^ 


[7 237 


22 


1071 


963 


159 19 6 


1849 


128 


42 


61 


273 


44 


1241 


1085 


345 18 


1850 


61 


47 


24 


[i 141 


37 


710 


620 


391 9 7 


1851 


63 


60 


51 


292 


9 


1108 


1085 


304 6 7 


1852 


56 


57 


3( 


.7 236 


6 


876 


903 


205 


1853 


121 


121 


76 


5 524 


10 


1802 


1882 


380 19 7 


1854 


142 


101 


10£ 


4 543 


26 


2133 


2311 


480 16 4 


1855 


104 


48 


41 


2 346 


9 


1115 


1098 


734 13 9 


1856 


156 


120 


9C 


569 


26 


2022 


2015 


507 15 4 


1857 


111 


91 


71 


509 


13 


1698 


1931 


618 18 2 


1858 


125 


179 


12C 


6 821 


22 


2564 


2782 


684 11 1 


1859 


177 


59 


63 


6 463 


47 


1689 


1604 


766 19 6 


1860 


184 


125 


158 


9 791 


15 


3138 


3944 


1111 5 10 


1861 


150 


57 


43 


3 242 


25 


1161 


1089 


1293 16 6 


1862 


154 


209 


170 


4 1004 


25 


3335 


3640 


1608 3 10 


1863 


182 


103 


111 


9 1058 


13 


2802 


2965 


1289 15 8 


1864 


215 


149 


76 


6 508 


23 


1997 


2227 


1591 7 10 


1865 


218 


105 


96 


771 


11 


2303 


2469 


1750 13 4 


1866 


193 


118 


116 


3 771 


7 


2444 


2613 


1739 4 


1867 


226 


117 


72 


682 


45^ 


[ 2004 


2042 


1940 


1868 


229 


107 


67 


8 600 


17 


1856 


1931 


1622 


1869 


303 


195 


110 


3 910 


14 


2878 


3096 


1572 


1870 


311 


127 


97 


6 754 


21 


2463 


2575 


1472 2 6 


1871 


280 


80 


93 


7 912 


43 


2533 


2649 


1285 


1872 


237 


99 


79 


6 601 


11 


1983 


2120 


1685 


1873 


232 


85 


81 


7 630 


12 


1951 


1979 


1151 16 


1874 


307 


93 


88 


4 672 


17 


2248 


2397 


960 


1875 


831 


185 


126 


5 712 


25 


2774 


3023 


1092 4 2 


1876 


238 


59 


44 


6 283 


11 


1229 


1268 


1128 9 7 


1877 


290 


93 


128 


5 674 


17 


2578 


2615 


725 16 6 


1878 


239 


74 


52 


9 349 


13 


1404 


1425 


1080 11 11 


1879 


171 


41 


38 


9 147 


12 


915 


899 


731 7 7 


1880 


313 


176 


123( 


3 514 


24 


2657 


2689 


476 8 1 


1881 


253 


79 


51( 


3 189 


21 


1253 


1286 


1126 1 11 


1882 


330 


323 


95! 


} 841 


5 


2714 


3369 


1083 3 3 


1883 


317 


219 


82( 


5 74 


26&60 


H.§ 1777 


1538 


1173 4 


1884 


332 


122 


105? 


i 447 


6 


2203 


2256 


1385 


1885 


428 


179 


106' 


429 


11 


2453 


2532 


995 6 


1886 


510 


244 


198£ 


493 


92 


3838 


4336 


1186 18 


1887 


399 


100 


63[ 


509 


35 


1984 


2107 


1611 5 


1888 


412 


113 


1024 


579 


12 


2437 


2441 


1417 11 


1889 


368 


92 


680 


334 


21 


1775 


1776 


789 16 8 


1890 


841 


152 


672 


107 


12 


1497 


1664 


1029 10 


1891 


413 


141 


733 


439 


50 


2070 


2007 


804 10 


1892 


328 


57 


773 


268 


17 


1661 1 


1653 


907 15 6 


1893 



icluding LiidicG. 



§ Fellows of the American Association were admitted as Eon. Members for thisMeetinp. 



Ixxiv 



DEPORT 1893. 



REPORT OF THE COUNCIL. 



Beport of the Council for the year 1892-93, presented to the General 
Committee at Nottingham on Wednesday, September 13, 1893. 

The Council have received reports from the General Treasurer during 
the past year, and his account from July 1, 1892, to June 30, 1893, 
which has been audited, will be presented to the General Committee. 

Invitations to hold the Annual Meeting of the Association at Bourne- 
month or at Ipswich in 1895 have been received, and will be brought 
before the General Committee on Monday ; communications in reference 
to future Meetings of the Association have been received from Liverpool 
and Toronto. 

The Council have been informed that Mr. Arthur P. Johnson, one of 
the Local Secretaries, having accepted an official appointment in London, 
was obliged to resign his office, and that Mr. Arthur Williams has 
allowed himself to be nominated Secretary in his place. 

The Council have elected the following Foreign Men of Science, who 
attended the Meeting at Edinburgh, Corresponding Members : — 



Dr. Svante Arrhenius, Stockholm. 
Prof. Marcel Bertrand, Paris. 
Prof. F. Blfving, Helsingfors. 
Prof. L6o Errera, Brussels. 
Prof. G. Fritsch, Berlin. 



Mr. D. C. Gilman, Baltimore. 
Dr. C. E. Guillaume, Sevres. 
Prof. Rosenthal, Erlangen. 
Dr. Maurits Snellen, Utrecht. 



Resolutions referred to the Council for consideration and action if 
desirable : — 

(«) That the Council be requested to draw the attention of the Local Govern- 
ment Board to the desirability of the publication of the ' Report on the 
Examination into Deviations from the Normal amongst 50,000 Children in 
various Schools,' which has been presented to that Board by the British 
Medical Association. 

The Council resolved that a letter should be addressed to the President 
of the Local Government Board in the sense of this resolution : — 

Bbitish Association foe the Advancement op Science, 
Burlington House, London, W., 
December 19, 1892. 
The Right Hon. Henry Fowler, M.P., 

President of the Local Government Board. 

SiB, — The Anthropological and Biological Sections of the British Association for 

the Advancement of Science at their last meeting had brought before them the 

question of the Deviation from the Normal in Children in Elementary Schools, in 

connection with a Report drawn up by a Committee of the International Congress! 



REPORT OF THE COUNCIL. IxXV 

of Hygiene and Demography. It is understood that this Report has been presented 
to your Honourable Board by the British Medical Association. The British Associa- 
tion for the Advancement of Science, having regard to the importance of the question 
from a physiological point of view, as bearing upon the health of the community, 
passed a resolution requesting the Council of the Association to urge upon your 
Honourable Board the importance of publishing the Report above referred to, and 
the Association appointed a committee of their body to continue the further collection 
of statistics on the subject. 

I am therefore instructed by the Council to submit this recommendation, and to 
urge upon your Honourable Board the importance of the publication of this Report. 
I have the honour to be. Sir, your most obedient servant, 

ARCH. GEIKIE, President. 

The following reply was received on January 29 : — 

Local Government Board, Whitehall, S.W., 

January 28, 1893. 
Sir, — I am directed by the Local Government Board to acknowledge the receipt 
of your letter of the 19th ultimo, in which, on behalf of the Council of the British 
Association for the Advancement of Science, you urge upon the Board the importance 
of publishing the Report made on behalf of the British Medical Association by Dr. 
F. Warner on the Physical and Mental condition of 50,000 school children ; and to 
state that, while the Board fully recognise the value of the Report in question, they 
do not consider that they can undertake its publication. 

I am, Sir, your obedient servant, 

WM. E. KNOLLTS, Assistant Secreta/ry. 
Sir A. Geikie, 
President of the British Association for the Advancement of Science. 

(J) That the Council be requested to draw the attention of Her Majesty's 
Government to the Anthropometric method for the measurement of criminals, 
which is successfully in operation in France, Austria, and other Continental 
countries, and which has been found effective in the identification of 
habitual criminals, and consequently in the prevention and repression of 
crime. 

Council resolved that — 

Considering the recognised need of a better system of identification than is now 
in use in the United Kingdom and its Dependencies, whether for detecting 
deserters who apply for re-enlistment, or old offenders among those who are 
accused of crime, or for the prevention of personation, more especially 
among the illiterate, the Council of the British Association express their 
opinion that the Anthropometric methods in use in France and elsewhere 
deserves serious inquiry as to their efficiency, the cost of their maintenance, 
their general utility, and the propriety of introducing them, or any modifi- 
cation of them, into the Criminal Department of the Home Office, into the 
Recruiting Departments of the Army and Navy, or into Indian and Colonial 
Administration. 

Copies of this resolution and the following letter, signed by the President 
of the Association, were sent to the Secretaries of State for the Home 
Department, Array, Navy, India, and the Colonies : — 

June 1893. 
The Council of the British Association for the Advancement of Science having 
had under consideration the question of the best means for the identification of 
criminals, I am desired to lay before you the inclosed Report on this subject which 
the Council have adopted. Good evidence has been submitted to them that anthro- 
pometric methods, that is to say, the classification of measurements of bodily marks 
and of finger prints, afford a ready and inexpensive method of identification, and the 
progress made abroad in organising these methods justifies the hope that the subject 
may be deemed worthy of serious inquiry by the various Government Departments 
of this country. 



IXX Vi REPOBT — 1893. 

It is believed by the Council that the facilities at the command of these Depart- 
ments would enable a more correct judgment to be formed, both of the real value to 
the nation of improved means of identification and of the efficiency and costs of the 
methods above referred to, than could be obtained through the exertions, however 
zealous, of private persons. 

I therefore venture to hope that you may be willing that inquiries be instituted 
in the Department over which you preside. The Council will be ready to furnish 
any information at their disposal which may be desired. 

I have the honour to be, your obedient servant, 

ARCH. GEIKIE, Presidmt. 

The following replies have been received : — • 

War Office, Pall Mall, S.W., Jutie 28, 1893. 
Sir, — I am directed by Mr. Secretary Campbell-Bannerman to acknowledge the 
receipt of your letter of the 19th instant, forwarding a copy of a Eeport from the 
British Association for the Advancement of Science relative to the anthropometric 
method of identifying persons charged with crime. 

In reply, I am to acquaint you that the working of this system in France was not 
long since the subject of careful consideration on the part of the Secretary of State 
for War, who came to the conclusion that, although the sj'stem appeared to be ad- 
mirably adapted for the identification of criminals, it was not desirable it should be 
introduced into the British Army. 

I am, Sir, vour obedient servant, 

RALPH THOMPSON. 
The President, 
British Association for the Advancement of Science, 
Burlington House, W. 

India Office, Whitehall, S.W., July 11, 1893. 
Sir, — I am directed by the Secretary of State for India in Council to acknowledge 
the receipt of your letter of the 19th ultimo, and, in reply, to state that anthropometry 
according to the system invented by M. Bertillon has been introduced into India by 
the Government, and is now being tried there as an experiment. 

I am. Sir, j'our obedient servant, 

GEORGE W. E. RUSSELL. 
Sir Archibald Geikie, LL.D., F.R.S., President, 

British Association for the Advancement of Science, 
Burlington House. 

Admiealtt, August 5, 1893. 
Sir, — My Lords Commissioners of the Admiralty having had under consideration 
your letter of the 19th June last, on the subject of an improved mode of registration 
of physical measurements, kc, of persons entered into the Government services with 
a view to the identification of criminals, I am commanded by their Lordships to 
acquaint you that they are not prepared to introduce the Continental system of 
anthropological examination into the Naval Recruiting Department, as the present 
mode of noting the physical measurements of all persons who may be entered, together 
with any particular marks or scars, is deemed sufhcient for official purposes, so far 
as the identification of men is concerned, and that, as a rule, no difficulty arises in 
identifying deserters. 

I am, Sir, your obedient servant, 

EVAN MACGREGOR. 
Sir Archibald Geikie, LL.D., President, 

British Association for the Advancement of Science, 
Burlington House, W. 

(c) That the letter of Professor E. Wiedemann and the communications from 
the Committees of Sections B and C on the subject of the headings of 
Reports be referred to the Council. 

The Council resolved that the subject of a Report should be mentioned 
first, then the names of the Committee, and finally the titles of any 
Appendices. 



REPORT OF THE COUNCIL. 



Ixxvii 



The Council received an invitation from the University and Citizcus 
of Padua to appoint a delegate to attend the celebration of the tliioo 
hundredth anniversary of the appointment of Galileo to the Chair ot' 
Mathematics in the University of Padua, and in accordance with tliis 
request they appointed Mr. Ludwig Mond, F.R.S., to join in tUii* 
celebration. 

The Report of the corresponding Societies Committee has been re- 
ceived, and will be presented to the General Committee. 

The Corresponding Societies Committee, consisting of Mr. Francis 
Galton, Professor R. Meldola, Sir Douglas Galton, Sir Rawson Rawson, 
Dr. J. G. Garson, Sir J. Evans, Mr. J. Hopkinson, Mr. W. Whitaker, 
Mr. G. J. Symons, Mr. W. Topley, Professor T. G. Bonney, Mr. T. V. 
Holmes, Mr. E. B. Poulton, Mr. Cuthbert Peek, and the Rev. Canon 
Tristram, is hereby nominated for reappointment by the General Com- 
mittee. 

The Council nominate Dr. J. G. Garson, Chairman, Mr. G. J. Symons, 
F.R.S., Vice-Chairman, and Mr. T. V. Holmes, P.G.S., Secretary, to the 
Conference of Delegates of CorrespondiDg Societies to be held during 
the Meeting at Nottingham. 

An Index to the Reports of the Association from 1831 to 1860 
was published in 1864, of which copies are still to be obtained. Mr. 
Griffith has for some time been engaged on the ai'duous task of preparing 
an Index to the Reports from 1861 to 1890. 

The Council are glad to be able to announce that this new Index is 
now in type, and will be on sale at a cost of 15s. within a few weeks. 

It is evident that the utility of the Annual Reports will be much 
increased, now that their contents are made more readily accessible by 
means of a good index. 

In accordance with the regulations the retiring Members of the- 
Council will be — 



Sir M. B. Grant-Duflf. 
Prof. G. F. FitzGerald. 
Prof. Koberts-Austen. 



Prof. Schafer. 
Prof. Schuster. 



The Council recommend the re-election of the other ordinary Members 
of the Council, with the addition of the gentlemen whose names are dis- 
tinguished by an asterisk in the following list : — 

Meldola, Prof. R., F.R.S. 
Preece, W. H., Esq., F.R.S. 
Ramsay, Prof. W., F.R.S. 
Eeinold, Prof. A. W., F.R.S. 
•Reynolds, Prof. J. Emerson, M.D., F.R.S. 
Sidgwick, Prof. H., M.A. 
Symons, G. J., Esq., F.R.S. 
♦Thomson, Prof. J. J., M.A., F.R.S. 
Unwin, Prof. W. C, F.R.S. 
Ward, Prof. Marshall, F.R.S. 
Whitaker, W., Esq., F.R.S. 
Woodward, Dr. H., F.R.S. 



Anderson, Dr. W., F.R.S. 

Ayrton, Prof. W. E., F.R.S. 

Baker, Sir B., K.C.M.G., F.R.S. 

Ball, Sir R. S., F.R.S. 

*Boys, Prof. C. Vernon, F.R.S. 

Edgeworth, Prof., M.A. 

Evans, Sir J., K.C.B., F.R.S. 

Glazebrook, R. T., Esq., F.R.S. 

Green, Prof. A. H., F.R.S. 

*Horsley, Prof. Victor, F.R.S. 

Liveing, Prof. G. D., F.R.S. 

Lodge, Prof. Oliver J., F.R.S. 

*Markham, Clements R., Esq., C.B , F.R.S. 



Ixxviii 



REPORT — 1893. 



Committees appointed by the G-eneral Committee at the 
Nottingham Meeting in September 1893. 

1. Receiving Grants of Money. 



Subject for Investigation or Purpose 



Making Experiments for improv- 
ing the Construction of Practical 
Standards for use in Electrical 
Measurements. 



Members of the Committee 



The Application of Photography 
to the Elucidation of Meteoro- 
logical Phenomena. 

[Last year's grant renewed.] 

For Calculating Tables of certain 
Mathematical Functions, and, 
if necessary, for taking steps to 
carry out the Calculations, and 
to publish the results in an 
accessible form. 



Considering the best Methods of 
Eecording the Direct Intensity 
of Solar Radiation. 



Chairman. — Professor G. Carey 
Foster. 

Secretary. — Mr. R. T. Glazebrook. 

Lord Kelvin, Professors W. E. 
Ayrton, J. Perry, W. G. Adams, 
and Oliver J. Lodge, Lord Ray- 
leigh. Dr. John Hopkinson, Dr. 
A. Muirhead, Messrs. W. H. 
Preece and Herbert Taylor, 
Professors J. D. Everett and A. 
Schuster, Dr. J. A. Fleming, 
Professors G. F. FitzGerald, 
G. Chrystal, and J. J. Thomson, 
Mr. W. N. Shaw, Dr. J. T. 
Bottomley, Rev. T. C. Fitz- 
patrick. Professor J. Viriamu 
Jones, Dr. G. Johnstone Stonej', 
Professor S. P. Thompson, and 
Mr. G. Forbes. 

Chairman. — Mr. G. J. Symons. 
Secretary. — Mr. A. W. Clayden. 
Professor R. Meldola and Mr. John 
Hopkinson. 

Chairman. — Lord Rayleigh. 
Secretary. — Professor A. Lodge. 
Lord Kelvin, Professor A. Caylej', 

Professor B. Price, Dr. J. W. 

L. Glaisher, Professor A. G. 

Greenhill, and Professor W. M. 

Hicks. 

Chairman. — Sir G. G. Stokes. 

Secretary. — Professor H. McLeod. 

Professor A. Schuster, Mr. G. John- 
stone Stoney, Sir H. E. Roscoe, 
Captain W. de W. Abney, Mr. C. 
Chree, Mr. G. J. Symons, and 
Mr. W. E. Wilson. 



Grants 



£ s. d. 
25 



10 



15 







\ 



COMMITTEES APPOINTED BT THE GENERAL COMMITTEE. 
1. jReceiving Grants of Money — continued. 



Ixxix 



Subject for lavestigation or Purpose 



To consider the establishment of 
a National Physical Laboratory 
for the more accurate deter- 
mination of Physical Constants, 
and for other Quantitative Re- 
search, and to confer with the 
Council of the Association. 



Preparing a new Series of Wave- 
length Tables of the Spectra of 
the Elements. 

[Last year's grant renewed.] 



To consider the best Method of 
establishing an International 
Standard for the Analysis of 
Iron and Steel. 

[Last year's grant partly renewed.] 



The Action of Light upon Dyed 

Colours. 
[Last J- ear's grant renewed.] 



Recording the Position, Height 
above the Sea, Lithological Cha- 
racters, Size, and Origin of 
the Erratic Blocks of England, 
Wales, and Ireland, reporting 
other matters of interest con- 
nected with the same, and tak- 
ing measures for their preserva- 
tion. 

The Description and Illustration 
of the Fossil Phyllopoda of the 
Palaeozoic Eocks. 



The Collection, Preservation, and 
Systematic Registration , of 
Photographs of Geological in- 
terest. 

[Last year's grant renewed.] 



Members of the Committee 




Chairman. — Professor Oliver J. 

Lodge. 
Secretary. — Mr. E. T. Glazebrook. 
Lord Kelvin, Lord Rayleigh, Sir 

H. B. Roscoe, Professors J. J. 

Thomson, A. W. Rucker, R. B. 

Clifton, G. F. FitzGerald, Carey 

Foster, J. Viriamu Jones, A. 

Schuster, and W. E. Ayrton. 

Cliairman. — Sir H. E. Roscoe. 
Secretary. — Dr. Marshall Watts. 
Mr. J. N. Lockyer, Professors J. 

Dewar, G. D. Liveing, A. 

Schuster, W. N. Hartley, and 

Wolcott Gibbs, and Captain 

Abney. 

Chairman. — Professor Roberts- 
Austen. 

Secretary. — Mr. Thomas Turner. 

Sir F. Abel, Messrs. E. Riley and 
J. Spiller, Professor J. W. Lang- 
ley, Mr. G. J. Snelus, and Pro- 
fessor W. A. Tilden. 

Chairman. — Professor T. E. Thorpe. 

Secretary .—YiolQssoT J. J. Hum- 
mel. 

Dr. W. H. Perkin, Prof. W. J. 
Russell, Captain Abney, Prof. W. 
Stroud, and Prof. E. Meldola. 

Chairman. — Professor E. Hull. 

Secretary. — Mr. P. F. Kendall. 

Professors W. Boyd Dawkins, T. 
McK. Hughes, T. G. Bonney, and 
J. Prestwich, Dr. H. W. Cross- 
key, Messrs. C. E. De Ranee, 
E. H. Tiddeman, J. W. Woodall, 
and Prof. L. C. Miall. 



Chairman.— Raw Prof. T. Wilt- 
shire. 
Secretary. — Professor T. E. Jones. 
Dr. H. Woodward. 

Chairman. — Professor J. Geikie. 

Secretary. — Mr. O. W. Jeffs. 

Prof. T. G. Bonney, Prof. Boyd 
Dawkins, Dr. V. Ball, Dr. T. 
Anderson, and Messrs. A. S. 
Reid, E. J. Garwood, W. Gray, 
H. B. Woodward, J. E. Bedford, 
R. Kidston, W. W. Watts, E. H. 
Tiddeman, and J. J. H. Teall. 



X J. rf. 
5 



10 



15 







15 



5 



10 



Ixxx 



REPOKT 1893. 

1. Reeeivitig Grants of Mancy — continued. 




To investigate the character of 
the high-level shell-bearing de- 
posits at Clava, Chapelhall, and 
other localities. 



The Investigation of the Eurj'- 
pterid-bearing Deposits of the 
Pentland Hills. 

To open further Sections in the 
neighbourhood of Stonesfield in 
order to show the relationship 
of the ' Stonesfield Slate ' to 
the underlying and overlying 
strata. 

Considering the advisability and 
possibility of establishing in 
other parts of the country Ob- 
servations upon the Prevalence 
of Earth Tremors similar to 
those now being made in Dur- 
ham in connection with coal- 
mine explosions. 



To explore the Calf Hole Cave, at 
the Heights, Skyrethorne, near 
Skipton. 



Occupation of a Table at the 
Zoological Station at Naples, 
to enable Mr. E. S. Moore to 
investigate the origin of the 
Eeproductive Organs in various 
types of fishes, &c., and to en- 
able Mr. E. J. Allen to continue 
his researches on the Decapod 
Crustacea. 

To enable Dr. S. J. Hickson to in- 
vestigate the development of 
Alcyoniwni at the Laboratory of 
the Marine Biological Associa- 
tion, Plymouth. 



Members of the Committee 



Chairman. — Mr. J. Home. 
Secretanj. — Mr. Dugald Bell. 
Messrs. J. Eraser, P. F. Kendall, 

J. F. Jamieson, and David 

Robertson. 

Chairman. — Dr. R. H. Traquair. 
Secretary. — Mr. M. Laurie. 
Professor T. Rupert Jones. 

Chairman. — Mr. H. B. Woodward. 
Secretary. — Mr. E. A. Walford. 
Professor A. H. Green, Dr. H. 
Woodward, and Mr. J. Windoes. 



Chairman. — l\Ir. G. J. S3'mons. 

Secretary .—Islr . C. Davison. 

Sir F. J. Bramwell, Mr. E. A. 
Cowper, Professor G. H. Darwin, 
Professor J. A. Ewing, Mr. Isaac 
Roberts, Mr. Thomas Gray, Sir 
John Evans, Professor J. Prest- 
wich, Professor B. Hull, Pro- 
fessor G. A. Lebour, Professor 
R. Meldola, Professor J. W. 
Judd, Mr. M. Walton Brown, 
Mr. J. Glaisher, Professor C. 
G. Knott, Professor J. H. 
Poynting, and Mr. Horace 
Darwin. 

« 

CJuiirman. — Mr. R. H. Tiddeman. 

Secretary. — Rev. E. Jones. 

Professor W. Boyd Dawkins, Pro- 
fessor L. C. Miall, Mr. P. F. 
Kendall, Mr. A. Birtwhistle, 
and Mr. J. J. Wilkinson. 

Chairman.— Jix. P. L. Sclater, 
Secretary. — Mr. Percy Sladen. 
Professor Ray Lankester, Pro- 
fessor J. Cossar Ewart, Pro- 
fessor M. Foster, Professor A. 
Milnes Marshall, and Mr. A. 
Sedgwick. 



Chairman. — Professor E. Eay 

Lankester. 
Secretary. — Mr. G. C. Bourne. 
Professor M. Foster and Professor 

S. H. Vines. 








25 



50 



5 



100 



15 



COMMITTEES APPOINTED BY THE GENERAL COMMITTEE. 
1. Reeeielng Grants of Money — continued. 



Ixxxi 



Subject for Investigation or Purpose 


Members of the Committee 


Grants 


To report on the present state of 


CJiairman. — Professor A. Newtcn. 


100 


s. d. 



our Knowledge of the Zoology 


Secretary.— Dr. Da^^d Sharp. 






of the Sandwich Islands, and to 


Dr. W. T. Blanford, Dr. S. J. Hick- 






take steps to investigate ascer- 


son, Professor Riley, Mr. 0. Sal- 






tained deficiencies in the Fauna, 


vin. Dr. P. L. Sclater, and Mr. 






with power to co-operate with 


Edgar A. Smith. 






the Committee appointed for 








the purpose by the Royal Society, 








and to avail themselves of such 








assistance in their investiga- 








tions as may be ofEered by the 








Hawaiian Government. 








The Marine Zoology of the Irish 


Chairman. — Professor W. A. Herd- 


40 





Sea. 


man. 








Secretary. — Mr. I. C. Thompson. 








Professor A. C. Haddon, Professor 








G. B. Howes, Mr. W. E. Hoyle, 








and Mr. A. 0. Walker. 






The Structure and Function of 


Chairman. — Professor E. A. Schii- 


10 





the Mammalian Heart. 


fer. 
Secretary. — Mr. Stanley Kent. 
Professor Sherrington. 






Climatology and Hydrography of 


Chairman. — Mr. E. G. Eavenstein. 


10 





Tropical Africa. 


Secretary.— T)!. H. R. Mill. 
Mr. G. J. Symons and Mr. Bald- 
win Latham. 






Geographical, Meteorological, and 


Cloairman. — Mr. Clements R. 


50 





Natural History observations in 


Markham. 






South Georgia or other Ant- 


Secretary.— Bt. H. R. Mill. 






arctic Island. 


Mr. J. Y. Buchanan and Mr. H. 
0. Forbes. 






Exploration of Hadramaut, 


Chairman. — Mr. H. Seebohm. 


30 





Arabia. 


Secretary. — Mr. J. Theodore Bent. 

Mr. E. G. Ravenstein, Dr. J. G. 

Garson, and Mr. G. W. Bloxam. 






The Methods of Economic Train- 


Chairman. — Professor W. Cun- 


10 





ing adopted in this and other 


ingham. 






countries. 


Secretary. — Professor E. C. K. 
Gonner. 

Professor F. T. Edgeworth, Pro- 
fessor H. S. Foxwell, Mr. H. 
Higgs, Mr. L. L. Price, and 
Professor J. S. Nicholson. 






For carrying on the Work of the 


Chairman. — Sir W. H. Flower. 


5 





Anthropometric Laboratory. 


Secretary. — Dr. J. G. Garson. 

Mr. G. W. Bloxam, Dr. Wilberforce 
Smith, Professor A. C. Haddon, 
and Professor B. C. A. AVindle. 







1S93, 



Ixxxii 



REPORT — 1893. 



1. Receiving Grants of Money — continued. 



Subject for Investigation or Purpose 



To organise an Ethnographical 
Survey of the United Kingdom. 



The Lake Village at Glastonbury. 



Anthropometric Measurements in 
Schools. 



To co-operate with the Committee 
appointed by the International 
Congress of Hygiene and De- 
mography in the investigation 
of the Mental and Physical Con- 
dition of Children. 

Corresponding Societies Com- 
mittee. 



Members of the Committee 



Cluiirinan. — Mr. E. W. Brabrook. 

Secretary. — Mr. G. \V. Bloxam. 

Mr. Francis Gallon, Dr. J. G. 
Garson, Professor A. C. Haddon, 
Dr. Joseph Anderson, Mr. J. 
Romilly Allen, Dr. J. Beddoe, 
Professor D. J. Cunningham, 
Professor W. Boyd Dawkins, 
Mr. Arthur Evans, Mr. E. Sidney 
Hartland, Sir H. Howorth, Pro- 
fessor R. Meldola, General Pitt- 
Rivers, and Mr. E. G. Raven- 
stein. 

Chairman. — Dr. R. Munro. 

Secretary. — Mr. A. Bulleid. 

Professor W. Boyd Dawkins, Gen- 
eral Pitt-Rivers, and Sir John 
Evans. 

Chairman. — Professor J. Cleland. 

Secretary. — Professor B. Windle. 

Mr. G. W. Bloxam, Mr. E. W. 
Brabrook, Dr. J. G. Garson, and 
Professor A. Macalister. 

Chairniaii. — Sir Douglas Gallon. 

Secretary. — Dr. Francis Warner. 

Mr. G. W. Bloxam, Mr. E. W. Bra- 
brook, Dr. J. G. Garson, and 
Dr. W. Wilberforce Smith. 



Chairman. — Professor R. Meldola. 

Secretary. — Mr. T. V. Holmes. 

Mr. Francis Gallon, Sir Douglas 
Gallon, Sir Rawson Rawson, Mr. 
G. J. Symons, Dr. J. G. Garson, 
Sir John Evans, Mr. J. Hopkin- 
son. Professor T. G. Bonney, Mr. 
W. Whitaker, Mr. W. Tople)', 
Professor E. B. Poullon, Mr. 
Culhberl Peek, and Rev. Canon 
H. B. Tristram. 



Grants 



£ s. d. 
10 



40 







20 



25 



2. Not receiving Chants of Money. 



Subject for Investigation or Purpose 


Members of the Committee 


Co-operating with the Scottish Meteoro- 
logical Society in making Meteoro- 
logical Observations on Ben Nevis. 


Chairman.— Ijord. McLaren. 
Secretary.— Yioiessor Crum Brown. 
Mr. John Murray, Dr. A. Buchan, Pro- 
fessor R. Copeland, and Hon. R. Aber- 

cromby. 



COMMITTEES APPOINTED BY THE GENERAL COMMITTEE. Ixxxiii 
2. Not receiring Grants of Money — continued. 



Subject for Investigation or Purpose 



The various Phenomena connected with 
the recalescent Points in Iron and 
other Metals. 



The Volcanic and Seismological Phe- 
nomena of Japan. 



To investigate the Phenomena accom- 
panying the Discharge of Electricit}' 
from Points. 



Comparing and Reducing Magnetic Ob- 
servations. 



The Collection and Identification of 
Meteoric Dust. 



The Rate of Increase of Underground 
Temperature downwards in various 
Localities of dry Land and under 
Water. 



To co-operate with Dr. Kerr in 
researches on Electro-optics. 



his 



That Mr. W. N. Shaw and the Rev. T. 
C. Fitzpatrick be requested to con- 
tinue their Report on the present state 
of our Knowledge in Electrolysis and 
Electro-chemistry. 



Members of the Committee 



Chairman. — Professor G. F. FitzGerald. 
Secretary. — Professor W. F. Barrett. 
Dr. John Hopkinson, Mr. R. A. Hadfield, 

Mr. F. T. Trouton, Professor W. C. 

Roberts- Austen, and Mr. H. F. Newall. 



Chairman. — Lord Kelvin. 

Secretary. — Professor J. Milne. 

Professor W. G. Adams, Mr. J. T. Bottom- 
ley, Professor A. H. Green, and Profes- 
sor C. G. Knott. 



Chairman. — Professor Oliver J. Lodge. 
Secretary. — Mr. A. P. Chattock. 
Professor Carey Foster. 

Chairman. — Professor W. G. Adams. 

Secretary. — Professor W. G. Adams. 

Lord Kelvin, Professor G. H. Darwin, 
Professor G. Chrystal, Mr. C. H. Cai'p- 
mael, Professor A. Schuster, Mr. C. 
Chree, Captain E. W. Creak, the Astro- 
nomer Royal, Mr. William Ellis, and 
Professor A. W. Riicker. 

Cliairman. — Mr. John Murray. 
Secretary. — Mr. John Blurray. 
Professor A. Schuster, Lord Kelvin, the 

Abbe Renard, Dr. A. Buchan, the Hon. 

R. Abercromby, Dr. M. Grabham, and 

Mr. John Aitken. 

Chairman. — Professor J. D. Everett. 

Secretary. — Professor J. D. Everett. 

Professor Lord Kelvin, Mr. G. J. Symons, 
Sir A. Geikie, Mr. J. Glaisher, Mr. \V. 
Pengelly, Professor Edward Hull, Pro- 
fessor J. Prestwich, Dr. C. Le Neve 
Foster, Professor A. S. Herschel, Pro- 
fessor G. A. Lebour, Mr. A. B. Wynne, 
Mr. W. Galloway, Mr. Joseph Dickin- 
son, Mr. G. F. Deacon, Mr. E. Wetliered, 
Mr. A. Strahan, and Professor Michie 
Smith. 

Cliairman. — Dr. John Kerr. 
Secretary. — Mr. R. T. Glazebrook. 
Lord Kelvin and Professor A. ^^^ Riicker. 



Ixxxiv 



REPOBT 1893. 

2. Not receiving Grants of Money — continued. 



Subject for Investigation or Purpose 



That Di-. J. Larmor and Mr, G. H. Bryan 
be requested to continue their Report 
on the present state of our Know- 
ledge in Thermodynamics, specially 
with regard to the Second Law. 

The Properties of Solutions . 



Reporting on the Bibliography of Solu- 
tion. 



The Continuation of the Bibliography 
of Spectroscopj'. 



The Action of Light on the Hydracids 
of the Halogens in presence of 
Oxygen. 



To inquire into the Proximate Chemical 
Constituents of the various kinds of 
Coal. 



To report on recent Liquirics into the 
History of Chemistry. 

The Investigation of the direct Forma- 
tion of Haloids from pure JIaterials. 



Isomeric Naphthalene Derivatives 



The Electrolytic Methods of Quanti- 
tative Analysis. 



The Rate of Erosion of the Sea-coasts of 
England and Wale?, and the Influence 
of the Artificial Abstraction of 
Shingle or other material in that 
action. 



Members of the Committee 



Cltairmnn. — Professor W. A. Tilden. 
Secretary. — Dr. W. W. J. Nicol. 
Profe.ssor W. Ramsay. 

Chairman. — Professor W. A. Tilden. 
Secretary. — Dr. \V. W. J. Nicol. 
Professors McLeod, Pickering, Ramsay, 
and Young. 

Chairman. — Professor H. McLeod. 
Secretary. — Professor Roberts- Austen. 
Mr. H. G. Madan and Mr. D. H. Nagel. 



Chairman. — Dr. W. J. Russell. 
Secretary. — Dr. A. Richardson. 
Captain Abney and Professors 
Hartley and W. Bamsaj'. 



Noel 



Chairman. — Sir I. Lowthian Bell. 
Secretary.— Vroie^-sor P.Phillips Bedson. 
Mr. Ludwig Mond, Professors Vivian B. 

Lewes and E. Hull, and Messrs. J. W. 

Thomas and H. Bauerman. 

Chairman. — Professor H. E. Armstrong. 
Secretary. — Professor Jolin Ferguson. 

Chairman. — Professor H. E. Armstrong. 
Secretari/. — Mr. W. A. Shenstone. 
Professor W. R. Dunstan and Mr. C. H. 
Bothamlej-. 

Chairman. — Professor W. A. Tilden. 
Secretary.— TioicssoT H. E. Armstrong. 

Chairman. — Professor J. Emerson Rey- 
nolds. 

Secretary. — Dr. C. A. Kohn. 

Professor Fraukland. Professor F. Clowes,. 
Dr. Hugh Marshall, Mr. A. E. Fletcher, 
Mr. D. H Nagel, Mr. T. Turner, and 
Mr. — Coleman. 

Chairman. — Mr. W. Whitaker. 

Secretaries. — Messrs. C. E. De Ranee and 
W. Topley. 

Messrs. J. B. Redman and J. W. Woodall, 
Maj.-Gen. Sir A. Clarke, Admiral Sir E. 
Ommanney, Capt. Sir G. Nares, Capt. 
J. Parsons, Capt. W. J. L. Wharton, 
Professor J. Prestwich, Mr. Edward 
Easton, Mr. J. S. Valentine, and Pro- 
fessor L. F. Vernon Harcourt. 



COMMITTEES APPOINTED BY THE GENEBAL COMMITTEE. 

2. Not receiving Grants of Money — continued. 



Ixxxv 



Subject for Investigation or Purpose 



Members of the Committee 



The Volcanic Phenomena of Vesuvius 
and its neighbourhood. 



To consider the best Methods for the 
Kegistration of all Type Specimens 
of Fossils in the British Isles, and 
to report on the same. 

To complete the Investigation of the 
Cave at Elbolton, near Skipton, in 
order to ascertain whether the re- 
mains of Palasolithic Man occur in 
the Lower Cave Earth. 

To carry on Excavations at Oldbury 
Hill, near Ightham, in order to ascer- 
tain the existence or otherwise of 
Eock Shelters at that spot. 

The Circulation of the Underground 
Waters in the Permeable Formations 
of England, and the Quality and 
Quantity of the Waters supplied to 
various Towns and Districts from 
these Formations. And that a Digest 
of the eighteen Keports should be 
prepared by the Committee, and sold 
in a separate form. 

To consider a project for investigating 
the Structure of a Coral Eeef by 
Boring and Sounding. 



For improving and experimenting with 
a Deep-sea Tow-net for opening and 
closing under water. 

To report on the present state of our 
Knowledge of the Zoology and Botany 
of the West India Islands, and to take 
steps to investigate ascertained de- 
ficiencies in the Fauna and Flora. 

To make a Digest of the Observations on 
the Migration of Birds at Lighthouses 
and Light-vessels. 



Cliairman. — Mr. H. Bauerman. 
Seoretar}/. — Dr. H. J. Johnston-Lavis. 
Messrs. F. W. Kudler and J. J. H. Teall. 

Chairman. — Dr. H. Woodward. 
Secretary. — Mr. A. Smith Woodward. 
Rev. G. F. Whidborne, Mr. R. Kidston, 
and Mr. J. E. Marr. 

Cliairman. — Mr. R. H. Tiddeman. 
Secretary. — Rev. E. Jones. 
Sir J. Evans, Dr. J. (i. Garson, Mr. W. 
Pengelly, and Mr. J. J. Wilkinson. 



Cliairman. — Sir J. Evans. 
Secretary. — Mr. B. Harrison. 
Professor J. Prestwich and Professor H. 
G. Seeley. 

Cliairman. — Professor E. Hull. 

Secretary. — Mr. C. E. De Ranee. 

Dr. H. W. Crosskey, Sir D. Galton, Pro- 
fessor J. Prestwich, and Messrs. J. 
Glaisher, P. F. Kendall, E. B. Marten, 
G. H. Morton, W. Pengelly, I. Roberts, 
T. S. Stooke, G. J. Symons, W. Topley, 

C. Tylden- Wright, E. Wethered, and 
W. Whitaker. 

Cliairman. — Professor T. G. Bonney. 

Secretary. — Professor W. J. Sollas. 

Sir Archibald Geikie, Professors A. H. 
Green, J. W. Judd, C. Lapworth, A. C. 
Haddon, Boyd Dawkins, G. H. Dar- 
win, and A. Stewart, Captain W. J. L. 
Wharton, Drs. H. Hicks, J. Murray, 
and H. B. Guppy, Messrs. F. Darwin, 
H. O. 'Forbes, G. C. Bourne, S. Hickson, 
A. R. Binnie, and J. W. Gregory, and 
Hon. P. Fawcett. 

Chairman. — Professor A. C. Haddon. 
Secretary. — Mr. W. E. Hoyle. 
Professor W. A. Herdman. 

Chairman. — Dr. P. L. Sclater. 

Secretary. — Mr. G. Murray. 

Mr. W. Carruthers, Dr. A. C. Gunther, Dr. 

D. Sharp, Mr. F. Du Cane Godman, 
and Professor A. Newton. 

Chairman. — Professor A. Newton. 
Secretary. — Mr. John Cordeaux. 
Mr. John A. Harvie-Brown, Mr. R. M. 
Barrington, Mr. W. E. Clarke, and Rev. 

E. P. Knubley. 



Ixxxvi 



BEPORT — 1893. 
2. Not rccekivg Grants of Money — continued. 




For taking steps to establish a Botanical 
Laboratory at Peradeniya, Ceylon. 



To consider proposals for the Legislative 
Protection of Wild Birds' Eggs. 



The Collection of Facts and Statistics 
bearing on tlie following Qnostions: — 

1. The inHnence of previoiis ferti- 

lisation of the female on her 
subsequent ofl'spring. 

2. The effect of material impres- 

sions during pregnancy on the 
offspring. 
The Committee are authorised to 
communicate with the Councils of the 
British Medical Society, the Koyal 
Agricultural Society, the Highland 
Agricultural Society, and the Royal 
Dublin Society, with the view to joint 
work. 

Compilation of an Index Generum et 
Specierum Animalium. 



Scottish Place-names 



The Teaching of Science in Elementary 
Schools. 



To report on Methods of determining 
the Drjne: s of Steam in boiler trials. 



Members of the Committee 



Chairman. — Professor M. Foster. 

Secretary. — Professor J. B. Farmer. 

Professor Bayley Balfour, Jlr. Thiselton- 
Dyer, Dr. H. Trimen, Professor Mar- 
shall Ward, Mr. W. CaiTuthers, Pro- 
fessor M. M. Hartog, Professor F. O. 
Bower, and Mr. W. Gardiner. 

Chairman.— Sir John Lubbock. 

Secretary. — Mr, H. E. Dresser. 

Mr. John Cordeaux, Mr. W. H. Hudson, 
Professor A. Newton, Mr. Howard 
Saunders, Mr. Thomas Henry Thomas, 
Canon Tristram, and Dr. C. T. Vachell. 

Chairman. — Dr. A. Eussel Wallace. 

Secretary. — Dr. James Clark. 

Dr. G. J. Komanes, Dr. S. J. Hickson, 

Professor E. A. Schiifer, and Dr. J. N. 

Langley. 



Chairmaji.—Sir \V. TL Flower. 

iSecretary. — Mr. W. Sclater. 

Dr. P. L. Sclater and Dr. H. Woodward. 



Chairman.— ^\T C. W. Wilson. 
Secretary. — Dr. J. Burgess. 
Mr. Coutts Trotter. 



Cliairman. — Dr. J. H. Gladstone. 

Secretary. — Professor H. E. Armstrong. 

Mr. S. Bourne, Dr. Crosskey, Mr. George 
Gladstone, Mr. J. Heywood, Sir J. 
Lubbock, Sir Philip Magnus, Professor 
N. Story Maskelyne, Sir H. E. Roscoc, 
Sir R. Temple, and Professor Silvanus P, 
Thompson. 



Cliairman. — Sir F. J. Bramwell. 

Secretary. — Professor W. C. Unwin. 

Professor T. H. Beare, Mr. Jeremiah 
Head, Professor A. P>. W. Kennedy, 
Profefsor Osborne Reynolds, and Mr. 
Mair Rumley. 



COMMITTEES APPOINTED BY THE GENERAL COMMITTEE. Ixxvii' 
2. Not receiving Grants of Money — continued. 



Subject for Investigation or Purpose 


Members of the Committee 


The Prehistoric and Ancient Eemains 
of Glamorganshire. 

To consider Uniformity in the Spelling 
of Barbaric and Savage Languages 
and Race Names. 

The Physical Characters, Languages, 
and Industrial and Social Condition 
of the North-Western Tribes of the 
Dominion of Canada, with power to 
utilise any portion of last year's grant 
that may remain after payment of 
expenses incurred. 


Cfiairma7i.—DT. C. T. Vachell. 

Secretary. — Mr. E. Seward. 

Lord Bute, Messrs. G. T, Clark, E. "W. 
Atkinson, Franklen G. Evans, James 
Bell, and T. H. Thomas, and Dr. J. 
G. G arson. 

Chairman. — Mr. F. Galton. 
Secretary. — Mr. C. E. Peek. 
Dr. E. B. Tylor, Professor A. C. Haddon, 
Mr. G. W. Bloxam, and Mr. Ling Roth. 

Chairman.— Dx. E. B. Tylor. 
Secretary. — Mr. G. W. Bloxam. 
Dr. G. M. Dawson, Mr. R. G. Haliburton, 
and Mr. H. Hale. 



Other Resolutions adopted hy the General Committee. 

That Dr. J. Larmor's paper entitled ' The Action of Magnetism on Light ; with a 
critical correlation of the various theories of Light-propagation ' be printed in extenso 
among the Reports. 

That Professor Percy Frankland's paper on ' Bacteriology in its relations to 
Chemical Science ' be printed in extenso among the Reports. 

That the paper by Mr. "W. Worby Beaumont on ' An Automatic Balance of Eeci - 
procating Mechanism ' be printed in exte?iso among the Reports. 

That at the next Meeting of the Association, and at such future Meetings as may 
seem to the Council desirable, there should be a separate Section for Physiology, 
Animal and Vegetable. 

That it is desirable that, for the purpose of securing co-ordinate action, a joint 
Organising Committee be appointed for the purpose of arranging provisionally the 
Proceedings of the Sections of Biology and Physiology. 



Resolutions referred to the Council for consideration, and action 

if desirable. 

That the recommendations regarding the times at which the Sections and Sec- 
tional Committees shall meet, which have been received from the Sectional Com- 
mittees, be referred to the Council. 

That the resolution received from the Committees of Sections C and G proposing 
a change in the rule relating to the appointment of Committees for special objects 
of Science be referred to the Council. 



Ixxxviii REPORT — 1893. 



s. 


d. 





















Synopsis of Grants of Money appropriated to Scientific Pur- 
poses by the General Committee at the Nottingham Meeting, 
September 1893. The Names of the Members entitled to call 
on the General Treasurer for the respective Grants are prefixed. 

Matliematics and Physics. 

£ 

♦Foster, Professor Carey — Electrical Standards 25 

*Symons, Mr. G.J. — Photographs of Meteorological Phenomena 

(renewed) 10 

*Ra3'leigb, Lord — Tables of Mathematical Functions 15 

*Stokes, Sir G. G. — Recording the Direct Intensity of Solar 

Radiation 15 

*Lodge, Professor 0. J. — National Physical Laboratory 5 

Chemistry and Mineralogy. 

*Roscoe, Sir H.— Wave-length Tables of the Spectra of the 

Elements (renewed) 10 

*Roberts-Austen, Professor — Analysis of Iron and Steel (re- 
newed) 15 

*Thorpe, Professor T. E. — Action of Light upon Dyed 

Colours 5 

Geology. 

*Hull, Professor E.— Erratic Blocks 15 

♦Wiltshire, Rev. T.— Fossil Phyllopoda 5 

*Geikie, Professor J. — Photographs of Geological Interest 

(renewed) 10 

*Horne, Mr. J.— Shell- bearing Deposits at Clava, Chapel- 
hall, &c 20 

♦Traquair, Dr. R. H.— Eurypterids of the Pentland Hills 5 

Woodward, Mr. H. B.— New Sections of Stonesfield Slate ... 25 

*Symons, Mr. G. J.— Observations on Earth Tremors 50 

Tidderaan, Mr. R. H.— Exploration of Calf Hole Cave 5 

Carried forward £235 

* Reappointed. 



SYNOPSIS OF GRANTS OF MONEY. Ixxxix 

£ 8. d. 

Brought forward 235 

Biology. 

♦Sclater, Dr. P. L.— Table at the Naples Zoological Station... 100 
*Lankester, Professor B. R. — Table at the Plymouth Biological 

Laboratory (renewed) 15 

♦Newton, Professor A. — Zoology of Sandwich Islands 100 

♦Herdman, Professor W. A. — Zoology of the Irish Sea 40 

Schafer, Professor B. A. — Structure and Function of the 

Mammalian Heart 10 

Geography. 

•Ravenstein, Mr. B. G. — Climatology and Hydrography of 

Tropical Africa 10 

Markham, Mr. Clements R. — Observations in South Georgia 50 

Seebohm, Mr. H. — Exploration in Arabia 30 

Economic Science and Statistics. 
*Cunningham, Professor W. — Methods of Economic Training 10 

A7ithropology. 

*Flower, Sir W. H. — Anthropometric Laboratory Statistics... 5 
*Brabrook, Mr. B. W. — Ethnographical Survey of United 

Kingdom 10 

Munro, Dr. R. — The Lake Village at Glastonbury 40 

Cleland, Professor J. — Anthropometrical Measurements in 

Schools 5 

*Galton, Sir D.— Mental and Physical Condition of Children 20 



*Garson, Dr. J. G. — Corresponding Societies Committee ... 25 

* Reappointed. 



£705 



The Annual Meeting in 1894. 
The Meeting at Oxford will commence on Wednesday, August 8, 

Place of Meeting in 1895. 
The Annual Meeting of the Association will be held at Ipswich, 



xc 



KEPonx — 1893. 



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



£ s. d. 



1834. 



Tide Discussions 20 

1835. 

Tide Discussions 62 

British Fossil Ichthyology ... 105 

£167 U 



1836. 

Tide Discussions 163 

British Fossil Ichthyology ... 105 
Thermometric Observations, 

&c 50 

Experiments on long-con- 
tinued Heat 17 1 

Eain-gauges 9 13 

Refraction 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 



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) ... 19 

Eailway Constants 41 

Bristol Tides 50 

Growth of Plants 75 

Mud in Rivers 3 

Education Committee 50 

Heart Experiments 5 

Land and Sea Level 267 

Steam- vessels 100 

Meteorological Committee ... 31 






1 
12 


6 

3 
8 

9 






10 
10 


6 


7 

5 



£932 2 2 



1839. 

Fossil Ichthyology 110 

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 103 

Railway Constants 28 

Land and Sea Level 274 

Steam-vessels' Engines 100 

Stars in Histoire Celeste 171 

Stars in Lacaille 11 

Stars in R.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 

Fossil Reptiles 118 

Mining: Statistics 50 



£1595 



1840. 

Bristol Tides 100 

Subterranean Temperature ... 13 

Heart Experiments 18 

Lungs Experiments 8 

Tide Discussions 50 

Land and Sea Level 6 

Stars (Histoire Celeste) 242 

Stars (Lacaille) 4 

Stars (Catalogue) 264 

Atmospheric Air 15 

Water on Iron 10 

Heat on Organic Bodies 7 

Meteorological Observations . 52 

Foreign Scientifi-c Memoirs... 112 

Working Population 1 00 

School Statistics 50 

Forms of Vessels 184 

Chemical and Electrical Phe- 
nomena 40 

Meteorological Observations 

at Plymouth 80 

Magnetical Observations 185 



s. 


d. 


2 





18 


6 


11 





4 


7 








7 


2 


1 


4 








18 


6 








16 


6 


10 











1 























7 


8 


2 


9 








11 











13 


6 


19 





13 











11 


1 


10 





15 











15 

















17 


6 


1 


6 














7 









13 9 



£1546 16 4 



1841. 

Observations on Waves 30 

Meteorology and Subterra- 
nean Temperature 8 8 

Actinometers 10 

Earthquake Shocks 17 7 

Acrid Poisons 6 

Veins and Absorbents 3 

Mud in Rivers 5 



GENERAL STATEMENT. 



XCl 



£ s. a. 

Marine Zoology 15 12 8 

Skeleton Maps 20 

Mountain Barometers 6 18 6 

Stars (Histoire C61este) 185 

Stars (Lacaille) 79 5 

Stars (Nomenclature of) 17 19 6 

Stars (Catalogue of) 40 

Water on Iron 50 

Meteorological Observations 

at Icivemess 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 Eed 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 



1842. 

Dynamometric Instruments . . 118 11 2 

Anoplura Britannice 52 12 

Tides at Bristol 69 8 

Gases on Light 30 14 7 

Chronometers 26 17 6 

Marine Zoology 15 

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 10 

British Belemnites 50 

Fossil Reptiles (publication 

of Report) 210 

Forms of Vessels 180 

Galvanic Experiments on 

Rocks 5 8 6 

Meteorological Experiments 

at Plymouth 68 

Constant Indicator and Dyna- 
mometric Instruments 90 

Force of Wind 10 

Light on Growth of Seeds ... 8 

Vital Statistics 50 

Vegetative Power of Seeds ... 8 1 11 

Questions on Human Race ... 7 9 

£1449 17 8 



1843. 
Revision of the Nomenclature 

of Stars ." 2 



£ s. d. 

Reduction of Stars, British 

Association Catalogue 25 

Anomalous Tides, Frith of 

Forth 120 

Hourly Meteorological Obser- 
vations at Kingussie and 
Inverness 77 12 8 

Meteorological Observations 

at Plymouth 55 0' 

Whewell's Meteorological Ane- 
mometer at Plymouth 10 , 

Meteorological Observations, 
Osier's Anemometer at Ply- 
mouth .'.. 20 

Reduction of Meteorological 

Observations 30 

Meteorological Instruments 

and Gratuities 39 6 

Construction of Anemometer 

at Inverness 56 12 2 

Magnetic Co-operation 10 8 10 

Meteorological Recorder for 

Kew Observatory 50 

Action of Gases on Light 18 16 1 

Establishment at Kew Ob- 
servatory, Wages, Repairs, 
Furniture, and Sundries ... 133 4 7 

Experiments by Captive Bal- 
loons 81 8 

Oxidation of the Rails of 

Railways 20 

Publication of Report on 

Fossil Reptiles 40 

Coloured Drawings of Rail- 
way Sections 147 18 3 

Registration of Earthquake 

Shocks .SO 

Report on Zoological Nomen- 
clature 10 

Uncovering Lower Red Sand- 
stone near Manchester 4 4 6 

Vegetative Power of Seeds ... 5 3 8 

Marine Testacea (Habits of) . 10 0, 

Marine Zoology 10 

Marine Zoology 2 14 11 

Preparation of Report on Brit- 
ish Fossil Mammalia 100 

Physiological Operations of 

Medicinal Agents 20 

Vital Statistics 36 5 8 

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 14 10 

Experiments on the Strength 

of Materials 60 

£1565 10 2 



XCll 



REPORT — 1893. 



£ 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 

Eevision of the Nomenclature 

of Stars 1842 2 9 6 

Maintaining the Establish- 
ment at Kew Observa- 
tory 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 

of the Lower Tertiary Strata 100 

Registering the Shocks of 

Earthquakes 1842 23 11 10 

Structure of Fossil Shells ... 20 

Eadiata and MoUusca of the 
^gean and Eed 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 Ships 100 

Inquiries into Asphyxia 10 

Investigations on the Internal 

Constitution of Metals 50 

Constant Indicator and Mo- 

rin's Instrmnent 184 2 10 

£981 12 8 



1845. 

Publication of the British As- 
sociation Catalogue of Stars 351 14 6 

Meteorological Observations 

at Inverness 30 18 11 

Magnetic and Meteorological 

Co-operation 16 16 8 

Meteorological Instruments 

at Edinburgh 18 11 9 

Eeduction of Anemometrical 

Observations at Plymouth 25 



£ 
Electrical Experiments at 

Kew Observatory 43 

Maintaining the Establish- 
ment at Kew Observatory 149 
For Kreil's Barometrograph 25 
Gases from Iron Furnaces... 50 

The Actinograph 15 

Microscopic Structure of 

Shells 20 

Exotic Anoplura 1843 10 

Vitality of Seeds 1843 2 

Vitality of Seeds 1844 7 

Marine Zoology of Cornwall . 10 
Physiological Action of Medi- 
cines 20 

Statistics of Sickness and 

Mortality in York 20 

Earthquake Shocks 184 3 15 

£831 



s, d. 

17 8 



5 






































7 




















14 



1846. 

British Association Catalogue 

of Stars 1844 211 

Fossil Fishes of the London 

Clay 100 

Computation of the Gaussian 

Constants for 1 829 5 

Maintaining the Establish- 
ment at Kew Observatory 146 

Strength of Materials 60 

Eesearches in Asphj'xia 6 

Examination of Fossil Shells 10 

Vitality of Seeds 1844 2 

Vitality of Seeds 1845 7 

Marine Zoology of Cornwall 10 

Marine Zoology of Britain ... 10 

Exotic Anoplura 1844 25 

Expenses attending Anemo- 
meters 11 

Anemometers' Repairs 2 

Atmospheric Waves 3 

Captive Balloons 1844 8 

Varieties of the Human Race 

1844 7 
Statistics of Sickness and 

Mortality in York 12 

£685 




8 
9 



15 

















16 


7 








16 


2 








15 


10 


12 


3 




















7 


6 


3 


6 


3 


3 


19 


8 


6 


3 









16 



1847. 

Computation of the Gaussian 

Constants for 1829 50 

Habits of Marine Animals ... 10 

Physiological Action of Medi- 
cines 20 

Marine Zoology of Cornwall 10 

Atmospheric Waves 6 9 3 

Vitality of Seeds 4 7 7 

Maintaining the Establish- 
ment at Kew Observatory 107 8 6 

£208 5 4 



GENERAL STATEMENT. 



XCUl 



£ i. d. 

1848. 
Maintaining the Establish- 
ment at Kew Observatory 171 15 11 

Atmospheric Waves 3 10 9 

Vitality of Seeds 9 15 

Completion of Catalogue of 

Stars 70 

On Colouring Matters 5 

On Growth of Plants 15 

£21?> 1 8 



1849. 

Electrical Observations at 

Kew Observatory 50 

Maintaining the Establish- 
ment at ditto 76 2 5 

Vitality of Seeds 5 8 1 

On Growth of Plants 5 

Eegistration of Periodical 

Phenomena 10 

Bill on Account of Anemo- 

metrical Observations 1-3 9 

£159 19 6 



1850. 
Maintaining the Establish- 
ment at Kew Observatory 255 18 
Transit of Earthquake Waves 50 

Periodical Phenomena 15 

Meteorological Instruments, 

Azores 25 

£345 18^0 



1851. 
Maintaining the Establish- 
ment at Kew Observatory 
(includes part 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 Piadiation .30 

Ethnological Inquiries 12 

Researches on Annelida 10 

£391 ir~7 



1852. 

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 1 



£ s. d. 
1853. 

Maintaining the Establish- 
ment at Kew Observatory 165 

Experiments on the Influence 

of Solar Radiation 15 

Researches on the British 

Annelida 10 

Dredging on the East Coast 
of Scotland 10 

Ethnological Queries 5 

£205 Q 

18.54. 

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 

£48(rT6~"4 



575 



1856. 
Maintaining the Establish- 
ment at Kew Observa- 
tory:— 

1854 £ 75 0\ 

1855 £500 0/ 

Strickland's Ornithological 

Synonyms 100 

Dredging and Dredging 

Forms 9 13 

Chemical Action of Light ... 20 

Strength of Iron Plates 10 

Registration of Periodical 

Phenomena 10 

Propagation of Salmon 10 

£73rT3 ~9 

1857. 

Maintaining the Establish- 
ment at Kew Observatory 350 

Earthquake Wave Experi- 
ments 40 

Dredging near Beli'flst 10 

Dredging on the West Coast 
of Scotland 10 



XCIV 



REPOBT — 1893. 



£ s. d. 

Investigations into the Mol- 

lusca of California 10 

Experiments on Flax 5 

Natural History of Mada- 
gascar 20 

llesearches on British Anne- 

■ lida 25 

Report 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^ 

1859. 
Maintaining the Establish- 
ment at Kew Observatory 500 

Dredging near Dublin 15 

Osteology of Birds 50 

, Irish Tunicata 5 

Manure Experiments 20 

British Medusidse 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 

£684 11 1 

1860. ''^^^~" 

Maintaining the Establish- 
ment at Kevr 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 



£ g. d. 
Chemico-mechanical Analysis 

of Rocks and Minerals 25 

Researches on the Growth of 

Plants 10 

Researches on the Solubility 

of Salts 30 

ResearchesontheConstituents 

of Manures 25 

Balance of Captive Balloon 

Accounts 1 13 6 

£766 ig^'G 



1861. 
Maintaining the Establish- 
ment at Kew Observatory.. 500 

Earthquake Experiments 25 

Dredging North and East 

Coasts of Scotland 23 

Dredging Committee : — 

1860 £50 \ _^ 

1861 £22 / '-^ 

Excavations at Dura Den 20 

Solubility of Salts 20 

Steam- vessel Performance ... 150 

Fossils of Lesmahagow 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 
00 
5 10 



1862. 

Maintaining the Establish- 
ment at Kew Observatory 500 

Patent Laws 21 6 

Molluscaof N.-W. of America 10 

Natural History by Mercantile 

Marine 5 

Tidal Observations 25 

Photoheliometer at Kew 40 

Photographic Pictures of the 

Sun 150 

Rocks of Donegal 25 

Dredging Durham and North- 
umberland 25 

Connection of Storms 20 

Dredging North-east Coast 

of Scotland 6 9 6 

Ravages of Teredo 3 11 

Standards of Electrical Re- 
sistance 50 

Railway Accidents 10 

Balloon Committee 200 

Dredging Dublin Bay 10 



QENBRAL STATEMENT. 



XCV 



£ i. 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 at Kew Observatory... 600 
Balloon Committee deficiency 70 
Balloon Ascents (other ex- 
penses) 25 

Entozoa 25 

Coal Fossils 20 

Herrings 20 

Granites of 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 

Electrical Construction and 

Distribution 40 

Luminous Meteors 17 

Kew Additional Buildings for 

Photoheliograph 100 

Thermo-electricity 15 

Analysis of Rocks 8 

Hydroida 10 

£1608 

































































3 10 


















































































3 10 



1864. 
Maintaining the Establish- 
ment at 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 ' 



£ ». d. 
Tidal Observations in the 

Humber 50 

Spectral Rays 45 

Luminous Meteors 20 

£1289 15 8 

1865. 
Maintaining the Establish- 
ment at 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 9 

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 

£1591 7~iO 

1866. 
Maintaining the Establish- 
ment at 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 50 

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 39 



XCVl 



REPOBl — 1893. 



£ «. d. 

Rigor Mortis 10 

Irish Annelida 15 

Catalogue of Crania 50 

Didine Birds of Mascarene 

Islands 50 

Typical Crania Researches ... 30 

Palestine Exploration Fund... 1 00 

£1750 13 4 

1867. 
Maintaining the Establish- 
ment at 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 

Alum 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 4 

North Greenland Fauna 75 

Do. Plant Beds 100 

Iron and Steel Manufacture... 25 

Patent Laws 30 

£1739 4 



1868. 
Maintaining the Establish- 
ment at Kew Observatory. . 600 

Lunar Committee 120 

Metrical Committee 50 

Zoological Record 100 

Kent's Hole Explorations ... 150 

Steamship Performances 100 

British Rainfall 50 

Luminous Meteors 50 

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 

Gre enland Explorations 1 00 

Fossil Flora 25 

Tidal Observations 100 

Underground Temperature ... 50 
Spectroscopic Investigations 

of Animal Substances 5 






































































































































£ 

Secondary Reptiles, &c 30 

British Marine Invertebrate 

Fauna 100 

£1940 

1869. 
Maintaining the Establish- 
ment at Kew Observatory. . 600 

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 Temperat ure ... 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 

Utilisation of Sewage 10 

Products of Digestion 10 

£ 1622 

1870. 
Maintaining the Establish- 
ment at Kew Observatory 600 

Metrical Committee 25 

Zoological Record 100 

Committee on Marine Faima 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, etc 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 
Kiltorcan Quarries Fossils ... 20 



«. d. 







o 
























c> 































































































(> 






























































































a 





















































a 



GENEBAL STATEMENT. 



xcvu 



£ 
Mountain Limestone Fossils 25 

Utilisation of Sewage 50 

Organic Chemical Compovmds 30 

Onny River Sediment 3 

Mechanical Equivalent of 

Heat 50^ 

£1572 



1872. 
Maintaining the Establish- 
ment at 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 Ant- 
agonism 10 

Essential Oils, Chemical Con- 
stitution, &c 40 

Mathematical Tables 50 

Thermal Conductivity of Me- 
tals 25 

£1285 

1893. 



s. 


d. 



























1871. 
Maintaining the Establish- 
ment at Kew Observatory 600 
Monthly Reports of Progi'ess 

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 2 6 

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 

















































£ «. d. 
1873. 

Zoological Record 100 

Chemistry Record 200 

Tidal Committee 400 

Sewage Committee 100 

Kent's Cavern Exploration... 150 

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 

£1685 

1874. 

Zoological Record 100 

Chemistry Record 100 

Mathematical Tables 100 

Elliptic Functions 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 

Mauritius Meteorological Re- 
search 100 

Magnetisation 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. 

Elliptic Functions 100 

Magnetisation of Iron 20 

British Rainfall 120 

Luminous Meteors 30 

Chemistry Record 100 

f 



xcvni 



REPORT — 1893. 



i, 3. d. 
Specific Volume of Liquids... 25 
Estimation of Potash and 

Phosphoric Acid 10 

Isometric Crcsols 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 Record 100 

Instructions for Travellers ... 20 

Intestinal Secretions 20 

Palestine Exploration 100 

£960 



1877. 
Liquid Carbonic Acids in 

Minerals 20 

Elliptic Functions 250 

Thermal Conductivity of 

Rocks 9 

Zoological Record 100 

Kent's Cavern 100 

Zoological Station at Naples 75 

Luminous Meteors 30 

Elasticity of Wires 100 

Dipterocarpae, Report on 20 



1876. 

Printing Mathematical Tables 159 4 2 

British Rainfall 100 

Ohm's Law 9 15 

Tide Calculating Machine ... 200 

Specific Volume of Liquids... 25 

Isomeric Cresols 10 

Action of Ethyl Bromobuty- 

rate on Ethyl Sodaceto- 

acetate 5 

Estimation of Potash and 

Phosphoric Acid 13 

Exploration of Victoria Cave, 

Settle 100 

Geological Record 100 

Kent's Cavern Exploration... 100 
Thermal Conductivities of 

Rocks 10 

Underground Waters 10 

Earthquakes in Scotland 1 10 

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 15 

Measuring Speed of Ships ... 10 
Effect of Propeller on turning 

of Steam-vessels 5 

£1092 4 2 















11 


7 







































£ g. d. 
Mechanical Equivalent of 

Heat 35 

Double Compounds of Cobalt 

and Nickel 8 

Underground Temperatures 50 

Settle 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 

Geological Record 100 

Anthropometric Committee 34 
Physiological Action of Phos- 
phoric Acid, &c 15 

£1128 9 7 



18 


















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 
Investigation of Underground 

Waters 15 

Transmission of Electrical 

Impulses through Nerve 

Structure 30 

Calculation of Factor Table 

for 4th Million 100 

Anthropometric Committee... 66 
Chemical Composition and 

Structure of less -known 

Alkaloids 25 

Exploration of Kent's Cavern 50 

Zoological Record 100 

Fermanagh Caves Exploration 15 
Thermal Conductivity of 

Rocks 4 16 6 

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. 



XCIX 



£ 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 25 

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 15 6 

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 14 9 

Atmospheric Electricity Ob- 
servations in Madeira 15 

Instrument for Detecting 

Fire-damp in Mines 22 

Instruments for Measuring 

the Speed of Ships 17 1 8 

Tidal Observations in the 

English Channel 10 

£1080 11 11 



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 

Specific Inductive Capacity 
of Sprengel Vacuum 20 

Completion of Tables of Sun- 
heat Coefficients 50 

Instrument for Detection of 

Fire-damp in Mines 10 

Inductive Capacity of Crystals 

and Paraffines 4 17 7 

Report on Carboniferous 
Polyzoa 10 



£ s. d. 

Caves of South Ireland 10 

Viviparous Nature of Ichthyo • 

saurus 10 

Kent's Cavern Exploration... 60 

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 

Electrical Standards 25 

High Insulation Key 5 

Tidal Observations 10 

Specific Refractions 7 3 1 

Fossil Polyzoa 10 

Underground Waters 10 

Earthquakes in Japan 25 

Tertiary Flora 20 

Scottish Zoological Station ... 50 

Naples Zoological Station ... 75 

Natural History of Socotra ... 50 
Anthropological Notes and 

Queries 9 

Zoological Record 100 

Weights and Heights of 

Human Beings 30 

£476 3 1 



1882. 

Exploration of Central Africa 100 

Fundamental Invariants of 

Algebraical Forms 76 111 

Standards for Electrical 

Measurements 100 

Calibration of Mercurial Ther- 
mometers 20 

Wave-length Tables of Spec- 
tra of Elements 60 

Photographing Ultra-violet 

Spark Spectra 25 

Geological Record 100 

Earthquake Phenomena of 
Japan 25 

Conversion of Sedimentary 
Materials into Metamorphic 
Rocks 10 

Fossil Plants of Halifax ...... 15 

Geological Map of Europe ... 25 

Circulation of Underground 
Waters 15 









KEPORT 1893. 



£ s. d. 

Tertiary Flora of North of 

Ireland 20 

British Pol}'zoa 10 

Exploration of Caves of South 

of Ireland 10 

Exploration of Raygill Fis- 
sure 20 

Naples Zoological Station ... 80 

Albuminoid Substances of 

Serum 10 

Elimination of Nitrogen by 

Bodily Exercise 50 

Migration of Birds 15 

Natural History of Socotra... 100 

Natural History of Timor-lai\t 100 

Eecord of Zoological Litera- 
ture 100 

Anthropometric Committee. . . 50 

£1126 1 11 



1883. 

Meteorological Observations 

on Ben Nevis 50 

Isomeric Naphthalene Deri- 
vatives 15 

Earthquake Phenomena of 

Japan 50 

Fossil Plants of Halifax 20 

British Fossil Polyzoa 10 

Fossil Phyllopoda of Palaeo- 
zoic Rocks 25 

Erosion of Sea-coast of Eng- 
land and Wales 10 

Circulation of Underground 
Waters 15 

Geological Record 50 

Exploration of Caves in South 
of Ireland 10 

Zoological Literature Eecord 100 

Migration of Birds 20 

Zoological Station at Naples 80 

Scottish Zoological Station... 25 

Elimination of Nitrogen by 

Bodily Exercise 38 3 3 

Exploration of Mount Eili- 
ma-njaro 500 

Investigation of Loughton 

Camp 10 

Natural History of Timor-laut 50 

Screw Gauges 5 

£1083 3 3 














































1884. 
Meteorological Observations 

on Ben Nevis 50 

Collecting and Investigating 

Meteoric Dust 20 

Meteorological Observatory at 

Chepstow 25 

Tidal Observations 10 

Ultra Violet Spark Spectra ... 8 4 



£ s. d. 
Earthquake Phenomena of 

Japan 75 

Fossil Plants of Halifax 15 

Fossil Polyzoa 10 

Erratic Blocks oE England ... 10 
Fossil Phyllopoda of Palaeo- 
zoic Rocks 15 

Circulation of Underground 

Waters 6 

International Geological Map 20 
Bibliography of Groups of 

Invertebrata 50 

Natural History of Timor-laut 50 

Naples Zoological Station ... 80 
Exploration of Mount Kili- 

ma-njaro, East Africa 500 

Migration of Birds 20 

Coagulation of Blood 100 

Zoological Literature Record 100 

Anthropometric Committee... 10 

£1173 4 



1885. 
Synoptic Chart of Indian 

Ocean 50 

Reduction of Tidal Observa- 
tions 10 

Calculating Tables in Theory 

of Numbers 100 

Meteorological Observations 

on Ben Nevis ,. 50 

Meteoric Dust 70 

Vapour Pressures, &c., of Salt 

Solutions 25 

Physical Constants of Solu- 
tions 20 

Volcanic Phenomena of Vesu- 
vius 25 

Raygill Fissure 15 

Earthquake Phenomena of 

Japan 70 

Fossil Phyllopoda of Palaeozoic 

Rocks , 25 

Fossil Plants of British Ter- 
tiary and Secondary Beds . 60 

Geological Record 50 

Circulation of Underground 

Waters 10 

Naples Zoological Station ... 100 
Zoological Literature Record. 100 

Migration of Birds 30 

Exploration of Mount Kilima- 
njaro 25 

Recent Polyzoa 10 

Marine Biological Station at 

Granton 100 

Biological Stations on Coasts 

of United Kingdom 150 

Exploration of New Guinea... 200 
Exploration of Mount Roraima 100 

£1385 













































































































































































































































GENEKAL STATEMEMT. 



CI 



18b6. £ s. d. 

Electrical Standards 40 

Solar Radiation 9 10 6 

Tidal Observations 50 

Magnetic Observations 10 10 

INIeteorological Observations 

on Ben Nevis 100 

Pliysical and Chemical Bear- 
ings of Electrolysis 20 

Chemical Nomenclature 5 

Fossil Plants of British Ter- 
tiary and Secondary Beds... 20 

Exploration of Caves in North 

Wales 25 

Volcanic Phenomena of Vesu- 
vius 30 

Geological Eecord. 100 

Fossil Phyllopoda of Palasozoic 

Eocks 15 

Zoological Literature Eecord . 100 

Marine Biological Station at 

Granton 75 

Naples Zoological Station 50 

Researches in Food-Fishes and 

Invertebrata at St. Andrews 75 

Migration of Birds 30 

Secretion of Urine 10 

Exploration of New Guinea... 150 

Regulation of Wages under 

Sliding Scales 10 

Prehistoric Eace in Greek 

Islands 20 

North-Western Tribes of Ca- 
nada 50 

£995 6 

1887. 

Solar Eadiation 18 10 

Electrolysis 30 

Ben Nevis Observatory 75 

Standards of Light (1886 

grant) 20 

Standards of Light (1887 

grant) 10 

Harmonic Analysis of Tidal 

Observations 15 

Magnetic Observations 26 2 

Electrical Standards 50 

Silent Discharge of Electricity 20 

Absorption Spectra 40 

Nature of Solution 20 

Influence of Silicon on Steel 30 
Volcanic Phenomena of Vesu- 
vius 20 

Volcanic Phenomena of Japan 

(1886 grant) 50 

Volcanic Phenomena of Japan 

(1887grant) 50 

Exploration of Cae Gwyn 

Cave, North Wales 20 

Erratic Blocks 10 

Fossil Phyllopoda 20 

Coal Plants of Halifax 25 



£ 
Microscopic Structure of the 

Eocks of Anglesey 10 

Exploration of the Eocene 

Beds of the Isle of Wight. . . 20 
Circulation of Underground 

Waters 5 

' Manure ' Gravels of Wexford 10 

Provincial Museum Reports 5 
Investigation of Lymphatic 

System 25 

Naples Biological Station ... 100 

Plj-mouth Biological Station 50 

Granton Biological Station... 75 

Zoological Eecord 100 

Flora of China 75 

Flora and Fauna of the 

Cameroons 75 

MigTation of Birds 30 

Bath}^-hypsographical Map of 

British Isles 7 

Eegulation of Wages 10 

Prehistoric Eace of Greek 

Islands 20 

Racial Photographs, Egyptian 20 

£ 1186 

1888. 

Ben Nevis Observatory 150 

Electrical Standards 2 

Magnetic Observations 15 

Standards of Light 79 

Electrolysis 30 

Uniform Nomenclature in 

Mechanics 10 

Silent Discharge of Elec- 
tricity 9 

Properties of Solutions 25 

Influence of Silicon on Steel 20 
Methods of Teaching Chemis- 
try 10 

Isomeric Naphthalene Deriva- 
tives 25 

Action of Light on Hydracids 20 

Sea Beach near Bridlington. . . 20 

Geological Record 50 

Manure Gravels of Wexford. . . 10 

Erosion of Sea Coasts 10 

Circulation of Underground 

Waters 5 

Palseontographical Society ... 60 
Pliocene Fauna of St. Erth... 50 
Carboniferous Flora of Lan- 
cashire and West Yorkshire 25 
Volcanic Phenomena of Vesu- 
vius 20 

Zoology and Botany of West 

Indies 100 

Flora of Bahamas 100 

Development of Fishes — St. 

Andrews 50 

Marine Laboratory, Plymouth 100 

Migration of Birds 30 

Flora of China 75 



i. d. 

















































































6 

















18 









G 


4 








2 


3 














11 


10 





















































































































Cll 



EEPORT — 1893. 



£ s. d. 

Naples Zoological Station ... 100 

Lymphatic System 25 

Biological Station at Granton 50 

Peradeniya Botanical Sta- 
tion 50 

Development of Teleostei ... 15 

Depth of Frozen Soil in Polar 

Eegions 5 

Precious Metals in Circula- 
tion 20 

Value of Monetary Standard 10 

Effect of Occupations on Phy- 
sical Development 25 

North-Western Tribes of 

Canada 100 

Prehistoric Pace in Greek 

Islands 20 

£1511 5 



1889. 

Ben Nevis Observatory 50 

Electrical Standards 75 

Electrolysis 20 

Observations on SurfaceWater 

Temperature 30 

Silent Discharge of Electricity 

on Oxygen 6 4 8 

Methods of teaching Chemis- 
try 10 

Action of Light on Hydracids 10 

Geological Record 80 

Volcanic Phenomena of Japan 25 

Volcanic Phenomena of Vesu- 
vius 20 

Fossil Phyllopoda of Paleo- 
zoic Rocks 20 

Higher Eocene Beds of Isle of 

Wight 15 

West Indian Explorations ... 100 

Flora of China 25 

Naples Zoological Station ... 100 

Physiology of Lymphatic 

System 25 

Experiments with a Tow-net 5 16 3 

Natural History of Friendly 

Islands 100 

Geology and Geography of 

Atlas Range 100 

Action of Waves and Currents 
in Estuaries by means of 
Working Models 100 

North-Westem Tribes of 

Canada 150 

Characteristics of Nomad 

Tribes of Asia Minor 30 

Corresponding Societies 20 

Marine Biological Association 200 

Bath ' Baths Committee ' for 

further Researches 100 

£1417 11 



1890. £ s. d. 

Electrical Standards 12 17 

Electrolysis 5 

Electro-optics 50 

Calculating Mathematical 

Tables 25 

Volcanic and Seismological 

Phenomena of Japan 75 

Pellian Equation Tables 15 

Properties of Solutions 10 

International Standard for the 

Analysis of Iron and Steel 10 

Influence of the Silent Dis- 
charge of Electricity on 

Oxygen 5 

Methods of teachingChemistry 10 

Recording Results of Water 

Analysis 4 10 

Oxidation of Hydracids in 

Sunlight 15 

Volcanic Phenomena of Vesu- 
vius 20 

Fossil Phyllopoda of the Pa- 
laeozoic Rocks 10 

Circulation of Underground 

Waters 5 

Excavations at Oldbury Hill 15 

Cretaceous Polyzoa 10 

Geological Photographs 7 14 11 

Lias Beds of Northampton- 
shire 25 

Botanical Station at Perade- 
niya 25 

Experiments with a Tow-net 4 3 9 

Naples Zoological Station ... 100 

Zoology and Botany of the 

West India Islands 100 

Marine Biological Association 30 

Action of Waves and Currents 

in Estuaries 150 

Graphic Methods in Mechani- 
cal Science 11 G 

Anthropometric Calculations 5 

Nomad Tribes of Asia Minor 25 

Corresponding Societies 20 

£799 16 8 

1891. 

Ben Nevis Observatory 50 

Electrical Standards 100 

Electrolysis 5 

Seismological Phenomena of 

Japan 10 

Variations of Temperature in 

Lakes 20 

Photographs of Meteorological 

Phenomena 5 

Discharge of Electricity from 

Points 10 

Ultra Violet Rays of Solar 

Spectrum 50 

International Standard for 

the Analysis of Iron and 

Steel 10 



GENERAL STATEMENT. 



cm 



I 



£ 
Isomeric Naphthalene Deriva- 
tives 25 

Formation of Haloids 25 

Action of Light on Dyes 17 

Geological Record 100 

Volcanic Phenomena of Vesu- 
vius 10 

Fossil Phyllopoda 10 

Photogpraphs of Geological 

Interest 9 

Lias Beds of Northampton- 
shire 25 

Registration of Type-Speci- 
mens of British Fossils 5 

Investigation of Elbolton 

Cave 25 

Botanical Station at Pera- 

deniya 50 

Experiments with a Tow-net 40 
Marine Biological Association 

at Plymouth 12 

Disappearance of Native 

Plants 5 

Action of Waves and Currents 

in Estuaries 125 

Anthropometric Calculations 10 
New Edition of ' Anthropo- 
logical Notes and Queries ' 50 
North - Western Tribes of 

Canada 200 

Corresponding Societies 25 



s. 


d. 






















5 











5 












10 















£1,029 10 



1892. 

Meteorological Observations 

on Den Nevis 50 

Photographs of Meteorological 

Phenomena 15 

Pellian Equation Tables 10 

Discharge of Electricity from 

Points 50 

■Seismological Phenomena of 

Japan 10 

Formation of Haloids 12 

Properties of Solutions 10 

Action of Light on Dyed 

Colours 10 

Erratic Blocks 15 

Photographs of Geological 

Interest 20 

Underground Waters 10 

Investigation of Elbolton 

Cave 25 

Excavations at Oldbury Hill 10 

■Cretaceous Polyzoa 10 

Table at Naples Zoological 

Station 100 

Table at Plymouth Biological 

Laboratory 17 

Improving a Deep-sea Tow- 
net 40 








































































































£ s. d. 

Fauna of Sandwich Islands... 100 
Zoology and Botany of West 

India Islands 100 

Climatology and Hydrography 

of Tropical Africa 50 

Anthropometric Laboratory... 5 
Anthropological Notes and 

Queries 20 

Prehistoric Remains in Ma- 

shonaland 50 

North - Western Tribes of 

Canada 100 

Corresponding Societies 25 

i864 10 



1893. 

Electrical Standards 25 

Meteorological Observations 

on Ben Nevis 150 

Tables of Mathematical 

Functions 15 

Recording the Direct Inten- 
sity of Solar Radiation 2 8 6 

Magnetic Work at the Fal- 
mouth Observatory 25 

Isomeric Naphthalene De- 
rivatives 20 

Erratic Blocks 10 

Fossil Phyllopoda 5 

Underground Waters 5 

Shell-bearing Deposits at 

Clava, Chapelhall, &c 20 

Eurypterids of the Pentland 
Hills 10 

Table at the Naples Zoological 

Station 100 

Table at the Plymouth Bio- 
logical Laboratory 30 

Fauna of Sandwich Islands 100 

Zoology and Botany of West 

India Islands 50 

Exploration of Irish Sea 30 

Physiological Action of 

Oxygen in Asphyxia 20 

Index of Genera and Species 

of Animals 20 

Exploration of Karakoram 
Mountains 50 

Scottish Place-names 7 

Climatology and Hydro- 
graphy of Tropical Africa 50 

Methods of Economic Train- 
ing 3 7 

Anthropometric Laboratory 5 

Exploration of Ancient Re- 
mains in Abyssinia 25 

North-Western Tribes of 

Canada 100 

Corresponding Societies Com- 
mittee 30 

£907 15 6 



civ EEroET — 1893. 



General Meetings. 

On Wednesday, September 13, at 8 p.m., in tbe Albert Hall, Sir 
Archibald Geikie, LL.D., D.Sc, For.Sec.R.S., F.R.S.B., P.G.S., resigned 
the office of President to Professor J. S. Bardon Sanderson, M.A., M.D., 
LL.D., D.C.L., F.R.S., F.R.S.E., who took the Chair, and delivered an 
Address, for which see page 3. 

On Thursday, September 14, at 8 p.m., a Soiree took place at the 
Castle. 

On Friday, September 15, at 8.30 p.m., in the Albert Hall, Professor 
Arthur Smithells, B.Sc, delivered a discourse on ' Flame.' 

On Monday, September 18, at 8.30 p.m., in the Albert Hall, Professor 
Victor Horsley, F.R.S., delivered a discourse on 'The Discovery of the 
Physiology of the Nervous System.' 

On Tuesday, September 19, at 8 p.m., a Soiree took place at the 
Castle. 

On Wednesday, September 20, at 2.30 p.m., in University College, the 
concluding General Meeting took place, 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 Oxford. [The Meeting is 
appointed to commence on Wednesday, August 8, 1894.] 



PEESIDENT'S ADDEESS. 



1893. 



ADDRESS 



BY 



J. S. BUEDON SANDERSON, 

M.A., M.D., LL.D., D.C.L., F.R.S., F.R.S.E., Professor of Physiology 

in the University of Oxford, 

PRESIDENT. 



We are assembled this evening as representatives of the sciences — men 
and women who seek to advance knowledge by scientific methods. The 
common ground on which we stand is that of belief in the paramount 
value o.f the end for which we are striving, of its inherent power to make 
men wiser, happier, and better ; and oar common purpose is to strengthen 
and encourage one another in our efforts for its attainment. We have 
come to learn what progress has been made in departments of knowledge 
which lie outside of our own special scientific interests and occupations, 
to widen our views, and to correct whatever misconceptions may have 
arisen from the necessity which limits each of ns to his own field of study ; 
and, above all, we are here for the purpose of bringing our divided ener- 
gies into effectual and combined action. 

Probably few of the members of the Association are fully aware of 
the influence which it has exercised during the last half-century and 
more in furthering the scientific development of this country. Wide as 
is the range of its activity, there has been no great question in the field 
of scientific inquiry which it has failed to discuss ; no important line of 
investigation which it has not promoted ; no great discovery which it has 
not welcomed. After more than sixty years of existence it still finds 
itself in the energy of middle life, looking back with satisfaction to what 
it has accomplished in its youth, and forward to an even more efficient 
future. One of the first of the national associations which exist in different 
countries for the advancement of science, its influence has been more felt 
than that of its successors because it is more wanted. The wealthiest 



B 2 



4 BEPORT — 1893. 

country in the world, which has profited more — vastly more — by science 
than any other, England stands alone in the discredit of refusing the 
necessary expenditure for its development, and cares not that other nations 
should reap the harvest for which her own sons have laboured. 

It is surely our duty not to rest satisfied with the reflection that 
England in the past has accomplished so much, but rather to unite and 
ao-itate in the confidence of eventual success. It is not the fault of 
governments, but of the nation, that the claims of science are not recog- 
nised. We have against us an overwhelming majority of the community, 
not merely of the ignorant, but of those who regard themselves as edu- 
cated, who value science only in so far as it can be turned into money ; 
for we are still in great measure — in greater measure than any other — a 
nation of shopkeepers. Let us who are of the minority — the remnant 
who believe that truth is in itself of supreme value, and the knowledge of 
it of supreme utility — do all that we can to bring public opinion to our 
side, so that the century which has given Young, Faraday, Lyell, Darwin, 
Maxwell, and Thomson to England, may before it closes see us pre- 
pared to take our part with other countries in combined action for the 
full development of natural knowledge. 

Last year the necessity of an imperial observatory for physical 
science was, as no doubt many are aware, the subject of a discussion in 
Section A, which derived its interest from the number of leading 
physicists who took part in it, and especially from the presence and active 
participation of the distinguished man who is at the head of the National 
Physical Laboratory at Berlin. The equally pressing necessity for a 
central institution for chemistry, on a scale commensurate with the 
practical importance of that science, has been insisted upon in this 
Association and elsewhere by distinguished chemists. As regards 
biology I shall have a word to say in the same direction this evening. 
Of these three requirements it may be that the first is the most pressing. 
If so, let us all, whatever branch of science we represent, unite our efforts 
to realise it, in the assurance that if once the claim of science to liberal 
public support is admitted, the rest will follow. 

In selecting a subject on which to address you this evening I have 
followed the example of my predecessors in limiting myself to matters 
more or less connected with my own scientific occupations, believing 
that in discussing wbat most interests myself I should have the best 
chance of interesting you. The circumstance that at the last meeting of 
the British Association in this town. Section D assumed for the first time 
the title which it has since held, that of the Section of Biology, suggested 
to me that I might take the word ' biology ' as my starting-point, giving 
you some account of its origin and first use, and of the relations which 
subsist between biology and other branches of natural science. 



addeess. o 

Origin and Meaning of the Term ' Biology.' 

The word 'biology,' which is now so familiar as comprising the snm 
of the knowledge which has as yet been acquired concerning living 
nature, was unknown until after the beginning of the present century. 
The term was first employed by Treviranus, who proposed to himself as 
a life-task the development of a new science, the aim of which should be 
to study the forms and phenomena of life, its origin and the conditions 
and laws of its existence, and embodied what was known on these subjects 
in a book of seven volumes, which he entitled ' Biology, or the Philosophy 
of Living Nature.' For its construction the material was very scanty, 
and was chiefly derived from the anatomists and physiologists. For 
botanists were entirely occupied in completing the work which Linnaeus 
had begun, and the scope of zoology was in like manner limited to the 
description and classification of animals. It was a new thing to regard 
the study of living nature as a science by itself, worthy to occupy a place 
by the side of natural philosophy, and it was therefore necessary to vindi- 
cate its claim to such a position. Treviranus declined to found this claim 
on its useful applications to the arts of agriculture and medicine, con- 
sidering that to regard any subject of study in relation to our bodily 
wants — in other words to utility — was to narrow it, but dwelt rather 
on its value as a discipline and on its surpassing interest. He commends 
biology to his readers as a study which, above all others, ' nourishes and 
maintains the taste for simplicity and nobleness ; which affords to the 
intellect ever new material for reflection, and to the imagination an in- 
exhaustible source of attractive images. ' 

Being himself a mathematician as well as a naturalist, he approaches 
the subject both from the side of natural philosophy and from that of 
natural history, and desires to found the new science on the fundamental 
distinction between living and non-living material. In discussing this 
distinction, he takes as his point of departure the constancy with which 
the activities which manifest themselves in the universe are balanced, 
emphasising the impossibility of excluding from that balance the vital 
activities of plants and animals. The difference between vital and 
physical processes he accordingly finds, not in the nature of the processes 
themselves, but in their co-ordination; that is, in their adaptedness to 
a given purpose, and to the peculiar and special relation in which the 
organism stands to the external world. All of this is expressed in a pro- 
position diflBicult to translate into English, in which he defines life as 
consisting in the reaction of the organism to extei'nal influences, and 
contrasts the uniformity of vital reactions with the variety of their 
exciting causes.' 

' ' Leben bestelit in der Gleichformigkeit der Reaktionen bei ungleichformigen 
Einwirkungen der Aussenwelt.' — Treviranus, Biologie oder PhilvsojjMe der lebenden 
Natur, Gottingen, 1802, vol. i. p. 83. 



6 KEPOET 1893. 

The purpose which I have in view in taking yon back as I have done 
to the beginning of the century is not merely to commemorate the work 
done by the wonderfully acute writer to whom we owe the first scientific 
conception of the science of life as a whole, but to show that this con- 
ception, as expressed in the definition I have given you as its foundation, 
can still be accepted as true. It suggests the idea of organisin as that to 
which all other biological ideas must relate. It also suggests, although 
perhaps it does not express it, that action is not an attribute of the 
organism but of its essence — that if, on the one hand, protoplasm is the 
basis of life, life is the basis of protoplasm. Their relations to each 
other are reciprocal. We think of the visible structure only in con- 
nection with the invisible process. The definition is also of value as 
indicating at once the two lines of inquiry into which the science has 
divided by the natural evolution of knowledge. These two lines may be 
easily educed from the general principle from which Treviranns started, 
according to which it is the fundamental characteristic of the organism 
that all that goes on in it is to the advantage of the whole. I need 
scarcely say that this fundamental conception of organism has at all 
times presented itself to the minds of those who have sought to under- 
stand the distinction between living and non-living. Without going 
back to the true father and founder of biology, Aristotle, we may recall 
with interest the language employed in relation to it by the physiologists 
of three hundred years ago. It was at that time expressed by the term 
consensus partium — which was defined as the concurrence of parts in 
action, of such a nature that each does qitod suum est, all combining 
to bring about one eSect ' as if they had been in secret council,' but at 
the same time cunstanti quadaw, naturoi lerjo} Professor Huxley has 
made familiar to us how a century later Descartes imagined to himself a 
mechanism to carry out this consensus, based on such scanty knowledge 
as was then available of the structure of the nervous system. The dis- 
coveries of the early part of the present century relating to reflex action 
and the functions of sensory and motor nerves, served to realise in a 
wonderful way his anticipations as to the channels of influence, afferent 
and efferent, by which the consensus is maintained ; and in recent times 
(as we hope to learn from Professor Horsley's lecture on the physiology 
of the nervous system) these channels have been investigated with 
extraordinary minuteness and success. 

Whether with the old writers we speak about co^isensus, with Treviranus 
about adaptation, or are content to take organism as our point of departure, 
it means that, regarding a plant or an animal as an organism, we concern 
ourselves primarily with its activities or, to use the word which best ex- 
presses it, its energies. Now the first thing that strikes us in beginning 
to think about the activities of an organism is that they are naturally 

' Bausner, De Consensu Partivm Hvmani Corjjoris, Amst., 155C, Pnef. ad lec- 
torem, p. 4. 



ADDRESS. 7 

distinguishable into two kinds, according as we consider the action of 
the whole organism in its relation to the external world or to other 
organisms, or the action of the parts or organs in their relation to each 
other. The distinction to which we are thus led between the infernal 
and external relations of plants and animals has of course always existed, 
but has only lately come into such prominence that it divides biologists 
more or less completely into two camps — on the one hand those who 
make it their aim to investigate the actions of the organism and its parts 
by the accepted methods of physics and chemistry, carrying this investi- 
gation as far as the conditions under which each process manifests itself 
will permit ; on the other those who interest themselves rather in con- 
sidering the place which each organism occupies, and the part which it 
plays in the economy of nature. It is apparent that the two lines of 
inquiry, although they equally relate to what the organism does, rather 
than to what it is, and therefore both have equal right to be included in 
the one great science of life, or biology, yet lead in directions which, 
are scarcely even parallel. So marked, indeed, is the distinction, that 
Professor Haeckel some twenty years ago proposed to separate the study 
of organisms with reference to their jolace in nature under the designa- 
tion of ' oecology,' defining it as comprising ' the relations of the animal 
to its organic as well as to its inorganic environment, particularly its 
friendly or hostile relations to those animals or plants with which it 
conies into direct contact.' • Whether this term expresses it or not, the 
distinction is a fundamental one. Whether with the cecologist we 
regard the organism in relation to the world, or with the physiologist as 
a wonderful complex of vital energies, the two branches have this in 
common, that both studies fix their attention, not on stuffed animals, 
butterflies in cases, or even microscopical sections of the animal or plant 
body — all of which relate to the framework of life — but on life itself. 

The conception of biology which was developed by Treviranus as far 
as the knowledge of plants and animals which then existed rendered 
possible, seems to me still to express the scope of the science. I should 
have liked, had it been within my power, to present to you both aspects 
of the subject in equal fulness ; but I feel that I shall best profit by the 
present opportunity if I derive my illustrations chiefly from the division of 
biology to which I am attached — that which concerns the internal rela- 
tions of the organism, it being my object not to specialise in either 
direction, but, as Treviranus desired to do, to regard biology as part — 
surely a very important part — of the great science of nature. 

The origin of life, the first transition from non-living to living, is a 

' These he identifies with 'those complicated mutual relations which Darwin 
designates as conditions of the struggle for existence.' Along with chorology — the 
distribution of animals — oecology constitutes what he calls Relatiotis-Physiologie. 
Haeckel, 'Entwickelungsgang u. Aufgaben der Zoolo^e, ' Jenaische Zeitschr., vol. v. 
1869, p. 353. 



8 REPOET 1893. 

riddle whicli lies outside of our scope. No seriously-minded person, 
however, doubts tliat organised nature as it now presents itself to us 
has become what it is by a process of gradual perfecting or advance- 
ment, brought about by the elimination of those organisms which failed 
to obey the fundamental principle of adaptation which Treviranus indi- 
cated. Each step, therefore, in this evolution is a reaction to external 
influences, the motive of which is essentially the same as that by which 
from moment to moment the organism governs itself. And the whole 
process is a necessary outcome of the fact that those organisms are most 
prosperous which look best after theu' own welfare. As in that part of 
biology which deals with the internal relations of the organism, the 
interest of the individual is in like manner the sole motive by which 
every energy is guided. We may take what Treviranus called selfish 
adaptation — ZweckmdssigTieit filr sich selher — as a connecting link 
between the two branches of biological study. Out of this relation 
springs another which I need not say was not recognised until after the 
Darwinian epoch — that, I mean, which subsists between the two evolu- 
tions, that of the race and that of the individual. Treviranus, no less 
distinctly than his great contemporary Lamarck, was well aware that 
the affinities of plants and animals must be estimated according to their 
developmental value, and consequently that classification must be founded 
on development ; but it occurred to no one what the real link was between 
descent and develojDment ; nor was it, indeed, until several years after the 
publication of the ' Origin ' that Haeckel enunciated that ' biogenetic 
law ' according to which the development of any individual organism is 
but a memory, a recapitulation by the individual of the development of 
the race — of the process for which Fritz Miiller had coined the excellent 
word ' phylogenesis ' ; and that each stage of the former is but a transitory 
reappearance of a bygone epoch in its ancestral history. If, therefore, 
we are right in regarding ontogenesis as dependent on phylogenesis, the 
origin of the former must correspond with that of the latter ; that is, 
on the power which the race or the organism at every stage of its 
existence possesses of profiting by every condition or circumstance for its 
own advancement. 

From the short summary of the connection between different parts of 
our science you will see that biology naturally falls into three divisions, 
and these are even more sharply distinguished by their methods than by 
their subjects ; namely, Physiology, of which the methods are entirely 
experimental ; Morphology, the science which deals with the forms and 
structure of plants and animals, and of which it may be said that the 
body is anatomy, the soul, development ; and finally CEcologij, which uses 
all the knowledge it can obtain from the other two, but chiefly rests on 
the exploration of the endless varied phenomena of animal and plant life 
as they manifest themselves under natural conditions. This last branch 
of biology — the science which concerns itself with the external relations of 



ADDRESS. 9 

plants and animals to each other, and to the past and present conditions 
of their existence — is by far the most attractive. In it those qualities of 
mind which especially distinguish the naturalist find their liighest 
exercise, and it represents more than any other branch of the subject 
what Treviranus termed the ' philosophy of living nature.' Notwith- 
standing the very general interest which several of its problems excite at 
the present moment I do not propose to discuss any of them, but rather 
to limit myself to the humbler task of showing that the fundamental idea 
which finds one form of expression in the world of living beings regarded 
as a whole — the prevalence of the best — manifests itself with equal dis- 
tinctness, and plays an equally essential part in the internal relations of 
the organism and in the great science which treats of them — Physiology. 

Origin and Scope of Modern Physiglogt. 

Just as there was no true philosophy of living natare until Darwin, 
we may with almost equal truth say that physiology did not exist as a 
science before Johannes Miiller. For although the sum of his numerous 
achievements in comparative anatomy and physiology, notwithstanding 
their extraordiuaiy number and importance, could not be compared for 
merit and fruitfulness with the one discovery which furnished the key to 
so many riddles, he, no less than Darwin, by his influence on his suc- 
cessors was the beginner of a new era. 

Miiller taught in Berlin from 1833 to 1857. During that time a 
gradual change was in progress in the way in which biologists regarded 
the fundamental problem of life. Miiller himself, in common with 
Treviranus and all the biological teachers of his time, was a vitalist, i.e., 
he regarded what was then called the vis vitalis — the Lebenshraft — as 
something capable of being correlated with the physical forces ; and as a 
necessary consequence held that phenomena should be classified or dis- 
tinguished, according to the forces which produced them, as vital or 
physical, and that all those processes — that is groups or series of phe- 
nomena in living organisms — for which, in the then very imperfect know- 
ledge which existed, no obvious physical explanation could be found, 
were sufficiently explained when they were stated to be dependent on so- 
called vital laws. But during the period of Miiller's greatest activity 
times were changing, and he was changing with them. During his long 
career as professor at Berlin he became more and more objective in his 
tendencies, and exercised an influence in the same direction on the men 
of the next generation, teaching them that it was better and more useful 
to observe than to philosophise ; so that, although he himself is truly 
regarded as the last of the vitalists — for he was a vitalist to the last — his 
successors were adherents of what has been very inadequately designated 
the mechanistic view of the phenomena of life. The change thus brought 
about just before the middle of this century was a revolution. It was not 
a substitution of one point of view for another, but simply a frank aban- 



10 EEPORT— 1893. 

donment of theory for fact, of speculation for experiment. Physiologists 
ceased to theorise because they found something better to do. May I try 
to give you a sketch of this era of progress ? 

Great discoveries as to the structure of plants and animals had been 
made in the course of the previous decade, those especially which had 
resulted from the introduction of the microscope as an instrument of 
research. By its aid Schwann had been able to show that all organised 
structures are built up of those particles of living substance which we 
now call cells, and recognise as the seats and sources of every kind of 
vital activity. Hugo Mohl, working in another direction, had given the 
name ' protoplasm ' to a certain hyaline substance which forms the lining of 
the cells of plants, though no one as yet knew that it was the essential 
constituent of all living structures — the basis of life no less in animals 
than in plants. And, finally, a new branch of study — histology — founded 
on observations which the microscope had for the first time rendered 
possible, had come into existence. Bowman, one of the earliest and most 
successful cultivators of this new science, called it physiological anatomy,' 
and justified the title by the very important inferences as to the secreting 
function of epithelial cells and as to the nature of muscular contraction, 
which he deduced from his admirable anatomical researches. From struc- 
ture to function, from microscopical observation to physiological experi- 
ment, the transition was natural. Anatomy was able to answer some 
questions, but asked many more. Fifty years ago physiologists had 
microscopes but had no laboratories. English physiologists — Bowman, 
Paget, Sharpey — were at the same time anatomists, and in Berlin 
Johannes Miiller, along with anatomy and physiology, taught compara- 
tive anatomy and pathology. But soon that specialisation which, how- 
ever much we may regret its necessity, is an essential concomitant of 
progress, became more and more inevitable. The structural conditions 
on which the processes of life depend had become, if not known, at least 
accessible to investigation ; but very little indeed had been ascertained of 
the nature of the processes themselves — so little indeed that if at this 
moment we could blot from the records of physiology the whole of the 
information which had been acquired, say in 1840, the loss would be diffi- 
cult to trace — not that the previously known facts were of little value, 
but because every fact of moment has since been subjected to experi- 
mental verification. It is for this reason that, without any hesitation, we 
accord to Miiller and to his successors Briicke, du Bois-Reymond, Helm- 
holtz, who were his pupils, and Ludwig, in Germany, and to Claude 
Bernard ^ in France, the title of founders of our science. For it is 

' The first part of the Physiological Anatomy appeared in 1843. It was concluded 
in 1856. 

- It is worthy of note that these five distinguished men were nearly contempo- 
raries : Ludwig graduated in 1839, Bernard in 1843, the other three between those 
dates. Three survive — Helmholtz, Ludwig. du Bois-Eeymond. 



ADDRESS. 1 1 

the work which they began at that remarkable time (1845-55), and which 
is now being carried on by their pupils or their pupils' pupils in England, 
America, France, Germany, Denmark, Sweden, Italy, and even in that 
youngest contributor to the advancement of science, Japan, that physio- 
logy has been gradually built up to whatever completeness it has at 
present attained. 

What were the conditions which brought about this great advance 
which coincided with the middle of the century ? There is but little 
diflficulty in answering the question. I have already said that the change 
was not one of doctrine, but of method. There was, however, a leading 
idea in the minds of those who were chiefly concerned in bringing it 
about. That leading notion was, that, however complicated may be the 
conditions under which vital energies manifest themselves, they can be 
split into processes which are identical in nature with those of the non- 
living world, and, as a corollary to this, that the analysing of a vital 
process into its physical and chemical constituents, so as to bring these 
constituents into measurable relation with physical or chemical standards, 
is the only mode of investigating them which can lead to satisfactory 
results. 

There were several circumstances which at that time tended to make 
the younger physiologists (and all of the men to whom I have just 
referred were then young) sanguine, perhaps too sanguine, in the hope 
that the application of experimental methods derived from the exact 
sciences would aiford solutions of many physiological problems. One of 
these was the progress which had been made in the science of chemistry, 
and particularly the discovery that many of the compounds which before 
had been regarded as special products of vital processes could be 
produced in the laboratory, and the more complete knowledge which had 
been thereby acquired of their chemical constitutions and relations. In 
like manner, the new school profited by the advances which had been 
made in physics, partly by borrowing from the physical laboratory various 
improved methods of observing the phenomena of living beings, but 
chiefly in consequence of the direct bearing of the crowning discovery of 
that epoch (that of the conservation of energy) on the discussions which 
then took place as to the relations between vital and physical forces; 
in connection with which it may be noted that two of those who (along 
with Mr. Joule and your President at the last Nottingham meeting) took 
a prominent part in that discovery — Helmholtz and J. R. Mayer — were 
physiologists as much as they were physicists. I will not attempt even 
to enumerate the achievements of that epoch of progress. I may, how- 
ever, without risk of wearying you, indicate the lines along which research 
at first proceeded, and draw your attention to the contrast between then 
and now. At present a young observer who is zealous to engage in re- 
search finds himself provided with the most elaborate means of investiga- 
tion, the chief obstacle to his success being that the problems which have 



12 REPORT— 1893. 

beeu. left over by his predecessors are of extreme difficulty, all of tbe 
easier questions having been worked out. There were then also difficul- 
ties, but of an entirely different kind. The work to be done was in itself 
easiei", but the means for doing it were wanting, and every investigator 
had to depend on his own resources. Consequently the successful men 
were those who, in addition to scientific training, possessed the ingenuity 
to devise and the skill to carry out methods for themselves. The work 
by which du Bois-Reymond laid the foundation of animal electricity 
would not have been possible had not its author, besides being a trained 
physicist, known how to do as good work in a small room in the upper 
floor of the old University Building at Berlin as any which is now done 
in his splendid laboratory. Had Ludwig not possessed mechanical apti- 
tude, in addition to scientific knowledge, he would have been unable to 
devise the apparatus by which he measured and recorded the variations 
of arterial pressure (1848), and verified the principles which Young had 
laid down thirty years before as to the mechanics of the circulation. 
Nor, lastly, could Helmholtz, had he not been a great deal more than a 
mere physiologist, have made those measurements of the time-relations of 
muscular and nervous responses to stimulation, which not only afford a 
solid foundation for all that has been done since in the same direction, 
but have served as models of physiological experiment, and as evidence 
that perfect work was possible and was done by capable men, even when 
there were no physiological laboi-atories. 

Each of these examples relates to work done within a year or two of 
the middle of the century.' If it were possible to enter more fully on the 
scientific history of the time, we should, I think, find the clearest evidence, 
first, that the foundation was laid in anatomical discoveries, in which it 
is gratifying to remember that English anatomists (Allen Thomson, 
Bowman, Goodsir, Sharpey) took considerable share ; secondly, that 
progress was rendered possible by the rapid advances which, during the 
previous decade, had been made in jjhysics and chemistry, and the partici- 
pation of physiology in the general awakening of the scientific spirit 
which these discoveries produced. I venture, however, to think that, 
notwithstanding the operation of these two causes, or rather combinations 
of causes, the development of our science would have been delayed had it 
not been for the exceptional endowments of the four or five young experi- 
menters whose names T have mentioned, each of whom was capable of 
becoming a master in his own branch, and of guiding the future progress 
of inquiry. 

Just as the affinities of an organism can be best learned fi'om its 
development, so the scope of a science may be most easily judged of by 

' The UnteTsuclnmgen iiher ilnerische EleotrieUat appeared in 1848 ; Ludwig's 
researches on the circulation, which included the first description of the ' kymo- 
graph ' and served as the foundation of the ' graphic method,' in 1847 ; Helmholtz's 
research on the propagation in motor nerves in 1851. 



ADDRESS. 13 

the tendencies whicli it exhibits in its origin. I wish now to complete 
the sketch I have endeavoured to give of the way in which physiology 
entered on the career it has since followed for the last half-century, by 
a few words as to the influence exercised on general physiological theory 
by the progress of research. We have seen that no real advance was 
made until it became possible to investigate the phenomena of life by 
methods which approached more or less closely to those of the phy- 
sicist, in exactitude. The methods of investigation being physical or 
chemical, the organism itself naturally came to be considered as a complex 
of such processes, and nothing more. And in particular the idea of 
adaptation, which, as I have endeavoured to show, is not a consequence 
of organism, but its essence, was in great measure lost sight of. Not, I 
think, because it was any more possible than before to conceive of the 
organism otherwise than as a working together of parts for the good of 
the whole, but rather that, if I may so express it, the minds of men were 
so occupied with new facts that they had not time to elaborate theories. 
The old meaning of the term 'adaptation ' as the equivalent of ' design ' had 
been abandoned, and no new meaning had yet been given to it, and con- 
sequently the word ' mechanism ' came to be employed as the equivalent of 
^process,' as if the constant concomitance or sequence of two events was in 
itself a sufficient reason for assuming a mechanical relation between them. 
As in daily life so also in science, the misuse of words leads to miscon- 
ceptions. To assert thab the link between a and b is mechanical, for no 
better reason than that i always follows a, is an error of statement, which 
is apt to lead the incautious reader or hearer to imagine that the relation 
between a and b is understood, when in fact its nature may be wholly 
■unknown. "Whether or not at the time which we are considering, some 
physiological writers showed a tendency to commit this error, I do not 
think that it found expression in any generally accepted theory of life. 
It may, however, be admitted that the rapid progress of experimental in- 
vestigation led to too confident anticipations, and that to some enthusiastic 
minds it appeared as if we were approaching within measurable distance 
of the end of knowledge. Such a tendency is, I think, a natural result 
of every signal advance. In an eloquent Harveian oration, delivered last 
autumn by Dr. Bridges, it was indicated how, after Harvey's great dis- 
covery of the circulation, men were too apt to found upon it explanations 
of all phenomena whether of health or disease, to such an extent that the 
practice of medicine was even prejudicially affected by it. In respect of 
its scientific importance the epoch we are considering may well be com- 
pared with that of Harvey, and may have been followed by an undue 
preference of the new as compared with the old, but no more permanent 
unfavourable results have shown themselves. As regards the science of 
medicine we need only remember that it was during the years between 
1845 and 1860 that Yirchow made those researches by which he brought 
the processes of disease into immediate relation with the normal processes 



14 EEPORT— 1893. 

of cell-development and growth, and so, by making pathology a part of 
physiology, secured its subsequent progress and'its influence on practical 
medicine. Similarly in physiology, the achievements of those years led 
on without any interruption or drawback to those of the following gene- 
ration ; while in general biology, the revolution in the mode of regarding 
the internal processes of the animal or plant organism which resulted 
from these achievements, prepared the way for the acceptance of the still 
greater revolution which the Darwinian epoch brought about in the views 
entertained by naturalists of the relations of plants and animals to each 
other and to their surroundings. 

It has been said that every science of observation begins by going out 
botanising, by which, I suppose, is meant that collecting and recording 
observations is the first thing to be done in entering on a new field of 
inquiry. The remark would scarcely be true of physiology, even at the 
■earliest stage of its development, for the most elementary of its facts 
could scarcely be picked up as one gathers flowers in a wood. Each of 
the processes which go to make up the complex of life requires separate 
investigation, and in each case the investigation must consist in first 
splitting up the process into its constituent phenomena, and then deter- 
mining their relation to each other, to the process of which they form 
part, and to the conditions under which they manifest themselves. It 
will, I think, be found that even in the simplest inquiry into the nature of 
vital processes some such order as this is followed. Thus, for example, 
if muscular contraction be the subject on which we seek information, 
it is obvious that, in order to measure its duration, the mechanical work 
it accomplishes, the heat wasted in doing it, the electro-motive forces 
which it develops, and the changes of form associated with these phe- 
nomena, special modes of observation must be used for each of them, 
that each measurement must be in the first instance separately made, 
under special conditions, and by methods specially adapted to the 
required purpose. In the synthetic part of the inquiry the guidance of 
experiment must again be sought for the purpose of discriminating 
between apparent and real causes, and of determining the order in which 
the phenomena occur. Even the simplest experimental investigations 
of vital processes are beset with difficulties. For, in addition to the 
extreme complexity of the phenomena to be examined and the un- 
certainties which arise from the relative inconstancy of the conditions 
of all that goes on in the living organism, there is this additional draw- 
back, that, whereas in the exact sciences experiment is guided by well- 
ascertained laws, here the only principle of universal application is that 
of adaptation, and that even this cannot, like a law of physics, be taken 
as a basis for deductions, but only as a summary expression of that 
relation between external exciting causes and the reactions to which 
they give rise, which, in accordance with Treviranus' definition, is the 
essentia] character of vital activity. 



ADDRESS. 15 

The Specific Energies of the Organism. 

When in 182o J. Miiller was engaged in investigating the physiology 
of vision and hearing he introduced into the discussion a term, ' specific 
energy,' the use of which by Helmholtz ' in his physiological writings has 
rendered it familiar to all students. Both writers mean by the word 
energy, not the ' capacity of doing woi^k,' but simply activity, using it in 
its old-fashioned meaning, that of the Greek word from which it is de- 
rived. With the qualification ' specific ' it serves, perhaps, better than any 
other expression to indicate the way in which adaptation manifests itself. 
In this more extended sense the ' specific energy ' of a part or organ — 
whether that part be a secreting cell, a motor cell of the brain or 
spinal cord, or one of the photogenous cells which produce the light 
of the glowworm, or the protoplasmic plate which generates the dis- 
charge of the torpedo — is simply the special action which it normally 
performs, its norma or rule of action being in each instance the interest 
of the organism as a whole of which it forms part, and the exciting cause 
some influence outside of the excited structure, technically called 
a stimulus. It thus stands for a characteristic of liviner structures 
which seems to be universal. The apparent exceptions are to be found in 
those bodily activities which, following Bichat, we call vegetative, because 
they go on, so to speak, as a matter of course; but the more closely we 
look into them the more does it appear that they form no exception to the 
general rule, that every link in the chain of living action, however uniform 
that action may be, is a response to an antecedent influence. Nor can it 
well be doubted that, as every living cell or tissue is called upon to act in 
the interest of the whole, the organism must be capable of influencing 
every part so as to regulate its action. For, although there are some in- 
stances in which the channels of this influence are as yet unknown, the 
tendency of recent investigations has been to diminish the number of such 
instances. In general there is no diSiculty in determining both the 
nature of the central influence exercised and the relation between it and 
the normal function. It may help to illustrate this relation to refer to the 
expressive word Auslosung by which it has for many years been designated 
by German writers. This word stands for the performance of function by 
the ' letting off"' of ' specific energies.' Carrying out the notion of ' letting 
off'' as expressing the link between action and reaction, we might com- 
pare the whole process to the mode of working of a repeating clock (or 
other similar mechanism), in which case the pressure of the finger on the 
button would represent the external influence or stimulus, the striking 
of the clock, tbe normal reaction. And now may I ask you to consider 
in detail one or two illustrations of physiological reaction — of the letting 
off of specific energy ? 

' Handh. der physiologischen Optik, 1886, p. 233. Helmholtz uses the word in 
the plural — the ' energies of the nerves of special sense.' 



16 BEPOET— 1893. 

The repeater may serve as a good example, inasmuch as it, is, in 
biological language, a highly differentiated structure, to which a single 
function is assigned. So also in the living organism, we find the best 
examples of specific energy where Miiller found them, namely, in the 
most differentiated, or, as we are apt to call them, the highest structures. 
The retina, with the part of the brain which belongs to it, together con- 
stitute such a structure, and will afford us therefore the illustration we 
want, with this advantage for our present purpose, that the phenomena 
are such as we all have it in our power to observe in ourselves. In 
the visual apparatus the principle of riormality of reaction is fully 
exemplified. In the physical sense the word ' light ' stands for ether 
vibrations, but in the sensuous or subjective sense for sensations. The 
swings are the stimulus, the sensations are the reaction. Between the 
two comes the link, the ' letting off,' which it is our business to under- 
stand. Here let us remember that the man who first recognised this 
distinction between the physical and the physiological was not a bio- 
logist, but a physicist. It was Young who first made clear (though his 
doctrine fell on unappreciative ears) that, although in vision the external 
influences which give rise to the sensation of light are infinitely varied, 
the responses need not be more than three in number, each being, in 
Miiller's language, a ' specific energy ' of some part of the visual appa- 
ratus. We speak of the organ of vision as highly differentiated, an 
expression which carries with it the suggestion of a distinction of rank 
between different vital processes. The suggestion is a true one ; for it 
would be possible to arrange all those parts or organs of which the 
bodies of the higher animals consist in a series, placing at the lower end 
of the series those of which the functions are continuous, and therefore 
called vegetative ; at the other, those highly specialised structures, as, e.g., 
those in the brain, which in response to physical light produce physiolo- 
gical, that is subjective, light ; or, to take another instance, the so-called 
motor cells of the surface of the brain, which in response to a stimulus 
of much greater complexity produce voluntary motion. And just as in 
civilised society an individual is valued according to his power of doing 
one thing well, so the high rank which is assigned to the structure, or 
rather to the 'specific energy' which it represents, belongs to it by 
virtue of its specialisation. And if it be asked how this conformity is 
manifested, the answer is, by the quality, intensity, duration, and ex- 
tension of the response, in all which respects vision serves as so good an 
example, that we can readily understand how it happened that it was in 
this field that the relation between response and stimulus was first 
clearly recognised. I need scarcely say that, however interesting it 
might be to follow out the lines of inquiry thus indicated, we can- 
not attempt it this evening. All that I can do is to mention one or two 
recent observations which, while they serve as illustrations, may perhaps 
be sufficiently novel to interest even those who are at home in the subject. 



ADDRESS. 17 

Probably everyone is acquainted with some of tlie familiar proofs that 
an object is seen for a much longer period than it is actually exposed to 
view ; that the visual reaction lasts much longer than its cause. More 
precise observations teach us that this response is regulated accordino- to 
laws which it has in common with all the higher functions of an organism. 

If, for example, the cells in the brain of the torpedo are 'let off' 

that is, awakened by an external stimulus — the electrical discharo-e 
which, as in the case of vision, follows after a certain interval, lasts a 
certain time, first rapidly increasing to a maximum of intensity, then 
more slowly diminishing. In like manner, as regards the visual appa- 
ratus, we have, in the response to a sudden invasion of the eye by lio-ht, a 
rise and fall of a similar character. In the case of the electrical organ 
and in many analogous instances, it is easy to investigate the time rela- 
tions of the successive phenomena, so as to represent them graphically. 
Again, it is found that in many physiological reactions, the period of 
rising ' energy ' (as Helmholtz called it) is followed by a period during 
which the responding structure is not only inactive, but its capacity for 
energising is so completely lost that the same exciting cause which a 
moment before 'let off' the characteristic response is now without effect. 
As regards vision, it has long been believed that these general charac- 
teristics of physiological reaction have their counterpart in the visual 
process, the most striking evidence being that in the contemplation of a 
lightning flash — or, better, of an instantaneously illuminated white disc ' — 
the eye seems to receive a double stroke, indicating that, althouo-h the 
stimulus is single and instantaneous, the response is reduplicated. The 
most precise of the methods we until lately possessed for investigating 
the wax and wane of the visual reaction, were not only difficult to carry 
out but left a large margin of uncertainty. It was therefore particularly 
satisfactory when M. Charpentier, of Nancy, whose merits as an in- 
vestigator are perhaps less known than they deserve to be, devised an 
experiment of extreme simplicity which enables us, not only to observe, 
but to measure with great facility both phases of the reaction. It is 
difficult to explain even the simplest apparatus without diagrams ; you 
will, however, understand the experiment if you will imagine that you 
are contemplating a disc, like those ordinarily used for colour mixino- ; 
that it is divided by two radial lines which diverge from each other at 
an angle of 60° ; that the sector which these lines enclose is white, the 
rest black ; that the disc revolves slowly, about once in two seconds. 
You then see, close to the front edge of the advancing sector, a black 
bar, followed by a second at the same distance from itself but much 
fainter. Now the scientific value of the experiment consists in this, that 
the angular distance of the bar from the black border is in proportion 
to the frequency of the revolutions — the faster the wider. If, for 

' The phenomenon is best seen when, in a dark room, the light of a luminous 
spark is thrown on to a white screen with the aid of a suitable lens. 

1893. n 



18 REPORT 1893. 

example, when the disc makes half a revolution in a second the dis- 
tance is ten degrees, this obviously means that when light bursts into 
the eye, the extinction happens one-eighteenth of a second after the 
excitation.' 

The fact thus demonstrated, that the visual reaction consequent on an 
instantaneous illumination exhibits the alternations I have described, has 
enabled M. Charpentier to make out another fact in relation to the visual 
reaction which is, I think, of equal importance. In all the instances, 
excepting the retina, in which the physiological response to stimulus has 
a definite time-limitation, and in so far resembles an explosion — in other 
words, in all the higher forms of specific energy, it can be shown experi- 
mentally that the process is propagated from the jiart first directly acted 
on to other contiguous parts of similar endowment. Thus in the simplest 
of all known phenomena of this kind, the electrical change, by which the 
leaf of the Dion^a plant responds to the slightest touch of its sensitive 
hairs, is propagated from one side of the leaf to the other, so that in the 
opposite lobe the response occui'S after a delay which is proportional to 
the distance between the spot excited and the spot observed. That in 
the retina there is also such propagation has not only been surmised from 
analogy, but inferred from certain observed facts. M. Charpentier has 
row been able by a method which, although simple, I must not attempt 
to describe, not only to prove its existence, but to measure its rate of 
progress over the visual field. 

There is another aspect of the visual response to the stimulus of light 
which, if I am not trespassing too long on your patience, may, I think, be 
interesting to consider. As the relations between the sensations of colour 
and the physical properties of the light which excites them, are among the 
most certain and invariable in the whole range of vital reactions, it is 
obvious that they afford as fruitful a field for physiological investigation 
as those in which white light is concerned. We have on one side 
physical facts, that is, wave-lengths or vibration-rates; on the other, 
facts in consciousness — namely, sensations of colour — so simple that 
notwithstanding their subjective character there is no difficulty in 
measuring either their intensity or their duration. Between these there 
are lines of influence, neither physical nor psychological, which pass from 
the former to the latter through the visual apparatus (retina, nerve, 
brain). It is these lines of influence which interest the physiologist. 
The structure of the visual apparatus afiTords us no clues to trace them 
by. The most important fact we know about them is that they must be 
at least three in number. 

It has been lately assumed by some that vision, like every other 
specific energy, having been developed progressively, objects were seen 

' Charpentier, ' Reaction oscillatoire de la Retine sous I'influence des excitations 
lumineuses,' Arclivres de Pltysiol., vol. sxiv. p. 541, and Propagation de V action 
oscillatoire, ice, p. 362. 



ADDRESS. 19 

by the most elementary forms of eye only in chiaroscuro, that afterwards 
some colours were distinguished, eventually all. As regards hearino- it 
is so. The organ which, on structural grounds, we consider to represent 
that of hearing in animals low in the scale of organisation — as, e.g., 
in the Ctenopliora — has nothing to do with sound, • but confers on its 
possessor the power of judging of the direction of its own movements in 
the water in which it swims, and of guiding these movements accordingly. 
In the lowest vertebrates, as, e.g., in the dogfish, although the auditory 
apparatus is much more complicated in structure, and plainly corresponds 
with our own, we still find the particular part which is concerned in 
hearing scarcely traceable. All that is provided for is that sixth sense, 
which the higher animals also possess, and which enables them to judge 
of the direction of their own movements. But a stage higher in the 
vertebrate series we find the special mechanisms by which we ourselves 
appreciate sounds beginning to appear — not supplanting or taking the 
place of the imperfect organ, but added to it. As regards hearing, 
therefore, a new function is acquired without any transformation or 
fusion of the old into it. We ourselves possess the sixth sense, by which 
we keep our balance and which serves as the guide to our bodily move- 
ments. It resides in the part of the internal ear which is called the 
labyrinth. At the same time we enjoy along with it the possession of the 
cochlea, that more complicated apparatus by which we are able to hear 
sounds and to discriminate their vibration-rates. 

As regards vision, evidence of this kind is wanting. There is, so far 
as I know, no proof that visual organs which are so imperfect as to be 
inca.pable of distinguishing the forms of objects, may not be affected 
differently by their colours. Even if it could be shown that the least 
perfect forms of eye possess only the power of discriminating between 
light and darkness, the question whether in our own such a faculty exists 
separately from that of distinguishing colours is one which can only be 
settled by experiment. As in all sensations of colour the sensation of 
brightness is mixed, it is obvious that one of the first points to be deter, 
mined is whether the latter represents a ' specific energy ' or merely a 
certain combination of specific energies which are excited by colours. 
The question is not whether there is such a thing as white lio-ht, but 
whether we possess a separate faculty by which we judge of lio-ht and 
shade — a question which, although we have derived our knowledge of it 
chiefly from physical experiment, is one of eye and brain, not of wave- 
lengths or vibration-rates, and is therefore essentially physiological. 

There is a Grerman proverb which says, 'Bei Nacht sind alle Katzen 
grau.' The fact which this proverb expresses presents itself experiment- 
ally when a spectrum projected on a white surface is watched, while the 

' Verworn, ' Gleichgewicht u. Otolithenorgan,' Pjtiiger's Arcldv, vol. 1. p. 423 ; 
also Ewald's researches on the Labyrinth as a Sense-organ ( Ueher das Endorgan 
des Nervus octavtts, Wiesbaden, 1892). 

c 2 



20 EEPOKT— 1893. 

intensity of the light is gradually diminished. As the colours fade away 
they become indistinguishable as such, the last seen being the primary 
red and green. Finally they also disappear, but a grey band of light 
still remains, of which the most luminous part is that which before was 
green.' Without entering into details, let us consider what this tells us 
of the specific energy of the visual apparatus. Whether or not the 
faculty by which we see grey in the dark is one which we possess in 
common with animals of imperfectly developed vision, there seems little 
doubt that there are individuals of our own species who, in the fullest 
sense of the expression, have no eye for colour ; in whom all colour sense 
is absent ; persons who inhabit a world of grey, seeing all things as they 
might have done had they and their ancestors always lived nocturnal 
lives. In the theory of colour vision, as it is commonly stated, no reference 
is made to such a faculty as we are now discussing. 

Professor Hering, whose observations as to the diminished spectrum 
I referred to just now, who was among the first to subject the vision of 
the totally colour-blind to accurate examination, is of opinion, on that 
and on other grounds, that the sensation of light and shade is a specific 
faculty. Very recently the same view has been advocated on a wide basis 
by a distingaished psychologist, Professor Ebbinghaus.'^ Happily, as 
regaids the actual experimental results relating to both these main 
subjects, there seems to be a complete coincidence of observation between 
observers who interpret them differently. Thus the recent elaborate 
investigations of Captain Abney ^ (with General Festing), representing 
graphically the results of his measurements of the subjective values of 
the difi'erent parts of the diminished spectrum, as well as those of the 
fully illuminated spectrum as seen by the totally colour-blind, are in the 
closest accord with the observations of Hering, and have, moreover, been 
substantially confirmed in both points by the measurements of Dr. Konig 
in Helmholtz' laboratory at Berlin.'* That observers of such eminence 
as the three persons whom I have mentioned, employing different methods 
and with a different purpose in view, and without reference to each 
other's work, should arrive in so complicated an inquiry at coincident 
results, augurs well for the speedy settlement of this long-debated 
question. At present the inference seems to be that such a specific 
energy as Hering's theory of vision postulates actually exists, and that 
it has for associates the colour-perceiving activities of the visual appa- 
ratus, provided that these are present ; but that whenever the intensity 

1 Hering, ' Dntersuch. eines total Farbenblinden,' PJiuger's Arch., vol. xlix., 1891, 
p. 5(53. 

2 Ebbinghaus, ' Theorie des Farbensehens,' Zeitschr.f. Psychol., vol. v., 1893, p. 145. 
' Abnej and Festing, Colour Photometry, Part III. Phil. Trans., vol. clxxxiiiA, 

1891. p. 531. 

* Kinig, ' Ueber den Helligkeitswerth der Spectralfarben bei verschiedener 
absobiter Intensitiit,' Beitrdge zur Psychologic, &c., ' Festschrift zu H. von Helmholtz,' 
Siebzigsten Geburtstage,' 1891, p. 309. 



ADDRESS. 21 

of the illumination is below the chromatic threshold — that is, too feeble 
to awaken these activities — or when, as in the totally colour-blind, they 
are wanting, it manifests itself independently ; all of which can be most 
easily understood on such a hypothesis as has lately been suggested in 
an ingenious paper by Mrs. Ladd Franklin, > that each of the elements of 
the visual apparatus is made up of a central structure for the sensation 
of light and darkness, with collateral appendages for the sensations of 
colour — it being, of course, understood that this is a mere diagrammatic 
representation, which serves no purposes beyond that of facilitating 
the conception of the relation between the several ' specific energies.' 

EXPEEIMENTAL PSYCHOLOGY. 

Resisting the temptation to pursue this subject further, I will now ask 
you to follow me into a region which, although closely connected with 
the subjects we have been considering, is beset with greater difficulties — - 
the subject in which, under the name of Physiological or Experimental 
Psychology, physiologists and psychologists have of late years taken a 
common interest — a borderland not between fact and fancy, but between 
two methods of investigation of questions which are closely related, 
which here, though they do not overlap, at least interdigitate. It is 
manifest that, quite irrespectively of any foregone conclusion as to the 
dependence of mind on processes of which the biologist is accustomed to 
take cognizance, mind must be regarded as one of the ' specific energies ' 
of the organism, and should on that ground be included in the subject- 
matter of physiology. As, however, our science, like other sciences, is 
limited not merely by its subject but also by its method, it actually takes 
in only so much of psychology as is experimental. Thus sensation, 
although it is psychological, and the investigation of its relation to the 
special structures by which the mind keeps itself informed of what goes 
on in the outside world, have always been considered to be in the physio- 
logical sphere. And it is by anatomical researches relating to the 
minute structure and to the development of the brain, by observation 
of the facts of disease, and, above all, by physiological experiment, 
that those changes in the ganglion cells of the brain and spinal cord 
which are the immediate antecedents of every kind of bodily action have 
been traced. Between the two — that is, between sensation and the 
beginning of action — there is an intervening region which the physio- 
logist has hitherto willingly resigned to psychology, feeling his incompe- 
tence to use the only instrument by which it can be explored — that of 
introspection. This consideration enables us to understand the course 
which the new study (I will not claim for it the title of a new science, 
regarding it as merely a part of the great science of life) has hitherto 

' Christine Ladd Franklin, ' Eine neue Theorie der Lichtempfindungen,' Zcitsclir. 
fur Psychologie, vol. iv., 1893, p. 211 ; see also the Proceedings of the last Psycho- 
logical Congress in London, 1892. 



22 REPORT— 1893. 

followed, and why physiologists have been unwilling to enter on it. The 
study of the less complicated internal relations of the organism has 
afforded so many difficult problems that the most difficult of all have 
been deferred ; so that although the psycho-physical method was initiated 
by E. H. Weber in the middle of the present century, by investigations ' 
which formed part of the work done at that epoch of discovery, and 
although Professor Wnndt, also a physiologist, has taken a larger share in 
the more recent development of the new study, it is chiefly by psycho- 
logists that the researches which have given to it its importance as a new 
discipline have been conducted. 

Although, therefore, experimental psychology has derived its methods 
from physical science, the result has been not so much that ^physiologists 
have become philosophers, as that philosophers have become experimental 
psychologists. In our own universities, in those of America, and still 
more in those of Germany, psychological students of mature age are to 
be found who are willing to place themselves in the dissecting-room side 
by side with beginners in anatomy, in order to acquire that exact know- 
ledge of the framework of the oi-ganism without which no man can 
understand its working. Those, therefore, who are apprehensive lest the 
regions of mind should be invaded by the insaniens sainentia of the 
laboratory, may, I think, console themselves with the thought that the 
invaders are for the most part men who before they became laboratory 
workers had already given their allegiance to philosophy ; their purpose 
being not to relinquish definitively, but merely to lay aside for a time, 
the weapons in the use of which they had been trained, in order to learn 
the use of ours. The motive that has encouraged them has not been any 
hope of finding an experimental solution of any of the ultimate problems 
of philosophy, but the conviction that, inasmuch as the relation between 
mental stimuli and the mental processes which they awaken is of the 
same order with the relation between every other vital process and its 
specific determinant, the only hope of ascertaining its nature must lie in 
the employment of the same methods of comparative measurement which 
the biologist uses for similar purposes. Not that there is necessarily 
anything scientific in mere measurement, but that measurement affords 
the only means by which it can be determined whether or not the same 
conformity in the relation between stimulus and reaction which we have 
accepted as the fundamental characteristic of life, is also to be found in 
mind, notwithstanding that mental processes have no known physical 
concomitants. The results of experimental psychology tend to show 
that it is so, and consequently that in so far the processes in question are 
as truly functions of organism as the contraction of a muscle, or as the 
changes produced in the retinal pigment by light. 

I will make no attempt even to enumerate the special lines of inquiry 

' Weber's researches were published in Wagner's Handrvorterhucli , I think, ir» 
1849, 



ADDRESS. 23 

•which during the last decade have been conducted with such vigour in 
all parts of the world, all of them traceable to the influence of the 
Leipzig school ; but will content myself with saying that the general 
purpose of these investigations has been to determine with the utmost 
atlainable precision the nature of psychical relations. Some of these 
investigations begin with those simpler reactions which more or less 
resemble those of an automatic mechanism, proceeding to those in which 
the resulting action or movement is modified by the influence of auxiliary 
or antagonistic conditions, or changed by the simultaneous or antecedent 
action on the reagent of other stimuli, in all of which cases the efi'ect 
can be expressed quantitatively ; others lead to results which do not so 
readily admit of measurement. In pursuing this course of inquiry the 
physiologist finds himself as he proceeds more and more the coadjutor 
of the psychologist, less and less his director; for whatever advantage 
the former may have in the mere technique of observation, the things 
with which he has to do are revealed only to introspection, and can be 
studied only by methods which lie outside of his sphere. I might in 
illustration of this refer to many recent experimental researches — such, 
for example, as those by which it has been sought to obtain exact data 
as to the physiological concomitants of pleasure and of pain, or as to the 
influence of weariness and recuperation, as modifiers of psychological 
reactions. Another outwork of the mental citadel which has been 
invaded by the experimental method is that of memory. Even here it 
can be shown that in the comparison of transitory as compared with 
permanent memory — as, for example, in the getting ofi" by heart of a 
wholly uninteresting series of words, with subsequent oblivion and 
reacquisition — the labour of acquiring and reacquiring may be measured, 
and consequently the relation between them ; and that this ratio varies 
according to a simple numerical law. 

I think it not unlikely that the only efi'ect of what I have said may 
be to suggest to some of my hearers the question. What is the use of 
such inquiries ? Experimental psychology has, to the best of my 
knowledge, no technical application. The only satisfactory answer I 
can give is that it has exercised, and will exercise in future, a helpful 
infiuence on the science of life. Every science of observation, and each 
branch of it, derives from the peculiarities of its methods certain ten- 
dencies which are apt to predominate unduly. We speak of this as 
specialisation, and are constantly striving to resist its infiuence. The 
most successful way of doing so is by availing ourselves of the counter- 
acting influence which two opposite tendencies mutually exercise when 
they are simultaneous. He that is skilled in the methods of introspec- 
tion naturally (if I may be permitted to say so) looks at the same thing 
from an opposite point of view to that of the experimentahst. It is, 
therefore, good that the two should so work together that the tendency 
of the experimentalist to imagine the existence of mechanism where none 



24 KEPOET— 1893. 

is proved to exist — of the psychologist to approacli the phenomena of 
mind too exclusively from the subjective side^ — may mutually correct and 
assist each other. 

Phototaxis and Chemiotaxis. 

Considering that every organism must have sprung from a unicellular 
ancestor, some have thought that unless we are prepared to admit a 
deferred epigenesis oi mind, we must look for psychical manifestations 
even among the lowest animals, and that as in the protozoon all the 
vital activities are blended together, mind should be present among them 
not merely potentially but actually, though in diminished degree. 

Such a hypothesis involves ultimate questions which it is unneces- 
sary to enter upon : it will, bowever, be of interest in connection with 
our present subject to discuss the phenomena which served as a basis for 
it — those which relate to what may be termed the behaviour of unicellular 
organisms and of individual cells, in so far as these last are capable of 
reacting to external influences. The observations which afford us most 
information are those in which the stimuli employed can be easily 
measured, such as electrical currents, light, or chemical agents in 
solution. 

A. single instance, or at most two, must suffice to illustrate the in- 
fluence of light in directing the movements of freely moving cells, or, as 
it is termed, phototaxis. The rod-like purple organism called by Engel- 
mann Bacterium photometricum ' is such a light-lover that if you place 
a drop of v^ater containing these organisms under the microscope, and 
focus the smallest possible beam of light on a particular spot in the field, 
the spot acts as a light trap and becomes so crowded with the little 
rodlets as to acquire a deep port- wine colour. If instead of making his 
trap of white light, he projected on the field a microscopic spectrum, 
Engelmann found that the rodlets showed their preference for a spectral 
colour whicb is absorbed when transmitted through their bodies. By 
the aid of a light trap of the same kind, the very well-known spindle- 
shaped and flagellate cell of Euglena can be shown to have a similar 
power of discriminating colour, but its preference is different. This 
familiar organism advances with its flagellum forwards, the sharp end of 
the spindle having a red or orange eye point. Accordingly, the light it 
loves is again that which is most absorbed — viz., the blue of the spectrum 
(line f). 

These examples may serve as an introduction to a similar one in 
which the directing cause of movement is not physical but chemical. 
The spectral light trap is used in the way already described ; the or- 

' Engelmann, ' Bacterium photometricum,' Onderzoeli. Physiol. Lab. Utrecht, vol. 
vii. p. 200 ; also ' Ueber Licht- u. Farbenperception niederster Organismen,' PflUger's 
Arch., vol. xsix. p. 387. 



ADDRESS. 25 

ganisms to be observed are not coloured, but bacteria of that common 
sort which twenty years ago we used to call Bacterium termo, and which 
is recognised as the ordinary determining cause of putrefaction. These 
organisms do not care for light, but are great oxygen-lovers. Conse- 
quently, if you illuminate with your spectrum a filament of a confervoid 
alga, placed in water containing bacteria, the assimilation of carbon and 
consequent disengagement of oxygen are most active in the part of the 
filament which receives the red rays (b to c). To this part, therefore, 
where there is a dark band of absorption, the bacteria which want 
oxygen are attracted in crowds. The motive which brings them together 
is their desire for oxygen. Let us compare other instances in which the 
source of attraction is food. 

The Plasmodia of the myxomycetes, particularly one which has been 
recently investigated by Mr. Arthur Lister,' may be taken as a typical 
instance of what may be called the chemical allurement of living proto- 
plasm. In this organism, which in the active state is an expansion of 
labile living material, the delicacy of the reaction is comparable to that 
of the sense of smell in those animals in which the olfactory organs are 
adapted to an aquatic life. Just as, for example, tlie dogfish is attracted 
by food which it cannot see, so the plasmodium of Badhamia becomes 
aware, as if it smelled it, of the presence of its food — a particular kind of 
fungus. I have no diagram to explain this, but will ask you to imagine 
an expansion of living material, quite structureless, spreading itself 
along a wet surface ; that this expansion of transparent material is 
bounded by an irregular coast-line ; and that somewhere near the coast 
there has been placed a fragment of the material on which the Badhamia 
feeds. The presence of this bit of Stereum produces an excitement at 
the part of the plasmodium next to it. Towards this centre of activity 
streams of living material converge. Soon the afHux leads to an out- 
growth of the Plasmodium, which in a few minutes advances towards the 
desired fragment, envelopes, and incorporates it. 

May I give you another example also derived from the physiology of 
plants ? Very shortly after the publication of Engelmann's observations 
of the attraction of bacteria by oxygen, PfeSer made the remarkable 
discovery that the movements of the antherozoids of ferns and of mosses 
are guided by impressions derived from chemical sources, by the allure- 
ment exercised upon them by certain chemical substances in solution — 
in one of the instances mentioned by sugar, in the other by an organic 
acid. The method consisted in introducing the substance to be tested, 
in any required strength, into a minute capillary tube closed at one end, 
and placing it under the microscope in water inhabited by antherozoids, 
which thereupon showed their predilection for the substance, or the 
contrary, by its effect on their movements. In accordance with the 

' Lister, ' On the Plasmodium of Badhamia utricularis, &c.,' Annals of Botany, 
No. 5, June 1888. 



26 REPORT — 1893. 

principle followed in experimental psychology, Pfeffer ' made it his object 
to determine, not the relative effects of different doses, but the smallest 
perceptible increase of dose which the organism was able to detect, with 
this result — that, just as in measurements of the relation between stimulus 
and reaction in ourselves we find that the sensational value of a stimulus 
depends, not on its absolute intensity, but on the ratio between that 
intensity and the previous excitation, so in this simplest of vital reagents 
the same so-called psycho-physical law manifests itself. It is not, how- 
ever, with a view to this interesting relation that I have referred to 
Pfeffer's discovery, but because it serves as a centre around which other 
phenomena, observed alike in plants and animals, have been grouped. 
As a general designation of reactions of this kind Pfefifer devised the 
term Chemotaxis, or, as we in England prefer to call it, Chemiotaxis. 
Pfeffer's contrivance for chemiotactic testing was borrowed from the 
pathologists, who have long used it for the purpose of determining the 
relation between a great variety of chemical compounds or products, and 
the colourless corpuscles of the blood. I need, I am sure, make no 
apology for referring to a question which, although purely pathological, 
is of very great biological interest — the theory of the process by which, 
not only in man, but also, as Metschnikoff has strikingly shown, in 
animals far down in the scale of develc»pment, the organism protects 
itself against such harmful things as, whether particulate or not, are able 
to penetrate its framework. Since Cohnheim's great discovery in 1867 
we have known that the central phenomenon of what is termed by 
pathologists inflammation is what would now be called a chemiotactic 
one ; for it consists in the gathering together, like that of vultures to a 
carcase, of those migratory cells which have their home in the blood 
stream and in the lymphatic system, to any point where the living tissue 
of the body has been injured or damaged, as if the products of dis- 
integration which are set free where such damage occurs were attractive 
to them. 

The fact of chemiotaxis, therefore, as a constituent phenomenon of 
the process of inflammation, was familiar in pathology long before it was 
understood. Cohnheim himself attributed it to changes in the channels 
along which the cells moved, and this explanation was generally accepted, 
though some writers, at all events, recognised its incompleteness. But 
no sooner was Pfeffer's discovery known than Leber,^ who for years had 
been working at the subject from the pathological side, at once saw that 
the two processes were of similar nature. Then followed a variety of 
researches of great interest, by which the importance of chemiotaxis in 
relation to the destruction of disease-producing microphytes was proved, 

' Pfeffer, Untersvch a. d. botan. Institute z. Tubingen, vol. i., part 3, 1884. 
- Leber, ' Die Anhaufung der Leucocj'ten am Orte des Entziindungsreizes,' &c. 
Die EntstehuTig der Enstiinduvg, &c., pp. 423-464, Leipzig, 1891. 



ADDRESS. 27 

that of Bucliner ' on the chemical excitability of leucocytes being 
among the most important. Mnch discussion has taken place, as many 
present are aware, as to the kind of wandering cells, or leucocytes, 
which in the first instance attack morbific microbes, and how they deal 
with them. The question is not by any means decided. It has, however, 
I venture to think, been conclusively shown that the process of destruc- 
tion is a chemical one, that the destructive agent has its source in the 
chemiotactic cells — that is, cells which act under the orders of chemical 
stimuli. Two Cambridge observers, Messrs. Kanthack and Hardy,- have 
lately shown that, in the particular instance which they have investigated, 
the cells which are most directly concerned in the destruction of morbific 
bacilli, aUhough chemiotactic, do not possess the power of incorporating 
either bacilli or particles of any other kind. While, therefore, we must 
regard the relation between the process of devitalising and that of 
incorporating as not yet sufficiently determined, it is now no longer 
possible to regard the latter as essential to the former. 

There seems, therefore, to be very little doubt that chemiotactic cells are 
among the agents by which the human or animal organism protects itself 
against infection. There are, however, many questions connected with 
this action which have not yet been answered. The first of these are 
chemical ones — that of the nature of the attractive substance and that 
of the process by which the living carriers of infection are destroyed. 
Another point to be determined is how far the process admits of adapta- 
tion to the pai'ticular infection which is present in each case, and to the 
state of liability or immunity of the infected individual. The subject is 
therefore of great complication. None of the points I have suggested 
can be settled by experiments in glass tubes such as I have described to 
you. These serve only as indications of the course to be followed in 
much more complicated and difficult investigations — when we have to do 
with acute diseases as they actually afiTect ourselves or animals of similar 
liabilities to ourselves, and find ourselves face to face with the question 
of their causes. 

It is possible that many members of the Association are not aware of 
the unfavourable — I will not say discreditable — position that this country 
at present occupies in relation to the scientific study of this great sub- 
ject — the causes and mode of prevention of infectious diseases. As 
regards administrative efficiency in matters relating to public health 
England was at one time far ahead of all other countries, and still re- 
tains its superiority ; but as regards scientific knowledge we are, in this 
subject as in others, content to borrow from our neighbours. Ihose who 
desire either to learn the methods of research or to carry out scientific 

' Buchner, 'Die chem. Reizbarkeit der liencocyten,' Sec, Berlitier Mi ii. Wuok., 1890^ 
1^0. 17. 

^ Kanthack and Hardy, ' On the Characters and Behaviour of the Wandering Cells- 
of the Frog,' Proceedings of the Boyal Society, vol. lii. p. 267. 



28 REPORT — 1893. 

inquiries have to go to Berlin, to Munich, to Breslau, or to the Pasteur 
Institute in Pai-is to obtain what England ought long ago to have pro- 
vided. For to us, from the spread of our race all over the world, the 
prevention of acute infectious diseases is more important than to any 
other nation. At the beginning of this address I urged the claims of 
pure science. If I could, I should feel inclined to speak even more 
strongly of the application of science to the discovery of the causes of 
acute diseases. May I express the hope that the effort which is now 
being made to establish in England an Institution for this purpose not 
inferior in efficiency to those of other countries, may have the sympathy 
of all present ? And now may I ask your attention for a few moments 
more to the subject that more immediately concerns us ? 



CONCLBSION. 

The purpose which I have bad in view has been to sbow that there 
is one principle — that of adaptation — which separates biology from the 
exact sciences, and that in the vast field of biological inquiry the end we 
have is not merely, as in natural philosophy, to investigate the relation 
between a phenomenon and the antecedent and concomitant conditions 
on which it depends, but to possess this knowledge in constant reference 
to the interest of the organism. It may perhaps be thought that this 
way of putting it is too teleological, and that in taking, as it were, as 
my text this evening so old-fashioned a biologist as Treviranus, I am 
yielding to a retrogressive tendency. It is not so. What I have desired 
to insist on is that organism is a fact which encounters the biologist at 
every step in his investigations ; that in referring it to any general 
biological principle, such as adaptation, we are only referring it to itself, 
not explaining it ; that no explanation will be attainable until the con- 
ditions of its coming into existence can be subjected to experimental 
investigation so as to correlate them with those of processes in the non- 
living world. 

Those who were present at the meeting of the British Association at 
Liverpool will remember that then, as well as at some subsequent meet- 
ings, the question whether the conditions necessary for such an inquiry 
could be realised was a burning one. This is no longer the case. The 
patient endeavours which were made about that time to obtain experi- 
mental proof of what was called abiogenesis, although they conduced 
materially to that better knowledge which we now possess of the con- 
ditions of life of bacteria, failed in the accomplishment of their purpose. 
The question still remains undetermined ; it has, so to speak, been ad- 
journed sine die. The only approach to it lies at present in the inves- 
tigation of those rare instances in which, although the relations between 
a living organism and its environment ceases as a watch stops when it 



ADDRESS. 29 

ha3 not been wound, these relations can be re-established — the process of 
life re-awakened — by the application of the required stimulus. 

I was also desirous to illustrate the relation between physiology 
and its two neighbours on either side, natural philosophy (including 
chemistry) and psychology. As regards the latter I need add nothing 
to what has already been said. As regards the foi-mer, it may be well 
to notice that although physiology can never become a mere branch of 
applied physics or chemistry, there are parts of physiology wherein 
the principles of these sciences may be applied directly. Thus, in the 
beginning of the century, Young applied his investigations as to the move- 
ments of liquids in a system of elastic tubes, directly to the phenomena 
of the circulation ; and a century before, Borelli successfully examined the 
mechanisms of locomotion and the action of muscles, without reference to 
any, excepting mechanical principles. Similarly, the foundation of our 
present knowledge of the process of nutrition was laid in the researches 
of Bidder and Schmidt, in 1851, by determinations of the weight and 
composition of the body, the daily gain of weight by food or oxygen, the 
daily loss by the respiratory and other discharges, all of which could be 
accomplished by chemical means. But in by far the greater number of 
physiological investigations, both methods (the physical or chemical and 
the physiological) must be brought to bear on the same question — to co- 
operate for the elucidation of the same problem. In the researches, for 
example, which during several years have occupied Professor Bohr, of 
Copenhagen, relating to the exchange of gases in respiration, he has 
shown that factors purely physical — namely, the partial pressures of 
oxygen and carbon dioxide in the blood which flows through the pul- 
monary capillaries — are, so to speak, interfered with in their action by the 
' specific energy ' of the pulmonary tissue, in such a way as to render this 
fundamental process, which, since Lavoisier, has justly been regarded as 
one of the most important in physiology, much more complicated than we 
for a long time supposed it to be. In like manner Heidenhain has proved 
that the process of lymphatic absorption, which before we regaided as 
dependent on purely mechanical causes — i.e., differences of pressure — is 
in great measure due to the specific energy of cells, and that in various 
processes of secretion the principal part is not, as we were inclined not 
many years ago to believe, attributable to liquid diffusion, but to the same 
agency. I wish that there had been time to have told you something of 
the discoveries which have been made in this particular field by Mr. 
Langley, who has made the subject of 'specific energy' of secreting-cells 
his own. It is in investigations of this kind, of which any number of 
examples could be given, in which vital reactions mix themselves up with 
physical and chemical ones so intimately that it is difficult to draw the 
line between them, that the physiologist derives most aid from what- 
ever chemical and physical training he may be fortunate enough to 
possess. 



30 EEPOET— 1893. 

There is, tberefore, no doubt as to the advantages which physiology 
derives from the exact sciences. It could scarcely be averred that they 
would benefit in anything like the same degree from closer association 
with the science of life. Nevertheless, there are some points in respect ot 
which that science may have usefully contributed to the advancement of 
physics or of chemistry. The discovery of Graham as to the characters 
of colloid substances, and as to the dififusion of bodies in solution through 
membranes, would never have been made had not Graham ' ploughed,' so 
to speak, ' with our heifer.' The relations of certain colouring matters to 
oxygen and carbon dioxide would have been unknown, had no experiments 
been made on the respii'ation of animals and the assimilative process in 
plants ; and, similarly, the vast amount of knowledge which relates to the 
chemical action of ferments must be claimed as of physiological origin. 
So also there are methods, both physical and chemical, which were 
originally devised for physiological purposes. Thus the method by which 
meteorological phenomena are continuously recorded graphically, origi- 
nated from that used by Ludwig (1847) in his ' Researches on the Circula- 
tion ' ; the mercurial pump, invented by Lothar Meyer, was perfected in 
the physiological laboratories of Bonn and Leipzig ; the rendering the 
galvanometer needle aperiodic by damping was first realised by du Bois- 
Reymond — in all of which cases invention was prompted by the require- 
ments of physiological researcb. 

Let me conclude with one more instance of a diiferent kind, which 
may serve to show how, perhaps, the wonderful ingenuity of contrivance 
which is displayed in certain organised structures — the eye, the ear, or 
the organ of voice — may be of no less interest to the physicist than to the 
physiologist. Johannes Miiller, as is well known, explained the com- 
pound eye of insects on the theory that an erect picture is formed on the 
convex retina by the combination of pencils of light, received from 
different parts of the visual field through the eyelets (ommatidia) 
directed to them. Years afterwards it was shown that in each eyelet an 
image is foi-med which is reversed. Consequently, the mosaic theory of 
Miiller was for a long period discredited on the ground that an erect 
picture could not be made up of ' upside-down ' images. Lately the 
subject has been reinvestigated, with the result that the mosaic theory 
has regained its authority. Professor Exner ^ has proved photographically 
that behind each part of the insect's eye an erect picture is formed of 
the objects towards which it is directed. There is, therefore, no longer 
any difficulty in understanding how the whole field of vision is mapped 
out as consistently as it is imaged on our own retina, with the difference, 
of course, that the picture is erect. But behind this fact lies a physical 
question — that of the relation between the erect picture which is photo- 
graphed and the optical structure of the crystal cones which produce it — 

' Exner, Die Pliysiologie dcr facettirten Augen von Krehsen u. Insecten, Leipzig, 
1891. 



ADDRESS. 31 

a question which, although we cannot now enter upon it, is quite as 
interesting as the physiological one. 

With this history of a theory which, after having been for thirty 
years disbelieved, has been reinstated by the fortunate combination of 
methods derived from the two sciences, I will conclude. It may serve 
to show how, thougli physiology can never become a part of natural 
philosophy, the questions we have to deal with are cognate. Without 
forgetting that every phenomenon has to be regarded with reference to 
its useful purpose in the organism, the aim of the physiologist is not to 
inquire into final causes, but to investigate processes. His question is 
ever How, rather than Why. 

May I illustrate this by a simple, perhaps too trivial, story, which 
derives its interest from its having been told of the childhood of one of the 
greatest natural philosophers of the present century ? ' He was even 
then possessed by that insatiable curiosity which is the first quality of 
the investigator ; and it is related of him that his habitual question was 
' What is the go of it ? ' and if the answer was unsatisfactory, ' What is 
the particular go of it ? ' That North Country boy became Professor 
Clerk Maxwell. The questions he asked are those which in our various 
ways we are all. trying to answer. 

' Zi/e of Clerk Maxnell (Campbell and Garnett), 1882, p. 28. 



EBPOETS 



ON THE 



STATE OF SCIENCE, 



1893. 



EEPORTS 



ON THE 



STATE OF SCIENCE. 



Corresponding Societies. — Report of the Committee, consisting of 
Professor K. Meldola {Chairman), Mr. T. V. Holmes (Secre- 
tary), Mr. Fkancis Gtalton, Sir Douglas Gtalton, Sir Eawson 
Eawson, Mr. Gr. J. Symons, Dr. J. Gr. Gtarson, Sir John Evans, 
Mr. J. HoPKiNSON, Professor T. Gr. Bonnet, Mr. W. Whitaker, 
Mr. W. ToPLEY, Professor E. B. Poulton, Mr. Cothbert Peek, 
and Eev. Canon H. B. Tristram. 

The Corresponding Societies Committee of the British Association beg 
leave to submit to the General Committee the following report of the 
proceedings of the Conference held at Edinburgh. 

The Council nominated Professor Raphael Meldola, F.R.S., Chair- 
man, Mr. G. J. Sjmons, F.R.S., Vice- Chairman, and Mr. T. V. Holmes, 
F.G.S., Secretary to the Conference. These nominations were confirmed 
by the General Committee at the meeting held at Edinburgh on Wednes- 
day, August 3. The meetings of the Conference were held on Thursday, 
August 4, and on Tuesday, August 9, at 3.30, in the Justiciary Court. 
The following Corresponding Societies, out of the sixty on the list, 
nominated delegates to represent them at the Edinburgh meeting : — ■ 

Bath Natural History and Antiquarian Rev. H. H. Winwood, M.A., 

Field Club. F.G.S. 

Belfast Natural History and Philosophi- Mr. Alexander Tate. 

cal Society. 

Belfast Natmalists' Field Club . . Mr. Wm. Gray, M.R.I.A. 

Birmingliam Natural History and Micro- Mr. Charles Pumphrey. 

scopical Society. 

Birmingham Philosophical Society . . Mr. J. Kenward, F.S.A. 

Bristol Naturalists' Society . . . Prof. Sydney Young, D.Sc. 

Burton-on-Trent Natural History and Mr. A. L. Stern, B.Sc. 

ArchiEological Society. 

Cardiff Naturalists' Society . . . Mr. T. H. Thomas. 

Chester Society of Natural Science . Mr. A. O. Walker, F.L.S. 

Chesterfield and Midland Counties Insti- Mr. M. H. Mills, F.G.S. 

tution of Engineers. 

D 2 



36 



EEPOBT 1893. 



Croydon Microscopical and Natural His- 
tory Club. 

Cumberland and Westmorland Associa- 
tion for the Advancement of Literature 
and Science. 

Dorset Natural History and Antiquarian 
Field Club. 

East Kent Natural History Society . 

East of Scotland Union of Naturalists' 
Societies. 

Essex Field Club 

Federated Institution of Mining Engi- 
neers. 

Glasgow, The Geological Society of . 

Hants Field Club 

Hertfordshire Natural History Society 
and Field Club. 

Inverness Scientific Society and Field 
Club. 

Isle of Man Natural History and Anti- 
quarian Society. 

Leeds Geological Association . 

Liverpool Engineering Society 

Liverpool Geographical Society 

Liverpool Geological Society . 

Malton Field Naturalists' and Scientific 
Society. 

Manchester Geographical Society . 

Manchester Geological Society 

Midland Union of Natural History Socie- 
ties. 

North of England Institute of Mining 
Engineers. 

North StafEordshire Naturalists' Field 
Club and Archfeological Society. 

Northamptonshire Natural History So- 
ciety. 

Paisley Philosophical Institution 

Perthshire Society of Natural Science 

Kochdale Literary and Scientific Society 

Somersetshire Archaeological and Natural 
History Society. 

Tyneside Geographical Society 

Warwickshire Naturalists' and Archaeo- 
logists' Field Club. 

Woolhope Naturalists' Field Club . 

Yorkshire Geological and Polytechnic 
Society. 

Yorkshire Naturalists' Union . 



Mr. Thos. Cashing, F.R.A.S. 
Mr. J. G. Goodchild, F.G.S. 

Mr. Morton G. Stuart, M.A. 

Mr. A. S. Reid, M.A., F.G.S. 
Mr. Robert Brown, R.N. 

Mr. T. V. Holmes, F.G.S. 
Mr. M. H. Mills, F.G.S. 

Mr. James Barclay Murdoch. 

Rev. A. G. Joyce. 

Dr. John Morison, F.G.S. 

Mr. John Home, F.R.S.E. 

Mr. P. M. C. Kermode. 

Mr. B. Holgate, F.G.S. 
Mr. G. P. Deacon, M.Inst.C.E. 
Mr. Jas. Irvine, F.R.G.S. 
Mr. G. H. Morton, F.G.S. 
Mr. M. B. Slater, F.L.S. 

Mr. Eli Sowerbutts, F.R.G.S. 
Mr. Mark Stirrup, F.G.S. 
Dr. T. Stacey Wilson, B.Sc. 

Prof. J. H. Merivale, M.A. 

Dr. J. T. Arlidge, M.A. 

Mr. Beeby Thompson, F.G.S. 

Mr. James Clark. 

Mr. Henry Coates, F.R.S.E. 

Mr. W. Watts, F.G.S. 

Mr. E. Chisholm Batten, M.A., 

F.R.S.E. 
Mr. G. E. T. Smithson. 
Mr. W. Andrews, F.G.S. 

Rev. J. O. Bevan, M.A. 
Mr. James W. Davis, F.G.S. 

Rev. E. P. Knubley, M.A. 



FIRST CONFERENCE, AUGUST 4, 1892. 

The Corresponding Societies Committee were represented by Professor 
R. Meldola (Chairman), Sir Douglas Galtou, Mr. G. J. Symons, Mr. W. 
Whitaker, Mr. E. B. Ponltou,-Mr. Cuthbert Peek, Dr. Garson, and Mr. 
T. V. Holmes (Secretary). 

The Chairman, after welcoming the delegates to the seventh Confer- 
ence which had been held under the new rules of the Association, said 
durino- the seven years of their existence they had, he ventured to think, 
done some good work for the Association and for themselves. They 



COREESPONDING SOCIETIES. 37 

occupied now in relation to tlie Association very much the same position 
as one of its Sectional Committees, and for that they were very largely 
indebted to Sir Douglas Galton, who had very keenly watched their 
proceedings, and had taken a great interest in them. The report of the 
Committee was then submitted, and the different subjects which had 
engaged attention during the year were dealt with under the heading 
of the Association Sections to which they belong. 

Section A. 

The Chairman introduced the subject of temperature variations in 
lakes, rivers, and estuaries. 

Meteorological FhoiograpJnj. — Mr.Clayden and Mr. Symons spoke of 
the desirability of obtaining photogi'aphs illustrating damage by whirl- 
winds and floods, and Mr. W. Watts (Rochdale) said that the society 
he represented was taking up the subject. Mr. Symons mentioned the 
Helm Wind of Crossfell, and the peculiar cloud accompanying it ; photo- 
graphs of the latter would be useful. Mr. Watts stated that a difficulty 
in photographing the effects of floods arose from the state of the weather 
during their occurrence, and Mr. Cashing (Croydon) exhibited photo- 
graphs of a recent thunderstorm. The Chairman then remarked that 
Mr. Kenward (Birmingham), who was unable to be present, had sent a 
letter stating that for some years in Birmingham meteorological observa- 
tions had been made in the building called ' The Monument.' 

Section B. 

The Chairman mentioned the subject of the conditions of the atmo- 
sphere in manufacturing towns, and Mr. Mark Stirrup (Manchester) and 
Mr. Watts (Rochdale) said that observations and experiments were l3eing 
made thereon in their respective districts. 

Section C. 

Mr. De Ranee (Section C) stated that the Eighteenth Report of the 
Committee on Underground Waters had been read that morning ; that 
the Committee thought it should be reappointed, and that a volume 
containing abstracts of the previous reports should be published. The 
Committee on Coast Erosion hoped to conclude its labours next year. 
The Committee on Erratic Blocks continued to do good work. The 
local societies could do much to assist this committee by noting the 
position of boulders, and by preserving them from destruction. 

Mr. Watts (Rochdale) spoke upon the denudation of high-lying 
drainage areas, and some observations he had made on the amount of 
material brought down by flood waters, and the degree of protection 
given by heather, grass, and peat. He was anxious that other districts 
should take up this inquiry in order that comparisons might be possible. 
In his district he had found that flood water, after a very heavy flood, 
had yielded 900 grains of fine material to the gallon, the material mainly 
consisting of leaves, fibi-es, seed spores, and little bits of peat. 

Dr. H. R. Mill said that something had recently been done in Germany 
to ascertain the amount of sediment in river water. He thought it very 



38 EEPOET — 1893. 

desirable that a series of observations should be made to determine the 
relative values of woodlands and heather in protecting land, and was 
inclined to suggest the formation of a committee for that purpose. Mr. 
Watts said he would be glad to give information as to the method 
followed in Rochdale. 

Geological Photography. — Mr. Jeffs, Secretary to the Photographic 
Committee, being absent, had asked Mr. Arthur S. Reid (East Kent) to 
speak about its work. Mr. Reid said that the number of the photographs 
was about 700. He exhibited a specimen volume of photographs, and 
explained the way in which they were mounted and bound. He thought 
it important that some uniform plan of photographing geological subjects 
should be adopted, and that the plates used should be orthochromatic or 
isochromatic. The Committee had, asked to be reappointed. He hoped 
the delegates would try to make their societies active in this matter. 

Mr. William Gray said that he thought the Belfast Naturalists' Field 
Club had its work fairly well represented by the photographs exhibited. 
They had sent more at first because they then had them in stock ; and 
their quality had improved. They were also photographing antiquities, 
and producing lantern-slides which were very valuable for educational 
purposes. His society had an excellent collection of geological and 
antiquarian lantern-slides which it would be delighted to place at the 
service of any of the other societies, or of any member of the British 
Association interested in educational work. 

Dr. T. Stacey Wilson mentioned that the Birmingham Philosophical 
Society had appointed a sub-committee for geological photography. 

Mr. J. Barclay Murdoch, as Secretary to the Glasgow Geological 
Society, said that his society had not sent in any photographs because it 
had been found difficult to organise the work. He had, however, drawn 
up a preliminary list of localities to be illustrated, and this list had been 
circulated among the members, who were asked to return either photo- 
graphs of the places named or information as to photographs of them 
already existing. 

The Chairman recommended orthochromatic plates. They might be 
more expensive, but they were decidedly preferable for geological photo- 
graphs. 

Section D. 

The Chairman invited remarks on the destruction of native plants and 
of wild birds' eggs. 

I)isap2^earance of Native Plants. — The Rev. E. P. Knubley (Yorks. 
Nat. Union) alluded to the report presented to Section D on this 
subject, which had been drawn up by Mr. D. E. Boyd. In it were men- 
tioned some of the causes leading to the disappearance of native plants, 
such as marine erosion, agricultural drainage, and the growth of towns 
and villages. In addition to these influences were the formation of 
herbaria, the exchange of botanical specimens, the removal of plants 
into gardens, and the large numbers of ferns and other plants exposed 
for sale ; and there were great difficulties in the way of any attempts at 
prohibitive legislation. Many plants had wholly or almost wholly dis- 
appeared from the west of Scotland. Mr. Watts said that two or three 
members of the Rochdale Society proposed to work at this subject. 
Mr. Mark Stirrup had a short paper by Mr. Leo H. Grindon on the dis- 



CORRESPONDING SOCIETIES. 39 

appearance of wild plants in the neighbourhood of Manchester. The 
Chairman thought it might be read at the second Conference. Mr. 
Cuthbert Peek remarked on the great difficulty of obtaining a conviction 
in cases in which ferns and other wild plants had been taken from private 
grounds. 

Destruction of Wild Birds' Eggs. — The Rev. E. P. Knubley said terrible 
damage had been done by the destruction of birds' eggs. It was a sei'ious 
matter, but it was very difficult to know what to do iu regard to it. For 
instance, take the case of the great skua, which nested in the Shetland 
Islands : in 1890 it is said that not a single chick was reared on the 
whole of the Foula colony. Every egg was taken, and in 1891 all the 
eggs of the first laying were taken by the inhabitants and sold to dealers. 
Other rare birds which nested in the Shetland Islands were also perse- 
cuted. He had it on good authority that last year not more than two or 
three nests of the red-throated diver got off their young ; and the black- 
throated divers were not more fortunate. One shilling apiece was given 
by dealers for the eggs of the red-tliroated diver, and 10s. a brace for 
those of the black-tliroated diver. The whimbrels, which also nested on 
the same islands, had been reduced to about twenty pairs, and were 
likely to disappear. The red-necked plialarope was very much iu the 
same circumstances. The dealers gave a commission to a local man, 
who was to get about 8d. a dozen for every egg collected of all sorts and 
kinds. The local men in turn got the herd boys to sweep tlie country of 
every egg they could lay hands on, big and little, and for these they got 
about Id. a dozen. That was one way in which parts of Scotland had 
been regularly swept, and that in spite of such protection as the owners 
could afford. They had men who followed about strangers all day, but 
the natives took the eggs at night. Then, again, he might mention 
that he heard that in Edinburgh there was a gentleman who made it 
his boast that he had over 100 eggs of the golden eagle. What was to 
be done with a case of that kind ? In some parts of England things 
were not any better. The nesting stations of the lesser tern which 
exi.sted on the Fifeshire coast, the Lincolnshire coast, and at Spurn, in 
Yorkshire, would shortly disappear altogether. The oyster-catcher and 
the Arctic tern had practically ceased to nest on the Lincolnshire and 
Yorkshire coasts, and the ringed plover was much scarcer than formerly. 
The redshanks and greenshanks had in many parts also been persecuted 
to the death. The nests of the bearded reedling, whose breeding station 
in the British Islands was the Norfolk Broads, had been to his own 
knowledge systematically poached for sale for a number of years. The 
only hope seemed to him to be in the creation of a public feeling against 
the extermination of these birds. It would be difficult to advocate any- 
thing like legislation. The most practical plan he had seen was this — 
that the Imperial Legislature should gr.ant powers to the County Councils 
to protect known nesting-places in their districts for certain months of 
the year, say from April 1 to June 30. Such a plan would be simple, 
and might be effective ; but for one thing they should endeavour to do 
all in their power to help the owners and occupiers of land to protect the 
birds and their eggs during the breeding season. They might also see if 
they could not enlist the aid of the gamekeepers, who, with the farmers 
and proprietors, were beginning to find out that all birds were not their 
enemies. Collectors and dealers should also be discouraged. Just as he 
came thei-e that day he had been told that 200 eggs of the stormy petrel 



40 REPORT— 1893. 

liad been taken from one island on the west coast of Ireland and given to 
one dealer. 

Mr. E. B. Poulton (Oxford) said that if they discouraged the purchase 
of eggs, the trade of the dealer would soon cease. 

Mr. G. J. Symons said it was an old saying that there would be no 
thieves if there were no receivers ; and possibly there would be no dealers 
if there were no collectors. They should discourage as much as they 
could this spoliation of the nests of rare birds. 

Mr. Mills (Chesterfield) thought it would do good if some small recog- 
nition were given to gamekeepers to assist in protecting the nests of 
the birds. 

The Chairman asked if it would not strengthen the hands of Mr. 
Knubley if the meeting was to pass some resolution on the subject. 

Sir Douglas Galton hoped any resolution of the kind would make an 
appeal to egg-collectors. 

Section E. 

The Chairman remarked that last year there had been a discussion on 
the cost and age of ordnance maps ; also on the teaching of geography in 
primary schools. 

Sir Douglas Galton said that a departmental committee on the subject 
of ordnance maps had been appointed, and he had been informed by Sir 
Archibald Geikie that its report would soon be published, and that it 
would be the means of removing many of the difficulties complained of. 
It was, of course, no use discussing the matter before the publication of 
the report. 

Mr. Eli Sowerbutts did not expect much from this departmental 
report, and had little information to offer about the teaching of geo- 
graphy in schools, as he had not had a reply from a single society. But 
there had been an examination about India in the upper schools of 
Yorkshire, Cheshire, and Lancashire. Three hundred pupils only asked 
for papers, and out of 103 who sat three passed. A Cheshire girl of 
fourteen was first, a Yorkshire man of thirty-one second, and a Yorkshire 
lad third. This examination amply demonstrated the extreme badness 
of the teaching of geography in these schools. He would be glad if the 
delegates would try and help them next year. The examination would be 
in Yorkshire, and they would go back to the primary schools. 

Section G. 

Flameless Explosives. — Professor Merivale said he had nothing to 
report. The Durham strike had interfered with their arrangements, the 
proposed laboratories having been utilised as stables. 

Section H. 

Dr. Garson reported that there had been no applications to the Com- 
mittee last year for aid in connection with anthropological exploration. 
He contended, however, that local bodies, when they meant to make such 
explorations, should give them notice. Valuable hints could be given 
them as to how they should proceed. Local committees intending to 
explore ancient dwellings, burial places, &c., should communicate with 



COERESPONDING SOCIETIES. 41 

the Committee in aid of Anthropological Exploration, 3 Hanover Square, 
London. General Pitt- Rivers was the cliairman of this committee, and 
no one could be better qualified to give advice as to the conduct of an 
exploration. Local societies might also do useful work by the description 
of specimens in local museums, accounts of which might be published in 
their ' Proceedings ' for the information of workers dwelling elsewhere. 

The Secretary, at the request of the Chairman, read an extract from 
a letter of Mr. Kenward, of Birmingham, giving particulars of an anthro- 
pometric laboratory established at Birmingham, like that of Mr. Francis 
■Galton at South Kensington. 



SECOND CONFERENCE, AUGUST 9. 

The Corresponding Societies Committee were represented by Professor 
R. Meldola (Chairman) and Messrs. Symons, Whitaker, Cuthbert Peek, 
Garson, Poulton, Rev. Canon Tristram, Sir Rawson Rawson, and 
T. V. Holmes (Secretary). 

The Chairman suggested that in future some subject in which the 
delegates generally were interested, such as the management of local 
museums, the relations of County Councils to technical instruction, or the 
working of the Technical Education Acts, should be brought before the 
Conference in the form of a short j^aper to serve as a basis of discussion. 
This proposition met with general approval. 

Mr. Symons mentioned that he had arranged with Mr. GrifiBth that 
delegates on the first day of the meeting of the British Association 
should be supplied with copies of the reports on subjects in which they 
were interested. This would give them longer time than they had at 
present to make themselves acquainted with the w'ork which was being 
done. 

Section A. 

Underground Waters. — Mr. Symons said that some remarks had been 
made on the circulation of underground waters, and he wished that when 
wells were sunk the temperature, as well as the depth, of the water 
should be taken. It was very easily done, as they had only to send down 
a thermometer in the bucket, and taring up the bucket full of water. If 
such observations were made at the same hour of the day throughout the 
year they would be of very considerable use. The depth of water in a 
well should always be measured from the surface of the ground. 

Mr. Whitaker said that it was also important that the variation in the 
depth of water in a well should be recorded. 

Section D. 

Disappearance of Native Plants. — Mr. Mark Stirrup read a letter 
written by Mr. Leo Grindon dealing with the disappearance of native 
plants during the last fifty years in the district within a radius of fifteen 
miles round Manchester. The wide, uncultivated moorlands (remarked 
Mr. Grindon) remained unchanged. Harsh and wiry grasses, a few ferns, 
heather, whortleberry, and ci^owberry still renewed themselves perennially 
there ; and in the flat country which had been and remained agricul- 



42 EEPORT— 1893. 

tural or pastoral there was but little change. The changes which had 
occurred were referable almost wholly to the enterprise and activity of 
the landowners, who had converted peat-mosses and sandy wastes into 
land profitable for agriculture or even for building purposes. Hence the 
disappearance of Gentiana pneumonanthe and Osmunda, with other less 
conspicuous moss and moor plants. However, in other quarters there is 
still no lack of the cotton sedge, the Lancashire asphodel, and the Erica 
tetralh'. But the dye-polluted streams are forsaken by the forget-me- 
nots and other water-loving plants, and many ponds within five or six 
miles of the town have been drained or filled up, or converted into lakes 
for the adornment of pleasure grounds. These changes have involved 
the loss of such plants as the Stratiotes, the Myriophyllnm, and various rare 
sedges, the Garex elovgata, for instance, once abundant. Fifty years ago 
the little dells, locally called ' doughs,' were noted for their curious 
botany. Mere Clough, near Prestwich Mere, once grew in plenty the 
Calamagrostis lanceolata, Ghrysosplenium alternifolium, Geum rivale, and 
various shade-loving carices. Now all are gone, partly through the 
felling of the trees and drying of the soil, partly because the clough 
being now a thoroughfare, much trampling down and destruction are 
done by the reckless and unobservant. 

Coming to the wilful and deliberate destruction of plants, Mr. Leo 
Grindon remarked that the professed botanists and simple collectors of 
specimens for the herbarium were but little to blame. The Manchester 
flora could not be said to have ever included species existing scarcely 
anywhere else, and the local botanists had therefore but little to answer 
for. Even the ' Field Naturalists,' who had been an organised body 
more than thirty years, could not be charged with wasteful gathering. 
Many of the members took home handfuls of wild flowers, but the plants 
taken were such as would never be missed. By whom, then, was the 
mischief done ? The herb-doctors or ' medical botanists ' had caused 
much destruction of plants supposed to have medicinal value, such as the 
Erythrcea centaurium.. They were often to be seen in the season returning 
home with plants under their arms which had been pulled up by the 
roots just as they were coming into bloom. Another destructive agency 
was that of the dealers in roots for the garden. One of them had once 
asked him to name a locality where he could dig up from 300 to 500 roots 
of a certain rather favourite fern, but without obtaining a reply. Another 
dealer brought with him a basket and trowel in order to bring away 'all 
there was ' from a particular spot, which was consequently not visited 
that afternoon, the botanical guide of the party having become aware of 
the dealer's plan. Besides ferns, dealers dug up immense numbers of 
primroses, cowslips, and oxlips, and had greatly diminished their num- 
bers. Thus the mischief done to the local flora was partly due to the 
progress of agriculture and manufactures and the increase in building, 
partly to the rapacity of the dealers in ferns and other plants. 

Mr. Mark Stirrup added that he could confirm Mr. Leo Grindon's 
remarks from his own experience of the disappearance of ferns and 
primroses in the neighbourhood of Manchester within the last fifteen or 
twenty years. In one case he remembered that a gentleman sent a horse 
and cart to a certain spot where the Osmunda grew, and removed all the 
specimens he could find. 

Mr. Sowerbutts thought it would be well for field naturalists' clubs 
to keep the exact localities in which rare plants grew for their own 



CORRESPONDING SOCIETIES. 43 

information only. He thought that Mr. Leo Grinclon was himself largely 
responsible for the eradication of rare plants around Manchester, as he 
had published a volume called ' Walks about Manchester ' in which their 
habitats were described. 

Mr. Coates (Perthshire) said their naturalists' field club, in publish- 
ing accounts of excursions or notices in papers of rare plants, only indicated 
generally where these were to be found ; and Mr. W. Gray said that the 
Belfast Naturahsts' Field Club acted in a similar way. 

As regards the extermination of native plants, Canon Tristram added 
that the neighbourhood of Durham was once one of the richest botanical 
districts in the north of England, but that during his lifetime some of the 
most interesting species of plants, and also some of the most interesting- 
species of butterflies and moths, had been exterminated. The ' lady's 
slipper' had disappeared. He had seen advertisements in the 'Gardener's 
Chronicle ' offering half a guinea for that plant, the advertisement 
always stating where it was supposed to be obtainable. The late 
Rowland Burton had remarked to him that the half-dozen plants of 
' lady's slipper ' on his property cost him more to protect them than his 
pheasants did. The butterfly, Erebia hlancliva, was no longer to be found 
in the county of Durham. The rarer orchids and the hart's-tongue fern 
were being exterminated in many districts, but public opinion had been 
thoroughly efiicient in the preservation of the ferns planted close to the 
walks on the banks of the river at Durham, and he looked to the formation 
of a public opinion as the best means of preserving plants elsewhere. 
Field clubs should make their members feel that their first object was to 
preserve, not to destroy. 

Mr. Mark Stirrup said that the preservation of rarities was enjoined 
by the Manchester societies. As regards the observations of Mr. Sower- 
butts, he did not think the plants mentioned were such as the dealers 
prized. 

Preservation of Wild Birds' Eggs. — The Rev. E. P. Knubley (Leeds) 
moved the following resolution, which was seconded by Mr. E. B. 
Poulton (Oxford) and agreed to: — 

' The Conference of Delegates, having heard of the threatened extermi- 
nation of certain birds, as British breeding species, through the destruction 
of their eggs, deprecates the encouragement given to dealers by collectors 
through their demands for British-taken eggs, and trusts that the 
Corresponding Societies will do all that lies in their power to interest and 
influence naturalists, landowners, and others in the preservation of such 
birds and their eggs.' 

On this subject Canon Tristram also spoke, and put in a strong plea 
for the preservation of birds of prey, pointing to the case of the mice 
plague in Dumfries and Lanark shires as a result of destroying the 
balance of nature by wholesale killing of birds of prey. The resolution 
brought forward by Mr. KnuVdey was cordially adopted by the meeting. 

Local Muse^tms. — The Rev. Canon Tristram (Durham) next addressed 
the delegates on the question of making their field clubs more useful. 
He strongly advocated that these clubs should combine natural history, 
archfeology, and geology ; and that their function should be, not to 
destroy, but to preserve all that was rare and curious in a district. 
Lately their field excursions in many places had been too much of picnic 
parties. On the subject of local museums, the Canon argued that, as a 
rule, these should only contain objects of local interest, and he suggested 



44 KBPOET — 1893. 

that an approach should be made to the County Councils in order to 
get assistance for forming museums and keeping them in order. Many 
museums had gone to utter decay from the -want of an endowment. 
Those at Newcastle, York, Manchester, Liverpool, and Norwich were all 
endowed. On the other hand, that at Lynn, in Norfolk, for want of 
an endowment was mouldering away. Local societies should try to pro- 
mote interest in the local museum, so that they might raise an endow- 
ment fund, by the help of wealthy residents and the County Council, in 
order to keep a curator, without whom a museum was of little use. 

Section H. 

Proposed Ethnological Survey. — Mr. Brabrook said he was deputed by 
the Committee of Section H to ask the approval and assistance of the 
Corresponding Societies in the organisation of an Ethnological Survey of 
the United Kingdom. The attempt to organise this survey was being 
made by a committee of delegates from the Society of Antiquaries, the 
Anthropological Institute, and the Folklore Society. These delegates 
represented the various points of view of the societies electing them, and 
he felt sure of the sympathy of the Corresponding Societies in this 
movement. The matter was one which would not brook delay ; every 
year tended to increase its difficulties, and if postponed much longer it 
■would become impossible to proceed at all. Several of the Corresponding 
Societies had been working in this direction, and it would only be necessary 
for them to follow the instructions which would be sent down to them by 
the Ethnological Survey Committee when it began its labours. From 
the reports of the Corresponding Societies he learnt that thirty-three 
of them had been at work on this subject during the last eight years, 
and that during that period 100 members of these societies had con- 
tributed papers on it to the ' Proceedings.' He would urge them, therefore, 
to look at men from the three points of view indicated. He agreed with 
the Rev. Canon Tristram that field clubs should include archeology 
among their subjects of study. It was absurd to look at man merely 
from the natural history point of view, and ignore his archaeological 
aspects. 

Preservation of Ancient Reviains. — Mr. Whitaker said that in the 
Hampshire district it had been found that a remonstrance against the 
destruction of ancient remains usually had a good effect. Proprietors 
often did not know the interest and value of antiquities on their estates, 
but cared for them after they became aware of it. Certain Government 
departments sometimes needed similar education. One of the best 
Hampshire tumuli was almost destroyed recently in the making of a rifle 
butt. 

Mr. W. Gi'ay remarked that, in Ireland, Government was very anxious 
to preserve all monuments, and that the Naturalists' Field Club of 
Belfast not only did its best to keep them uninjured but also photo- 
graphed them. He had pleasure in exhibiting some of these photographs, 
copies of which might be obtained by anyone interested in geology or 
archfeology on application to the local secretary. 

The Chairman was sure the Corresponding Societies would do their 
best to assist Mr. Brabrook, and he would ask that gentleman if he 
would point out in what way the societies could best help him. 

Mr. Brabrook said it was a little difficult to do so because the 



CORRESPONDlNa SOCIETIES. 45 

material was so abundant. He had there the result of an archisolowical 
survey of Kent and a scheme applicable to the county of Gloucester. 
There were also the books prepared by the Anthropological Institute and 
the Folklore Society. All these works gave instructions for working 
in the way desired. But their bulk made it necessary that the Committee 
should devise something smaller for the exploration, and that would be 
the first of its labours. The Committee would then send a pamphlet 
containing the needed suggestions to every Corresponding Society. 

Baihuay Facilities. — -Mr. Sowerbutts thought better terms might be 
obtained from the railway companies for delegates and others travelling 
to meetings of the British Association. The Chairman and Mr. Symons 
promised to represent the matter to the Council of the Association. 
The Corresponding Societies Committee now have to report that in accord- 
ance with this promise a strong committee of the Council was appointed, 
on the motion of Professor Meldola, and a representation made to the 
authorities at the Clearing House, but no concession could be obtained 
beyond what is allowed by Traffic Regulation No. 30, viz., ' Members are 
allowed during a Meeting to take railway tickets at the town where the 
Meeting is held at a single fare for the double journey to places within a 
distance of fifty miles.' 

The Committee recommend the retention of all the societies at 
present on the list, with the exception of the Barnsley Naturalists' and 
Scientific Society, which had not filled in and returned the schedule at the 
time of the Meeting of the Committee. 

In order to make the publications of the Corresponding Societies 
available for reference, the Committee decided to have them bound. 
Accordingly Mr. Topley and Mr. T. V. Holmes (Secretary) were in- 
structed to examine them and to select for binding some of the more 
complete and valuable. Fifty-eight volumes have already been bound 
and placed on the shelves of the Association. Others will be added from 
time to time as the amount of the grant available for this purpose may 
allow. 



46 



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49 



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CORRESPONDING SOCIETIES. 



51 



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CORBESPONDING SOCIETIES. 



53 



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-11 






05 












CO 






ft? 



o 



« 










CO 
"CO - 



0:1 (N m 

"00 00 00 



CO CO 



O 1— I CO to ^ 00 
02 lO <M C-l t~ 

CO ^H -^ I— I I— I 



N «D IM 

CO C5 CD 
<M (M CO 



05 N CO O CO t~ 

t~- G5 (M CO CO -* 

I— I rH I— I C^ t— ( 



l~- CD CO 
O -* t- 



X 



=3m 



CO 
00 



o 

fa 



l-l 00 

> . > 

x^ 



^ 
•^ 



-t 



-U 






^^ 



o 
.02 



o 






.0 

'-si 



o 
Q 



o 

o 

CO 



o 
o 

CO 



c3 ffi So 
o . J o 

CO _ " t/3 

g a 

c 2 



tin 0) 



rT^ • o 

^ffi 32 
o . 'C 

a a -c 
.£; 3 o 



a> 



fa o 

a 

o m oD 

<u g c 
2 fe o 

M O 

^ rC O -r 

goS 

+^ '^ -^ ^ 

a "^ a "^ 
O 



•ill 



?< '-' t> s; 

O Q) o !3 

•^ 02 «- '^ ■ 



.2 '^ 

r-| TO 

J) o 
'o 
<u c 

a g 
at> 

a; ^3 

■*^ CI 
o 



a 

a 

o 

• o 



';3 






bo 

> 
■ ci 



OJ 



^^ . 



O be, 



00 



^ O ni S 

CO w o a 
o -w Qj a 



w d M 

^ g ID 

'3 o a 

^ ^ 0) 

'^ c " 

0) a> cd 

B "o E 



CI =1 £ 

o <U rt 

2 ^ -^ 
.-SS o 

go: 



3 
•CC 



03 

m c« t- _ce 

O H> 



o .2 



.a 



1 a 

TO ;h 



o OJ 

O !- 



•° .2 
m ^ 

s-i 

.2 cl 

3 a 

CO o 

o^ 

bn =* 

a^ 

a o 

pa fa 

HO 



cs a <! 

02 cS _ 

S 02 S 

» D a 

Sis CI 



E^ tn < 
(D •r' 



a 

a«' 

o <+-< 

l< 

OJ o 
pd ".S 

-a o 



W CO (M 

O^ C^ Oi 

00 00 00 



CO 
CO 



CO 



CO ■* »a 
CO O CO 

r-l CO 



o 












<5 §? 



o 

a 



l-H oj O CQ OJ m 
.^ ^3 ^ ^ - 



Ofa 



Cl 



<u 



c^ c^ c3 c^ 



►^ggsgg 



S^-j 



fl 


L-l 





M 


CI) 




pO 


-a 




cs 


c« 


0) 



S o ,^ 
S '-I o 



a 



- o 
'Ph 



> • 


0) 


P3 


a 1-5 





s ^ 


ft cS 


to J= 


X CO 






o 

02 



O 

a 

3 

Q 



o 



o 
P3 



egg 



■ d^ 
gcofa" 

P- a 
OodP 



I — I 

ft 

T: 
cS 

-a 

<u 
'tn 

a 
o 



3 

a 



^ ^ o 



.2 '^ 
> S 
op5 

aW 

Sag 
l^fa 

.2 Jfcs 

-.^ ^ O 

-►^ Ci r— 






CJ 



OJ n. 



.2 ^ 



<u ^ . 
gco 

2=n o 

:s o Q 
og.a 

-a ^S 



■ffi^d 



- a . p - 

m cS m tj !>i 

-*3 3 

32 CO 



u 



: Ph :;d 



w 



-3 

a . 

H 



t^ 



;a2 



• o ^ 

; o 5 

iHP 



ON THE PELLIAN EQUATION. 



73 



Tables connected with the Pellian Equation from the 'point where 
the work luas left by Degen in 1817. — Report of the Committee, 
consisting of Professor A. Cayley, Dr. A. E. Forsyth, Professor 
A. Lodge, and Professor J. J. Sylvester. (Dratvn up by 
Professor Cayley.) 

We have on the Pellian Equation Degen's tables, the title of which is 
' Canon Pellianus sive Tabula simplicissimam fequationis celebratissim£e 
y^=ax!^ + l solutionem pro singulis numeri dati valoribus ab 1 usque ad 
1000 in numeris rationalibus iisdemque integris exhibens. Autore Carolo 
Ferdinando Degen. Hafnise, apud Gerhardum Bonnierum, mdcccxvii. 8°. 
Introductio, pp. v-xxiv. Tabula I. Solutionem sequationis y^ — aa;^— 1=0 
exhibens, pp. 3-106. Tabula II. Solutionem sequationis y^ — ax"+l=0, 
quotiescunque valor ipsius a talem admiserit, exhibens, pp. 109-112.' 

The mode of calculation is explained in the Introduction, and illustrated 
by the examples of the numbers 209, 173. 

As to the first of these the entry in Table I. is 





14, 2, 


5, 


3, 


(2) 


209 


1,13, 

3220 
46551 


5, 


8, 


11 



where the first line gives the expression of v/209 as a continued frac 
tion, viz., we have 



a/209 = 14 + 



2 + 



1^ 

5 + 



1 

3 + 



1 

2 + 



1 
3 + 



1 

5 + 



1^ 

2 + 



1^ 

28 + 



2+ ""'■' 



the denominators being 2, 5, 3, (2), 3, 5, 2, then 28, which is the double 
of the integer part 14, and then again 2, 5, 3, (2), 3, 5, 2, and so on, the 
parentheses of the (2) being used to indicate that this is the middle term 
of the period. 

The second row gives auxiliary numbers occurring in the calculation 
of the first row and having a meaning, as will presently appear. Observe 
that the 11 which comes under the (2) should also be printed in paren- 
theses (11), but this is not done. 

The process for the calculation of the x, y is as follows : 



209 


14 


1 





+ 1 


2 


14 


1 


- 13 


5 


29 


2 


+ 5 


3 


159 


11 


- 8 


(2) 


506 


35 


+ (11) 


3 


1171 


81 


- 8 


5 


4019 


278 


+ 5 


2 


21266 


1471 


- 13 


28 


46551 


3220 


+ 1 



viz., writing down as a first column the numbers of the first row, and 
beginning the second column with l, 14 (i4 the number at the head of 



74 



EEPOET — 1893. 



the first column), and the third column with o, l, we calculate the num- 
bers of the second column, 29=2.14 + 1, 159=5.29 + 14, 506=3.159 + 29, 
&c., and the numbers of the third column in like manner, 2=2.1+0, 
11 = 5.2+1, 35=3.11+2, &c. ; and then writing down as a fourth column 
the numbers of the second row with the signs +, — alternately, we have 
a series of equations y^— aa;^=:+A, viz., 

1^-209.0= =+1 

14- -209.1- =-13 
29- -209.2* = -I- 5 

the last of them being 

(46551)=-209(3220)== + 1 

this last corresponding as above to the value + 1, and the numbers 46551 
and 3220 being accordingly the y and x given in the fourth and third 
rows of the table. 

As to the second of the foregoing numbers, 173, the only difference ia 
that the period has a double middle term, viz., the entry in the Table I. 
is 



173 



13, 6, ( 1, 1) 
1, 4, (13, 13) 

190060 
2499849 



The first row gives the expression of \/173, viz., that is 

11 !1 1 1 



a/173 = 13 + 



6-f (1)+ (l)-H 6-h 26 + 



&c., 



the denominators being 6, 1, 1, 6, then 26 (the double of the integer part 
13), and then again 6, l, l, 6, and so on. In the second row I remark 
that Degen prints the parentlaeses (13, 13) for the double middle term. 

The process for the calculation of the x, y is similar to that in the 
former case, viz., we have 





17 


3 




13 


1 





+ 1 


6 


13 


1 


- 4 


(!) 


79 


6 


-H13 


92 


7 


-13 


6 


171 


13 


+ 4 


26 


1118 


85 


- 1 



where the second and third columns begin 1, 13 and 0, l respectively, 
and the remaining terms are calculated 79 = 6.13 + 1, 92^1.79 + 13, &c., 
and 6=6.1 + 0, 7=1.6 + 1, &c. ; and then writing down as a fourth column 
the terms of the second row with the signs + , — alternately, we have 



1=- 173.0= 


= -1- 1 


13= -173.1- 


= - 4 


792-173.6= 


= +13 



the last equation being 

(1118)=-173(85)==- 1 

the term for the last equation being always in a case such as the present 



ON THE PELLIAN EQUATION. 



75 



one, not +1, but — l. The final numbers 1118, 85 are consequently 
entered not in Table I., but in Table II., viz., the entry in this table is 



173 



85 
1118 



and thence we calculate the numbers y, x of Table I., viz., these are 

2499849 = 2.(1118)= + ! 
190060=2.1118.85 

Generally Table II. gives for each value of a, comprised therein, 
values of a-, y, such that 2/^=a«^—l, and then writing yi=2y^ + l, Xi = 2xy, 
we have 

= (^2ax- — ly = ia''x* — iax" + 1 = a . 4a;^(aa;-— 1) + 1 = aa;,' + 1 



Vi 



SO that .T,, yi are for the same value of a the values of x, y in Table I, 

It is to be remarked that the heading of Table II. is not perfectly accu- 
rate, for it purports to give for every value of a, for which a solution 
exists, a solution of the equation y'^=ax^—l. What it really gives is the 
solution for each value of a for which the period has a double middle 
term. But if a.=:a^ + l, then obviously we have a solution 7/ = a, x=ly 
and for any such value of a the period has a single middle term, viz., the 
entry in Table I. is 



and we in fact have 



a- + l 


a, (2a) 




1, 1 




2a 




2a- + 1 



aP + 1 


a 


1 







+ 1 


(2a) 


a 




1 


-1 


2a 


2a' +1 




2a 


+ 1 



that is 

l--(a=+l)0= =+1 

a=-(a=+ 1)1- =-1 

(2a-+l)--(a- + l) (2a)2= +1 

The foregoing instances of the calculation of x, y in the case of the 
numbers 209 and 173 suggest a table which may be regarded as an ex- 
tended form of Degen's tables ; viz., such a table, from a=2 to a^99, is 
as follows : 

Specimen of extended form of Table in regard to the Pellian Equation. 



a 


y 


X 


y2-ax2 


a 


y 


X 


■tp—ax"^ 


2 


1 1 
(2) 1 

2 3 



1 
2 


+ 1 
- 1 
+ 1 


5 


2 1 

(4) 2 

4 9 



1 
4 


+ 1 
- 1 
+ 1 


3 


1 1 

0) 1 

2 2 




1 
1 


-1- 1 
- 2 

+ 1 


6 


2 1 

(2) 2 

4 5 



1 

2 


-1- 1 
- 2 
+ 1 



76 EEPOET — 1893. 

Specimen of extended Foem of Pellian Equation Table — continued. 



a 


V 


X 


y^-ax^ 


a 


y 


X 


y'^—ax^ 


7 


2 


1 





+ 1 


20 


4 


1 





+ 1 




1 


2 


1 


- 3 




(2) 


4 


1 


- 4 




(1) 


3 


1 


+ 2 




8 


9 


2 


+ 1 




1 
4 


f; 


2 


_ 3 














8 


3 


+ 1 


21 


4 
1 


1 

4 




1 


+ 1 
- 5 












8 


2 


1 





+ 1 




1 


5 


1 


+ 4 




(1) 


2 


1 


- 4 




(2) 


9 


2 


- 3 




4 


3 


1 


+ 1 




1 
1 
8 


23 
32 
55 


5 

7 

12 


+ 4 
- 5 
+ 1 


10 


3 

(6) 


1 
3 




] 


+ 1 
- 1 
















6 


19 


6 


+ 1 


22 


4 
1 
2 

(4) 

2 
1 
8 


1 

4 

5 

14 

61 

136 

197 



1 

1 

3 

13 

29 
42 


+ 1 

- 6 
+ 3 

- 2 
+ 3 

- 6 
+ 1 


11 


3 

(3) 
6 


1 

3 

10 



1 
3 


+ 1 
- 2 
+ 1 












12 


3 

(2) 
6 


1 
3 

7 




1 
2 


+ 1 
- 3 

+ 1 












23 


4 

1 
(3) 


1 
4 
5 



1 
1 


+ 1 
- 7 
+ 2 












13 


3 


1 





+ 1 




1 


19 


4 


- 7 




1 


3 


1 


- 4 




8 


24 


5 


+ 1 




(1) 

1 
6 


4 

7 

11 

18 


1 
2 
3 
5 


+ 3 

- 3 
+ 4 

- 1 












24 


4 

(1) 

8 


1 
4 
5 



1 
1 


+ 1 
- 8 
+ 1 


14 


3 

1 
2 
1 
6 


1 
3 

4 
11 
15 




1 
1 
3 
4 


+ 1 


26 


5 


1 





+ 1 




— 5 

+ 2 

- 5 
+ 1 




(10) 
10 


5 

51 


1 

10 


- 1 
+ 1 






















27 


5 
(5) 


1 
5 




1 


+ 1 
_ 2 


15 


3 


1 





+ 1 




(1) 
6 


3 

4 


1 
1 


- 6 
+ 1 




10 


26 


5 


+ 1 






















28 


5 
3 

(2) 
3 

10 


1 

5 

16 

37 

127 




1 

3 

7 

24 


+ 1 

- 3 
+ 4 

- 3 
+ 1 


17 


4 

(8) 

8 


1 

4 

33 




1 
8 


+ 1 
- 1 
+ 1 


18 


4 


1 





+ 1 














(4) 


4 


1 


- 2 


29 


5 


1 





+ 1 




8 


17 


4 


+ 1 




2 

(1) 

2 
10 


5 
11 
16 

27 
70 


1 
2 
3 
5 
13 


- 6 

+ 5 

- 3 
+ 2 

- 1 


19 


4 
2 
1 
3 


1 

4 

9 

13 




1 
2 
3 


+ 1 

- 3 

+ 5 

- 2 














1 


48 


11 


+ 5 


30 


5 


1 





+ 1 




2 


61 


14 


- 3 




(2) 


5 


1 


- 5 






170 


39 


+ 1 




10 


11 


2 


+ 1 



ON THE PELLIAN EQUATION. 



77 



Specimen op 


EXTENDED FOEM OF PELLIAN EQUATION TABLE— COWlfMM 


led. 


a 


y 


X 


y^ — ax^ 


a 
43 


y 


X 


tp—ax"^ 


31 


5 


1 





+ 1 1 


6 


1 





+ 1 




1 


5 


1 


- 6 




1 


6 


1 


- 7 




1 


6 


1 


+ 5 




1 


7 


1 


+ 6 




3 


11 


2 


- 3 




3 


13 


2 


- 3 




(5) 


39 


7 


+ 2 




1 


46 


7 


+ 9 




3 


206 


37 


- 3 




(5) 


59 


9 


- 2 




1 


657 


118 


+ 5 




1 


341 


52 


+ 9 




1 


863 


155 


- 6 




3 


400 


61 


- 3 




10 


1520 


273 


+ 1 




1 

1 
12 


1541 
1941 
3482 


235 
296 
531 


+ 6 
- 7 
+ 1 


32 


6 


1 
5 
6 



1 
1 


+ 1 

- 7 
+ 4 




1 
(1) 


44 


6 


1 





+ 1 




1 


11 


2 


- 7 




1 


6 


1 


- 8 




10 


17 


3 


+ 1 




1 

1 

(2) 


7 
13 

20 


1 

2 
3 


+ 5 

- 7 
+ 4 


33 


5 


1 





+ 1 




1 


6 


1 


- 8 




1 


53 


8 


- 7 




(2) 

1 


6 


1 


+ 3 




1 


73 


11 


+ 5 




17 


3 


- 8 




1 


126 


19 


- 8 




10 


23 


4 


+ 1 




12 


199 


30 


+ 1 


34 


5 


1 





+ 1 


45 


6 


1 





+ 1 




1 


5 


1 


- 9 




1 


6 


1 


- 9 




(4) 


6 


1 


+ 2 




2 


7 


1 


+ 4 




1 


29 


5 


- 9 




(2) 


20 


3 


- 5 




10 


35 


6 


+ 1 




2 


47 


7 


+ 4 














1 

12 


114 
161 


17 
24 


- 9 

+ 1 


35 


5 
(1) 


1 
5 




1 


+ 1 
-10 












• 


10 


6 


1 


+ 1 


46 


6 
1 
3 
1 

1 
2 

(6) 
2 


1 

6 

7 

27 

34 

61 

156 



1 

1 
4 
5 
9 
23 


+ 1 

-10 
+ 3 

- 7 
+ 6 

- 5 
+ 2 


37 


6 

(12) 

12 


1 

6 

73 




1 

12 


+ 1 
- 1 
+ 1 












38 


6 


1 





+ 1 




997 


147 


- 5 




(6) 


6 


1 


— 2 




1 


2150 


317 


+ 6 




12 


37 


6 


+ 1 




1 


3147 


464 

781 


- 7 
+ 3 














3 


5297 


39 


G 


1 





+ 1 




1 


19038 


2807 


-10 




(4) 


6 


1 


- 3 




12 


24335 


3588 


+ 1 




12 


25 


4 


+ 1 












47 


6 


1 





+ 1 












40 


G 


1 





+ 1 




1 


6 


1 


- 1 




(3) 


6 


1 


- 4 




(5) 


7 


1 


+ 2 




12 


19 


3 


+ 1 




1 
12 


41 

48 


6 

7 


-11 

+ 1 


41 


6 

© 


1 
6 




1 


+ 1 
- 5 


48 


6 


1 





+ 1 




13 


2 


+ 5 




(1) 


6 


1 


-12 




12 


32 


5 


- 1 




12 


7 


1 


+ 1 


42 


6 


1 





+ 1 


50 


7 


1 





+ 1 




(2) 


6 


1 


- 6 




(14) 


7 


1 


- 1 




12 


13 


2 


+ 1 




14 


99 


14 


+ ^ 



78 



REPORT 1893. 



Specimen of extended Foem of Pellian Equation TAB-LE—co>iti?med. 



a 




y 


X 


y^—ax^ 


a 


y 


X 


t/^-ax- 


51 


7 


1 





+ 1 




(7) 


23 


8 


_ 2 




(7) 


7 


1 


- 2 




2 


169 


22 


+ 5 




14 


50 


7 


+ 1 




1 
14 


361 

530 


47 
69 


-10 

+ 1 


52 


7 
4 


1 
7 



1 


+ 1 
- 3 


60 


7 


1 





+ 1 




1 


29 


4 


+ 9 




1 


7 


1 


-11 




(2) 


36 


5 


- 4 




(2) 


8 


1 


+ 4 




1 


101 


14 


+ 9 




1 


23 


3 


-11 




4 


137 


19 


- 3 




14 


31 


4 


+ 1 




14 


649 


90 


+ 1 












61 


7 

1 


1 
7 




1 


+ 1 
-12 


53 


7 


1 





+ 1 




3 


7 


1 


- 4 




4 


8 


1 


+ 3 




(^^ 


22 


3 


+ 7 




3 


39 


5 


- 4 




\l) 


29 


4 


- 7 




1 


125 


16 


+ 9 




3 


51 


7 


+ 4 




(-\ 


164 


21 


- 5 




14 


182 


25 


- 1 




\2) 
1 
3 


453 
1070 
1523 


58 
137 
195 


+ 5 
- 9 
+ 4 


54 


7 


1 





+ 1 




2 


7 


1 


- 6 




4 


5639 


722 


- 3 




1 


15 


2 


+ 9 




1 


24079 


3083 


+ 12 




(6) 


22 


3 


_ 2 




14 


29718 


3805 


- 1 




1 

2 


147 
169 


20 
23 


+ 9 
- 5 














62 


7 


1 





+ 1 




14 


485 


66 


+ 1 




1 
(6) 

1 


7 
8 


1 
1 


-13 
+ 2 
-13 


55 


7 


1 





+ 1 




55 


7 




2 


7 


1 


- 6 




14 


63 


8 


+ 1 




(2) 


15 


2 


+ 5 
























2 


37 


5 


- 6 


63 


7 


1 





+ 1. 




14 


89 


12 


+ 1 




(1) 


7 


1 


-14 










+ 1 

- 7 




14 


8 


1 


+ 1 


56 


7 
(2) 


1 

7 



1 


65 


8 


1 





+ 1 




14 


15 


2 


+ 1 




(16) 
16 


8 
129 


1 

16 


- 1 
+ 1 


57 


7 
1 


1 

7 



1 


+ 1 
- 8 










66 


8 


1 





+ 1 




1 


8 


1 


+ 7 




(8) 


8 


1 


- 2 




(4) 


15 


2 


- 3 




16 


65 


8 


+ 1 




1 
1 


68 
83 


9 
11 


+ 7 
- 8 












67 


8 


1 





+ 1 




14 


151 


20 


+ 1 




5 

2 

1 


8 
41 
90 


1 
5 

11 


- 3 
+ 6 

- 7 


58 


7 


1 





+ 1 






1 


7 


1 


- 9 




1 


131 


16 


+ 9 




1 


8 


1 


+ 6 




(7) 


221 


27 


- 2 




fl^ 


15 


2 


- 7 




1 


1678 


205 


+ 9 




Vi; 


23 


3 


+ 7 




1 


1899 


232 


- 7 




1 


38 


5 


- 6 




2 


3577 


437 


+ 6 




1 


61 


8 


+ 9 




5 


9053 


1106 


- 3 




14 


99 


13 


- 1 




16 


48842 


5967 


+ 1 


59 




1 





+ 1 


68 


8 


1 





+ 1 






7 


1 


-10 




(4) 


8 


1 


- 4 






8 


1 


+ 5 




16 


33 


4 


+ 1 



ON THE PBLLIAN EQUATION. 



79 



Specimen of extended Fokm of Pellian Equation TABhE—continued. 



a 


y 


.r 


y- — ax- 


a 


!/ 


X 


i/'—ax^ 


69 


8 


1 





+ 1 




1 


26 


3 


- 8 




3 


8 


1 


- 5 




1 


35 


4 


+ 9 




3 


25 


3 


+ 4 




5 


61 


7 


- 3 




1 


83 


10 


-11 




(4) 


340 


39 


+ 4 




(4) 


108 


13 


+ 3 




5 


1421 


163 


- 3 




1 


515 


62 


-11 




1 


7445 


854 


+ 9 




3 


623 


75 


+ 4 




1 


8866 


1017 


- 8 




3 


2384 


297 


- 5 




2 


16311 


1871 


+ 5 




16 


7775 


936 


+ 1 




1 
16 


41488 
57799 


4759 
6630 


-12 
+ 1 


70 


8 
2 


1 

8 



1 


+ 1 
- 6 






77 


8 


1 





+ 1 




1 


17 


2 


+ 9 




1 


8 


1 


-13 




(2) 


25 


3 


- 5 




3 


9 


1 


+ 4 




1 


67 


8 


+ 9 




(2) 


85 


4 


- 7 




2 


92 


11 


- 6 




3 


79 


9 


+ 4 




16 


251 


30 


+ 1 




1 
16 


272 
351 


31 
40 


-13 
+ 1 


71 


8 
2 


1 
8 



1 


+ 1 

- 7 




78 


8 


1 





+ 1 




2 


17 


2 


+ 5 




1 


8 


1 


-14 




1 


42 


5 


-11 




(4) 


9 


1 


+ 3 




(7) 


59 


7 


+ 2 




1 


44 


5 


-14 




1 


455 


54 


-11 




16 


53 


6 


+ 1 




2 
2 


514 
1483 


61 
176 


+ 5 

- 7 












79 


8 


1 





+ 1 




16 


3480 


413 


+ 1 




1 
(7) 


8 
9 


1 

1 


-15 














+ 2 


72 


8 


1 





+ 1 




1 


71 


8 


-15 




(2) 


8 


1 


- 3 




16 


80 


9 


+ 1 




16 


17 


2 


+ 1 












80 


8 


1 





+ 1 












73 


8 


1 





+ 1 




(1) 


8 


1 


-16 




1 


8 


1 


- 9 




16 


9 


1 


+ 1 




1 


9 
17 


1 
2 


+ 8 
- 3 












82 


9 


1 





+ 1 




\5) 


94 


11 


+ 3 




(18) 
18 


9 


1 


- 1 




1 


487 


57 


- 8 




163 


18 


+ 1 




1 
16 


581 
1068 


68 
125 


+ 9 
- 1 












83 


9 
(9) 


1 
9 




1 


+ 1 
— 2 












74 


8 
1 


1 
8 
9 



1 
1 


+ 1 
-10 

+ 7 




18 


82 


9 


+ 1 


84 


9 


1 





+ 1 




\U 


17 


2 


- 7 




(6) 


9 


1 


- 3 




1 


26 


3 


+ 10 




18 


55 


6 


+ 1 




16 


43 


5 


- 1 












85 


9 


1 





+ 1 












75 


8 


1 





+ 1 




4 


9 


1 


- 4 




1 


8 


1 


-11 




(^^ 


37 


4 


+ 9 




(1) 


9 


1 


+ 6 




\l) 


46 


5 


- 9 




1 


17 


2 


-11 




4 


83 


9 


+ 4 




16 


26 


3 


+ 1 




18 


378 


41 


- 1 


76 


8 


1 





+ 1 


86 


9 


1 





+ 1 




1 


8 


1 


-12 




3 


9 


1 


- 5 




2 


9 


1 


+ 5 




1 


28 


3 


+ 10 



80 



REPORT 1893. 



Specimen op extended Fokm of Pellian Equation Table — continued. 



a 


y 


X 


y^-nx^ 


a 


y 


X 


y^-ax^ 




1 


37 


4 


- 7 




4 


839 


87 


+ 4 




1 


65 


7 


+ 11 




1 


3491 


363 


-11 




(8) 


102 


11 


- 2 




1 


4330 


449 


+ 7 




1 


881 


95 


+ 11 




1 


7821 


811 


-12 




1 


983 


106 


- 7 




18 


12151 


1260 


+ 1 




1 
3 


1864 

2847 


201 
307 


+ 10 
- 5 












94 


9 


1 





+ 1 




18 


10405 


1122 


+ 1 




1 
2 


9 
10 


1 
1 


-13 

+ 6 














87 


9 


1 





+ 1 




3 


29 


3 


- 5 




(3) 


9 


1 


- 6 




1 


97 


10 


+ 9 




18 


28 


3 


+ 1 




1 
5 

1 


126 

223 

1241 


13 
23 

128 


-10 
+ 3 
-15 


88 


9 


1 





+ 1 




2 


9 


1 


- 7 




(8) 


1464 


151 


+ 2 




1 


19 


2 


+ 9 




1 


12953 


1336 


-15 




(1) 


28 


3 


- 8 




5 


14417 


1487 


+ 3 




1 


47 


5 


+ 9 




1 


85038 


8771 


-10 




2 


75 


8 


- 7 




1 


99455 


10258 


+ 9 




18 


197 


21 


+ 1 




3 
2 
1 


1 84493 

6 52934 

14 90361 


19029 

67345 

1 53719 


- 5 
+ 6 
-13 


89 


9 


1 





+ 1 




2 


9 
19 


1 
2 


- 8 




18 


21 43295 


2 21064 


+ 1 




(^\ 


+ 5 














y 


66 


7 


- 5 


95 


9 


1 





+ 1 




2 


217 


23 


+ 8 




1 


9 


1 


-14 




18 


500 


53 


- 1 




(2) 

1 
18 


10 
29 
39 


1 
3 
4 


+ 5 
-14 
+ 1 


90 


9 


1 
9 





+ 1 




(2) 


1 


— 9 














18 


19 


2 


+ 1 


96 


9 

1 
(3) 


1 

9 
10 



1 
1 


+ 1 
-15 
+ 4 


91 


9 


1 





+ 1 




1 


9 


1 


-10 




1 


39 


4 


-15 




1 


10 


1 


+ 9 




18 


49 


5 


+ 1 




5 


19 




— 3 














(1) 


105 


11 


+ 14 


97 


9 


1 





+ 1 




5 


124 


13 


- 3 




1 


9 


1 


-16 




1 


725 


76 


+ 9 




5 


10 


1 


+ 3 




1 


849 


89 


-10 




1 


59 


6 


-11 




18 


1574 


165 


+ 1 




1 

/1\ 


69 

1 '>S 


7 
13 


+ 8 

Q 


92 


9 


1 





+ 1 




(i) 


197 


20 


+ 9 




1 


9 


1 


-11 




1 


325 


33 


- 8 




1 


10 


1 


+ 3 




1 


522 


53 


+ 11 




2 


19 


2 


- 7 




5 


847 


86 


- 3 




(4) 


48 


5 


+ 4 




1 


4757 


483 


+ 16 




2 


211 


22 


— 7 




IS 


5604 


569 


- 1 




1 
1 


470 
681 


49 
71 


+ 3 
-11 














98 


9 


1 





+ 1 




13 


1151 


120 


+ 1 




1 
(8) 


9 

10 


1 
1 


-17 
















93 


9 


1 





+ 1 




1 


89 


9 


-17 




1 


9 


1 


-12 




18 


99 


10 


+ 1 




1 
1 


10 
19 


1 

2 


+ 7 
-11 














99 


9 


1 





+ 1 




4 


29 


3 


+ 4 




(I) 


9 


1 


-18 




(6) 


135 


11 


- 3 




18 


10 


1 


+ 1 



ON THE PELLIAN EQUATION. 81 

The meaning hardly requires explanation ; for each number a we 
have a series of pairs of increasing numbers, y, x, satisfying a series of 
equations y^^ax^dib ; thus 



y 


X 


y'—ar' 


1 





1-14.0 = 1 


3 


1 


9-14.1 =-5 


4 


1 


16-14.1 = +2 


11 


3 


121-14.9 =-5 


15 


4 


225-14.16= +1 



The following table, calculated under the superintendence of the 
Committee, extends froma=1001 to a^lSOO (square numbers omitted) ; 
it is (with slight typographical variations) nearly but not exactly in the 
form of Degen's Table I., the chief difference being that for a number a 
having a double middle term, or of the form a^ + \ (such number being 
further distinguished by an asterisk), the x, y entered in the table are the 
solutions, not of the equation y'^:=.aa'!^-\-\, but of the equation y-:=ax^ — \. 
As T-emarked above, if we have y'^=ax^ — \, then writing 2/i=2i/2 + l and 
a!,=2a;2/, we obtain y^^^axi^ + l. 

Moreover, for each value of a, in the first line, the first term, which is 
the integer part of v'a, is separated from the other by a semicolon, 
and the 1, which is the corresponding first term of the second line, is 
omitted. 

The calculations were made by C. B. Bickmore, M.A., of New 
College, Oxford : his values for x and y have been revised as presently 
mentioned, but it has been assumed that his values for the periods and 
subsidiary numbers (forming the first and second lines of each division of 
the table) are accurate ; in fact, any error therein would cause the resulting 
values of x and y to be wildly erroneous ; but (except in a single instance 
which was accounted for) the errors in x and y were in every case in a 
single figure or two or three figures only. 

The values of x and y were in every case examined by substitution in 
the equation {y'^^=ax' + l, or y'^=ax'^ — '\., as the case may be) which 
should be satisfied by them. These verifications were for the most part 
made by A. Graham, M.A., of the Observatory, Cambridge. As already 
mentioned, some errors were detected, and these have been, of course, 
corrected. The values of x, y given in the table thus satisfy in every 
case the proper equation i/2=aa!^ + l, or y-=^ax'^ — \ ; on the ground above 
referred to it is believed that the periods and subsidiary numbers are 
also accurate. 

It may be remarked, in regard to the verification of the equation 
y~=.a:i'r-+\ for large values of x and y, it is in practice easier and safer to 
calculate ax'^-±\, and then to compare the square root thereof with the 
given valne of y, than to further calculate the value of y"^. 



1893. 



82 



REPORT 1893. 



05 O 
CO o 

CO «o 



00 I— 

lo as 
CO to 

lO 00 

CO 50 

O 



in «o 

00 S<) 
(N O 

o 



o 
o 



o 
o 



cS 

H 

CD 






O vO 



CO 



■1 vo 
M 






O o> 
CO as 
t- 1— I 

05 ^ 

■* O 
CO CO 
I-H CO 
•<*( CO 
N OS 

>n o 

00 O 



■* ■* 



CO ^ 
CO CO 

in t^ 

OS as 
lO -^ 

o ^ 
CO o 

05 >0 

OS 



1-1 yr, 

CO 



«-l CO 



1- O 



O 

o 



CO 



O 

o 



M 1-1 






CO 

o 
o 






« o 



■^ CO 

tCoo 






M to 
M 



M O 



1-1 CO 



o 

o 



00 lO 

-^ m 

b- ■* 
^ lO 
(M O 

OS CO 
-*i Tit 

t^ i-H 

lO <M 

la o 
lo 00 

O CO 
•^ CO 
iM lO 

CO t— 

^ CO 
CO (M 
to lO 



s 


N 


" 


CO 
lO 


\o 


cR 




»o 


1-1 


CO 
CO 


M 


ro 



O CO 



•-1 lO 
lO 



11 t^ 

ro 



I- o 

CO 









■I CO 



\n o 



1-1 CO 
CO 



1-1 On 



lO CO 
i-H t- 



O 
O 



1-1 lO 



o 









1—1 CO 
■* o 



"-I 00 
■— CO 






o 
o 



M O 



11 t^ 



GO 
O 

o 



COlO 

n 

fo>o 



H 00 



* 

O 

o 



lO CO 
CO c^ 

00 



O OS 

1—1 as 

-H CO 

O ^ 

CO CO 

1-1 C<) 
O (M 
1-1 C-J 

CO 



CO 

11 1-1 
~— ' CO 

ro i^- 



n 0\ 



* 

O 






1- o 

lO 



lO oo 

00 <-t 

as CO 
« to 
to CO 

CO t-C 
N CO 

<-i a> 
00 



•00 



00 r^ 
rovo" 



n ro 



ro o\ 



N CT> 



ro 
• ro 

n 



1—1 

o 



lO 



CO 



ON THE PELLIAN EQUATION. 



83 





CO lO 


CO .-1 


00 ta 


(M t- 


CO OS 


OS 


CO rH 


OS 


(M CO 


rH (M 


rH (M 


(M 10 


00 CO 




CO CO 


t~ t~ 


10 


OS rt 


CO OS 


CO CO 


i-l i-H 


00 


CO (M 


CO 


CO 


00 N 


CO OS 




iM a 


00 


w 


Oi M 


CO ■* 


10 1^ 


to 


cs 












00 CO 




CO CO 


^ N 




■^ t~ 


00 


CO — ( 




CD 10 


r^ 






rH 


-4i 




■* lO 


rH 10 




00 OS 


N in 


CO M 




rH 










10 lO 




rH CO 


« 




•0 « 


t- 


-*< CO 




tH to 










rM fH 




■*! 






« 

to CO 
OS 0: 

00 

OS 
OS 

<M 
CO 


CO 


CO CO 
t- OS 

OS 
OS 00 

hH 

CO 
"hT'n" 

CO-— 

n" d^ 
to 

HI 




CD iM 

in 00 
01 00 

CD •* 

CD 00 
CO 10 
CD M 

c:s t- 

(M CO 

^ 

00 
(M 

10 (-- 

CO hH 
00 iM 

OS to 

CO 

to""" 

HI 

to hT 

'—' HI 

hT^O 
CO 

hT to 
N 

hT CO 

CO 
N 

M 

M 

>^ CO 
CO 

>* cf 

HI ^^ 

IH 

hTio 

IH 

rf to 

IH 

>opf 

HI 

N 10 










^ CO 
CO 

ft 




—•,-. 






" CO 


"Jo:;:; 


00 tC 




hTvo 














O ro 








i-< 






CO 














N -— 






U-) HI 




cot^ 




^ ^ 




















*^ 


rot^ 


HI 




M t^ 














"od" 






COO 




hT rf 




PJ 














ro 






H* 


" 


CO 




pT CO 














« „ 






#S -N 


M \0 






M 














« in 








M 


HI to 


















N 






•* 


n 


ri 




CO to 










^ CO 




-T a; 






T? CO 


>0 ON 


"^ VO 














_-^ 




N 






1— < 


""00" 


CO 




hT ^ 










cf I-C 




" 2! 


C^ 0\ 




0" o\ 


CO 


CO^ 




Tl- 










N 




CO 


^^ PI 




•^ *. 


hT r^ 


HI 




vo cf; 










vo" a\ 










HI 0> 


N 




















M m 


.V « 




'S- 


« « 


hT i-C 




CO 










•H Qv 




ft 


VO 




r. r. 


HI 


Tl- 




fi 










CO 










r^oo 


CO 




















LO 


vo d\ 


SS 


00" rC 


Owo" 


hT l^ 


M-S 


8^ 


CO^-* 




_ 




pT ci 




« CO 


lO 


10 


VO 


hT rC 
to 


hToo" 
to 


to 


hT 


HI HI 


HI N 


^s 


CO^— ' 


« CO 




CO 


CO 


CO 


CO 


CO 


HI 

CO 


CO 


CO 


HI 

CO 


HI 
CO 


CO 


CO 


CO 












* 






* 















'^ 


10 


<X> 


t^ 


00 


Oi 





hH 


«<» 


CO 


10 


lyS 


t- 




1—1 


r— ( 


i-H 


1— 1 


I-H 


1—1 


(>1 


(M 


CM 


(M 


(M 


CM 


CM 













































rH 


I— 1 


1— ( 


I— 1 


i-H 


I-H 


1— I 


I— t 


I-H 


I-H 


I-H 


I— ( 


I-H 



a 2 



84 



REPORT — 1893. 



(O CO 


•* lO 


^ 1-H 


t- o 


oo t^ 


CO CO 


■* lO 


to CD 


(M lO 


lo oq 


CO t^ 


•-H O 


T^t C5 


i-H ^H 


00 .-1 


CO a> 


I- o 


lO 


03 05 


OJ 00 


CO !N 


Ol (M 


O 00 


C-l CD 


<M IM 


IM 


»o 


00 CD 


-* <M 


CO -M 


C<1 


O --t 


■* CO 


t— 1 


CO (M 


00 oo 


^ (M 


05 lO 


1-H 




lO CD 


t~ i-H 


<M -* 




^ -+I 


to 


T-H 


CO t~ 


-H CO 


oo •* 


CO P- 






0> CO 


00 I-H 


00 CD 




(M t- 


»— f 




(N •* 


CD CO 


t-o 


O CO 






00 ^ 


CT> O 


O CO 




O 1-* 






00 


o 


•* -*< 


CO CD 






CD CO 


CO h- 


t~ CO 




CO CD 








(M 


lO 


-*< 00 






O 05 


la O 


CO 'il 




^!H 03 










I-H 


CO -+I 






t- ■* 


>0 CO 


»o ^ 




o to 












CO CO 






lO 05 


t- ■* 


t- t- 




CO l^ 












^ 05 






CO t- 


cq 00 


C5 CO 




05 CO 












t- CO 






O CO 


00 


(M t^ 




00 CO 












CO CO 






CO l^- 




O-H 




CO o 












CO CO 






0> 




CO 




,-t CO 

oo oo 
1— ( 












to t- 

.-1 o 

to 05 
p- t^ 

t- CO 

CO CD 
O 'it 
O CT> 
CO I-H 
lO CO 

f-H Ci 

-*< 

►H tC 

PI 

CO 
POVO 

IH 

CO 

pf pT 
PJ 

vo" d^ 

«*^o 
























T? CO 








































5.^ 












^ 
























Ovo 




































hTc? 




N T? 












I-T CO 






"o ^ 




CO^^ 
















CO 






N — ' 


2^5 


i-r»o 

CO 




CO 












IH IH 
CO 






























w CO 


^ 


•* •» 




" «^ 












to d 






>*■ 


CI 


M OS 

p« 




c^ 


















'^-o 


cT i-T 


kH 




CO 












IH IH 

to 








•> * 


_^ 




pT 1.^ 












c^ to 






^ 


"^ 


pT ^ 




C4 














i 




fcT rC 




^ ^ 




pT^ 












I-T PO 


1 






X 1-4 

CO 


M CO 
CO 




cor:: 










"o'Co 


PI 

pfvo 


J 




11 


« cR 






*^ 










^•^ 


N -^^^ 






CO»C 


*^ 




M* w 










pT CO 


- - IH PI 

P) CO CO^- 






M 


CO 


^^ 




PJ 










p< 


N ^^ 






i-TfC 




m 




1-" t^ 










I-T .^ 


cooo" " S 






CO 

N o 


COT? 

•• .1, 

•-< vn 






CO 
COVO 

CO cj; 






pToo 
'-' PI 


PO 1-4 
CO "-4 


CO 
pT i-T 

PI 
pT pT 


„- r^ -4* O 






P< 


vo'tj; 


^^ 




*^ 


^.^ 




vo cf! 




p» 


CO "^ 






«* pT 


cT w* 






00 tC 


C« P) 
^-^ p) 




« o" 


lO'* 


« ds 


« o" " S* 






M 


p» 


CO dl 




k1 1-4 




^■^^^ 


'i- 




PI 


CO N 






« d^ 


M l-l 


•» « 




lO 


pT to 


« o 
^^-2 


N i-T 


i-T d! 


i-T CO 


cope 






•* 


rt 


^ o 




K M 


PI 


P4 


T^ 


CO 
















t-~oo 
















vo ^ 


pTio 


0\S 


-> «> 


00 00* 




vo" o 


to I-T 


to pT 


T? CO 


•^ 'f 


Tt U^ 


IH 




'-' 


»-» 


OS r^ 




pC di 


*~* 


•"• 


IH 


1-4 


•"* 






N 




f* 


N 


r» 


N 


P) 


N 


P) 


P) 


PJ 


PI 


PI 


CO 


CO 


CO 


CO 


CO 


CO 


PO 


CO 


CO 


CO 


CO 


PO 


PO 












* 








* 








GO 


Oi 


o 


r— I 


G^ 


CO 


^ 


»o 


o 


b- 


GO 


Oi 


o 


G<l 


G<1 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


^ 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


1—1 


rH 


T— I 


I-H 


I-H 


1—1 


I— 1 


T— ( 


I— 1 


I— 1 


I— 1 


1—1 


I— 1 



ON THE PELLIAN EQUATION. 



85 



CO t- 

00 ■* 

CO CO 

00 Oi 

ec o 



(M O 

oo 



CO s^ 

00 C3 

t^ to 

i-H t~ 



O rt 

>* o 

•O 05 



05 









- o 



(N .-I 



■* to 






CO 



r~oo 






N N 



^ ro 









VO 0\ 



CO 



CO 



1 VO 






fO 



I 00 



N ro 



CO 



CO 



•^^ 



»Ol^ 



•— CO 

coocT 



M M 
0) 



CO O 



CO 



o 



N 
CO 

* 

'^ 
O 



CO 



CO 

o 



CO 



>0 T? 



to CO 

I-H iO 

IM O 

tP rH 

00 ta 

t~ -* 
<M O 
CO t- 

(M 00 

CO 



C^ M 

CO—' 



in o 



•H r^ 

CO 



I- lo 



1-. Tj- 

co 



■ 00 
CO 



cor>. 

i-i 



00 tr~ 

(M O 
IN 00 

-* CO 

CO 



oo ta 

(M O 

'H 00 

<M Oi 

00 •<*< 
o 



CO l-< 



CO 



O 



o 






CO 

o 



O CO 



t-l ON 

-4- 



CO 



M CO 
P) 



i-i CO 
CO 



CO 

'f pT 



►H t^ 



N CO 

PJ 



CO 



o 



1-1 CO 
CO 






CO 



CO' 

o 



CO O 

as e-l 

Tt< to 

O <M 

■*H 00 

lO o 
CO in 

■* CO 

t^ to 

Ttt CO 



o o> 

00 



1-) 

cT>^ 



*N CO 



1^00 

m i-H 



►1 CO 

It- 



co"0 



I* CO 



w O 



M ON 



CO 






CO 



o 



O VO 



M lO 
M 



N VO 



CO 



o 
o 



o t- 

xn o 
N in 
CO to 
t- oo 

05 O 
IN I— 

i-i in 
C5 to 
in 00 

to »o 
O "o 

lO CO 
I-H ii> 
O CO 

o o 

to .-H 
-* -!t( 
«D N 

to N 

l> t^ 

IN 05 

OO to 
CO ■<»< 

OS 



IN b- 

I— I to 
I-I b- 

05 O 

l^O 

to (N 

CO CO 

a I-H 

I-H h- 
i-H 00 

CO 



N tn 



•" 


^ 


00 


rC 


cf 


d 

CO 




CO 


tC O? 


VO 


d 


•* 

w 


I-I 


»M 


C^ 



■1 OS 

c< 

CO 

cTvd 

>* lO 
I-I 



P) CO 
-..MM 

►H o CO--' 

CO—- 

IH I-I IH to 

CO "T 



O Oi 
IN •* 

to 



C^ 1-1 
M 






CO 



O 



VO I*- 



■* CO 



►H r^ 
-a- 



t^oo 

COOv 



NOO 



CO 



^ CO 



P) ON 



CO 



(M CO 

»o »o 
o o 



86 



REPORT — 1893. 



to lO 

»— t <yi 

-H 00 

m CO 

O "5 

o o 

lO to 

•* lO 
to (M 

00 CO 

CO la 

Cti lO 

o to 
i-i CO 

CO 





fj_ 


'f 


lA 




►-* 


«*ioo" 


tT 


N 


*^ 


CO 


tn 


u-> 




i~t 


M 




M4 




^4 


CO 


N 


^ 




p» 


N 





Tf fO 






O 



N <Ji 






vo c^ 



W O 



CO 



o 



lO 00 

to 



to 



p< 11 






o 



05 O 
OU ■* 

(M 05 

CO N 

■-I la 

C: 00 
O CO 
(M "5 

O 05 

Ti< CO 

QO CO 

o t^ 

t^ CO 

CO to 

CO 



' — ■ m 






CD 

o 









^ m 



M 
























to 



CO 



o 



to CO 

•* <M 

1—1 CO 

CO to 
lO CO 

O 00 

CO 



1-1 o 

OD 1-^ 

O CO 

oo to 

to 00 

00 -^ 

CO CO 

00 00 

t— t 05 

JO 



CO o> 
lO CO 
oo CO 
■* 00 

to CO 

(M CO 



N < 

co^ 






CO 



CO 



CO 

o 









CO 






M CO 



N to 
M 



►- O 

CO 



o 



^ o 

(M CO 

in »o 

^H 1—1 
C5 1-1 

Oi rH 

OO C5 
<M to 
00 00 

O (M 

CO 1— ( 

00 -* 
IN C-l 

C5 



vo •* 



»^ Ov 

>o i-T 



N o 



N CO 






1- 00 
M 



CO O 
M 



as to 
o 






Ov 
M 



CO 



CO 



o 

O 






I 00 



CO 



CO 

1— I 

O 



in -* 

00 (M 

to <M 
(M t- 

rH OS 

"*< O 
t 1 

0<1 CO 

lO 00 

1— t -^ 

CO iM 

lO CO 
CO lO 



to^- 



f< ro 






11 00 
CO 



CO 



o 



^ CO 



CO 



CO 

vo cf! 

1 CO 
W 00 



CO 



CO t^ 

cTvo" 



ro 



1—1 »o 
<N CO 

to 









ON 
CO 



CO 



CO 

ID 

o 



O C5 

to 05 
1—1 Ci 

CO t~ 

CO to 

»o to 

CO 



lO t^ 

o o 
o eo 



■ 00 



»o 

M 



o 



o 



M O 



N 1-1 



1-t ON 
CO 






zo 
o 



to 



^-' lO 






1-. Ov 
CO 



11 CO 






CO 



CD 

CO 

o 



ON THE PELLIAN EQUATION. 



87 





CO 00 


•^ t- 


ta (M 


00 ^ 


O 05 


t- l>. 


«o 00 


CD in 


<35 to 


O 03 


O 05 


CO h- 


in CD 




o> 


05 O 


CO 00 


CO a> 


00 o; 


O o<i 


00 CD 


lr~ (M 


C<1 <N 


rH tH 


to 02 


as 


<M t- 






O <M 


(M t- 


1-H --S* 


00 t- 


rt 05 


CO CO 


-* T)f 


t- Ol 


-»< -* 


t- CO 


r-i 


CO 00 






CO OJ 


lO C-) 


O 00 


00 


O rH 


7-1 lO 


to CT> 


o ■* 


CO 


to <M 




t^ CO 






»o CO 


rH rH 


05 -*< 


<M 


(M 00 


^ 


O 00 


rH t- 


r-f 


rH IM 




Oi k- 






CO lO 


CO CO 


05 




t- O 




I-H -*l 


■* to 




t- lO 




^ in 






1-H 


IM C-l 


IM 




«0 rH 




CO 


O tr- 




CO 




in O 






f-H 


i^ 00 

^ to 

■* CT3 
00 O 
|-_ CO 

CO rH 

CO O 
CO Oi 
Ci lO 

o t- 
-* t~ 

CO tH 
00 C5 
.-H O 

CD 

'5'rn 

S. "^ 

•-T in 

■*« 
i-T rC 

w in 

foin 

i-T cR 

N 
»n T? 

I-T tC 
m 

N in 






i-H t^ 

poCo" 

HI IH 

PO 






io to 

rH 00 

lO 00 

CO 
— • m 

VO ON 

pTvo 
PI 

pT i-T 




CM 




00 

1-H 

"urco" 
~-' PI 








rC d\ 






«l •^ 






P) 














•^ - 






1-1 PO 






•> -s 








•« ^ 








m N 






CO 






r- ■* 








►H m 








iH 






^ •s 






m 








PO 








•s ^ 






"^d- w 






















ro ON 






t-l 






i-T in 








pnrC 








^ 


^-v^-^ 




M 0\ 




^^ 


w 








i-i 








■>? in 


p) m 




^ 




^si, 


i-T cR 








■<? ■>? 








t-i 












pn 














vo"? 


i-T rn 


M ^ 


VO ON 


00 I^ 




pTin 


O VO 




fs 




pT in 








p) 


PO 




«■ en 




M 


1-1 








PI 






^-.' 


■s »^ 


^ ^ 


-« •» 


en 




^ 


•> «< 




^ ^ 




•N .S 






^ ^ 


H. VO 


IH IH 


M 00 


•I *i 




►H O 


pn On 




►H On 




PI N 






in M 


fn 


ro 


m 


•H N 




rn 


IH 




m 




M 






M 


^ ^ 






tn 






^ 














•s •> 


1-. ON 


in i-T 


1-1 in 


.\ .% 




>-* 1-1 


P) W 




in tJ 




►h" cj; 






w 0\ 


M 




M 


VO ON 


ONt^ 


m 


P) 


^-.-^ 


,-t 




p) 






rntC 


pfvo" 


n in 


l-T T? 


On ^^ 


pT po 


l-T cS 


« s 


N d\ 




iH in 






tCoo 




P) 


PO 


•* 




p» 


PT) 




p) 




en 


































N i-T 


pT O 


pT 0\ 


pToo 


cf tC 


PONO 


pnin 


POt? 


■* en 


t?pr 


3- " 


in o 






N 


PI 


" 


»H 


IH 


l-t 


»H 


•I 


tH 


•^ 


•~' 


rH 




w" <^ 


" ■^ 


« v^ 


i-Tvo 


>H tC 


hToo" 


i-To; 


w o 


i-T rT 


w N 


hT rn 


w 'f 


►H m 




•* 


■<d- 


■* 


•<a- 


■* 


•<1- 


•* 


m 


m 


m 


m 


m 


m 




N 


N 


N 






N 


M 


PI 


p) 


P) 


p) 


PI 


P» 




ro 


ro 


fn 


PO 


PD 


m 


PO 


m 


to 


PO 


PO 


pn 


pn 








* 








* 
















t~ 


GO 


O 


o 


,— 1 


CM 


CO 


■^ 


iO 


zo 


t^ 


OO 


Oi 




ZD 


CD 


CO 


b~ 


t^ 


t^ 


t- 


t- 


t^ 


t^ 


t^ 


t^ 


t^ 




o 


O 


o 


o 


o 


O 


o 


O 


o 


O 


O 


o 


O 




1—1 


1 — 1 


I— I 


T— 1 


I— 1 


I— 1 


,— 1 


I-H 


1— 1 


rH 


,— 1 


I— 1 


,—1 



88 



EEPORT — 1893. 





^H i-H 


CO lO 


05 rt 


I-H (M 


O 05 


tH 03 


(M lO 


CO CO 


^ CO 


1— CO 


CO o 


(M 1— 


lO CO 




to C5 


-*( ,-1 


to O 


rH to 


O 05 


-* r-H 


5^ IM 


CO CO 


CO 


CO 


CO o; 


(M <N 


Tj< rH 




1-1 C<1 


CO <^ 


CO I-H 


00 


CT 05 


lo OS 


t- 


o 






O 


t~ 


ta o 




UD 


O rt 

O -( 
CO o 

t- t- 

00 -H 

—1 o 

CI rt 

C-] to 
(M 'O 

rH O 

00 »o 

00 CO 

o 

^^ M 

N ^ 

" d 

N 

i-H ro 

<^ 

""oo 

N 

rOvcT 


00 (M 

CO to 

!M 

I-H 

N 




CO G5 
05 i-H 

OJ C5 

to t~- 

O^ CO 

OO 

05 'H 
(M O 

o <^^ 

(M eo 

rf CO 
■•^ 05 
O CO 

•^ s 

I-H O 
00 ^ 

*^ to 
<o o" 

•H t-l 
►H iC 

11 
"^ 

IH 

CO 
N 

vn 

M 
N ^ 


t- 

i-H 




I-H 






I-H 




00 
I-H 














CI 11 














iH 'ro 




ro O 
■ — ' c^ 


^ lO 


cTvo 




"> M 


— CO 














CO 






" 


M 


"^—^ 


-v -. 


^ r. 


O CO 


n cl 










n ro 










0^vo 


w in 


u-1 ■^ 


CJ ^^ 


CO'-^ 










■— ' CO 




VO OS 


1^00 


00 l^ 




•H 


I-H 


















w MS 


»-« t^ 


hToo" 


" d\ 


" o' 


Kl I-H 


i-T fj" 


►h" CO 


■^"5 
^^S- 


Co"cr 

vo — 


co'n" 


cTro 
ri ^ 


vo T? 




ii-1 


vn 


>ri 


m 


vo 


VO 


vo 


vo 








^ 




• •* 


• >v 


• •s 


••^ 


• •V 


..N 


• n 


• •s 


.-, 


..V 


■ *v 


■ •s 


■ -. 




N 


N 


N 


N 


N 


N 


r» 


N 


N 


CO 


CO 


CO 


CO 




m 


CO 


CO 


ro 


CO 


ro 


CO 


CO 


CO 


CO 


ro 


CO 


CO 








* 














* 






* 




o 


I-H 


CM 


CO 


^ 


>o 


CD 


t^ 


CO 


o 


T— 1 


(Tq 


CO 




CO 


OO 


QO 


OO 


CO 


00 


CO 


OO 


GO 


Oi 


OS 


05 


OS 




o 


O 


O 


o 


o 


o 


O 


O 


O 


O 


O 


o 


o 




I-H 


I— 1 


I-H 


— f 


1— ( 


I-H 


I— 1 


I— I 


I-H 


iH 


1—1 


I— 1 


1—1 



ON THE PELLIAN EQUATION. 



89 



>-i 00 
05 O 
t- 00 

to CO 

■* lO 

TtH 00 

o >o 

CO o 

O 00 

lO Oi 
■* 00 





-2- 


" 




^ 


^ 




m 


VO 


o" 




•-« 


6\ tZ 


ro d\ 




►-< 


N 




w 




m" 





" 00 









o 



I CD 



in <M 

i-H O^ 
CO 



.-I «D 

CO i-H 

to o 



OS 

o 



N 00 



CO 

o 









CO CI 

lO o 
CO oo 






fivo 






00 00 

OS 

o 



N 






00 
o 



>o to 

t- CO 

lO IC 

■^ 1—1 
la 00 

t^ CO 

lO 50 

O -H 

00 CO 






r<1 






M 



O 



I^ 

ro 



>o O 



Oi 
O 



:0 Gi 



CO I-H 

I- o 
iM CO 

CO i—t 

t^ CO 
CM 



c<» CO 

00 tH 
00 ■* 

« c^ 

-* 00 

CO CO 






O 

o 



N ■ — • 






CO 



lO •* 

-* N 

.-H O 
1—1 lO 

1—1 -*l 

CD t^ 

to IM 

O CO 

t- -* 

CO 



N 0\ 



VO ON 



"1 



O >£> 






o 



W ON 



CO 












CO i>- 



t- CO 

lO 00 

00 -ti 



ro 

CO 



CO 

o 



N CO 



N lO 



O 



IM lO 

1-1 o 



t^ a» 






O 



1^ VO 



CO 

o 



90 



REPORT — 1893. 





la to 


O 05 


t- o 


O 05 


CO o 


to ^ 


to CO 


in CO 


m to 


O 05 


in 00 


to CO 

CM rH 
rH CM 


■* in 




as iM 


I— 1 -^ 


1— t ^H 


to 05 


o 


t- o 


in to 


Tjl CS 


to C] 


(M as 


-# .-H 


to m 




(M o 


la CO 


to to 


OS 


»H 


in 


o -* 


i^ cj 


in rH 


CO t^ 


to i-H 


CO N 




OO CI5 


CO »o 


CO S-1 


rH 




<M 


>-l M 


to IM 


to o 


00 o 


CO -H 


to t^ 




<-l « 


t-i i~ 


CO Tt( 








oq c 


in o 


CO to 


CO IM 


■* •* 




■* m 




N N 


o »*< 


t- in 








w 


•-I (M 


l-H in 


i-H to 


in in 




35 to 




t- 


CO o 

CO CO 

to OO 

CO 05 

O CO 
O t- 
(M O 

-H O 

00 in 
»^ 1-1 

lO 

1—4 

(o"2 


in i-H 

03 o 
IC o 

CO to 

<M O 
CO c^ 
00 o 

to 










I- CO 

-* O 

in 00 

rt GO 
1-H t^ 

CO •-^ 
00 —1 

to 


■* 


■* 


in "*< 
00 s^ 

CO OO 

in t- 

as o 
m 03 
in to 
as to 
in 00 

IM o> 

t- CO 

(M to 

to OS 

o 
fT « 

— ' N 

H^ IH 




•— 1 

CO 
































<— ^ 


















»v « 










•> •* 


















n-M 










ro « 


















IH 










N 












^-v--^ 






* ., 






















I-I CO 






IH On 










On t^ 












CO 






■»!• 










»> •* 




























xrt N 












»-i CO 






VO 0\ 










t-t 












^- CO 












































N t>. 












•» •. 






IH t^ 










M 


'^'^ 










VO O 






CO 












N 
















r> •% 










mvo 
















►HOO 










i-t 


Ni;; 










t^ On 






N 












""' N 


























w On 










coi-^ 






IH I^ 










ro 


^ 










l-H 






CM 










.. « 


'i-ro 










•V -s 






« X 










N " 












I-I M 






IH On 










N 


^ 










■* 






CO 










•s « 


M 1^ 










r. r> 






n A 










N fO 


Tj- 










COlO 






VO ■<t 










N 












M 






IH 










n "s 


N C3 










•* « 






•s -t 










■-■ Ov 


r) 










M ON 






Ovt^ 










N 












CO 






•» •\ 












M On 
















N IH 










►I VO 


C4 










P< P) 






CO 










m 












N 






•* X 










•V •» 


►^tC 










•« ^ 






M CO 










VO ON 


ro 










■"^ ir> 


^_^ 




N 




_^_ 






•"Too" 


VO rf 










•V r> 


lo o 




M cm" 




CM CO 






^ 


HI 










O VO 


^^ 




lO 




































•*r^ 


ro tr> 








00 t^ 


« »s 


M o; 


'g^ 


•>? CO 




VO O 






M 


tH 










>-< lO 


^ 


s_^ 


IH 




M 






fOVO 


totC 








•H r^ 


00 , 


lo i-T 


fT CO 


lO CM 




M Oi 




t-t 


IH 








^ 


t^ 




N 


IH 




CO 






«^ >s 


., « 








^ « 


•s « 


„ 


•^ as 


«s <% 




•\ •* 




•^ ^ 


W ON 


►H TT 








fOVO 


►H ON 


•"i- ■* 


IH O 


CM CO 




IH V> 




l^ On 


Tl- 


M- 








k~l 


CO 


IH 


-* 


CM 


CM VO 


CM 




cq" ro 


i-T f^ 


\r, M 






r^oo 


corC 


w vo" 


►T lo 


lO M 


hTvo" 


CM 


i-Too" 




N 


N 


»-4 






►1 


N 


CO 


IH 


CO 




CO 
































>-<" rC 


tToo' 


ro On 


i£, o 




hH l-H 


" rC 


►H CO 


IH O^ 


pT lO 


cm" t^ 


CO tC 


•* CO 




CO 


N 


" 


■^ 


-^^-, 


■<1- 


CO 


CO 


CM 


CM 


CM 


•H 


IH 




fooo" 


r^ cS 


ro O 


CO M 


to N 


N to 


N 'f 


rTio 


cTvo 


cf rC 


eM'oo" 


cf cS 


cT o 






i-i 


N 


N 




M 


M 


N 


M 


N 


CM 


CM 


CO 




• •s 


• •, 


•.I 


• •N 


• •s 


• •\ 


• •> 


• -^ 


• •V 


• •V 


■ •\ 


• *. 


• ^ 




<^ 


ro 


to 


(O 


to 


to 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




CO 


ro 


CO 


CO 


CO 


(O 


CO 


CO 


CO 


CO 


CO 


CO 


CO 








* 










* 






* 








1?- 


00 


CI 


o 


rH 


CN 


CO 


■^ 


lO 


ZO 


t^ 


CO 


OS 




O 


o 


o 


1— 1 


I— 1 


I— 1 


T— I 


I— 1 


I— I 


1—1 


1—1 


.—1 


1—1 




I— I 
I— 1 


I— 1 
I— 1 


1-H 
1—1 


1— 1 
I— 1 


rH 


1— I 


1—1 
I— 1 


1 — 1 


T— 1 


1—1 


1—1 
1—1 


1—1 


1—1 
1—1 



ON THE PELLIAN EQUATION. 



91 





lO I-H 


O •-> 


oq (r- 


o: <M 


O 05 


■»*( ^ 


00 lO 


lO -^ 


O^ 


la 00 


CO t- 


00 lO 


(N t- 




<D O 


C^ lO 


ZO 


Gi OO 


Tj( TtH 


CO O 


-H O 


•^ (M 


i^ »o 


CO 


I-H CO 


^ CO 


CO -*< 




So 


CO 03 




r^ -t* 


t- o 


00 o 


t~ cq 


CO (M 


CO 


I— 1 


■* 


C5 -H 


CO Ht 




cc «o 


00 'it 




-* (M 


t- o 


1-1 Tt< 


<M -H 


rt lO 


e<i 






O 00 


CO >o 




IM 


»o to 




1-1 CO 


00 CO 


Oi o 


as 


lO 








1— t CO 


CO 00 




1—4 


W5 CO 




(M 5£> 


t- CO 


N ^ 












CO 


(M 00 
CO ITS 
00 o 






t- ■* 




CO (M 


U3 O 


O CO 


















C5 O 




(M CO 


l^ o 


O !>) 


















m i-i 




,-( lO 


-i< (M 


CD t~ 














■"3^ xo 
05 CO 






05 lO 




rH UO 


t- (N 


rl O 


















cc 00 




t- tH 


CO CO 


»o CO 














^ rjl 
xa -rtt 
CO Oi 

CO CO 

1-1 (M 






id Gi 




lO o 


(M 


t^ 


















•^ ,-H 




CO CO 


ffq 


1-1 


















1— t 




05 O 


























CO 

f— ! 


















rH OO 
CO 






































^^ 


















VO ^ 
1-1 *— ' 






^-^ 




"ro N 


















*"— ' 










ro^-* 


















»s #1 






I-I o 






















N I"^ 






^ 




fOtC 




v5"ON 














N 






corC 




»-t 


















ef "f 






M 




M~ tC 


(o 2 


« "? 














M 






rt m 




•* 


v_^ 


1- 














cool 






HH 




^ 


«\ .N 


•s •% 














»-« 










O vo 


M XT, 


N O 














•^ « 






M Cf^ 




i-t 


N 
















t^ CT> 






^ 




•> •* 


•* •\ 


•> ■% 














»v •* 










N t^ 


1-1 N 


1-. \o 














xr, N 






tCoo 




W 


ro 


CO 














•"• 






I-Tio 




cT pT 




i-T lo 














cf cS 






CO 




M 


N 


N 














N 












tn 


" 5- 












->4- CO 


tCoo" 






•% n 




•N *» 


•* •\ 


r\ r\ 












^— ' 1-1 


i-T rC 






cnvo 




1-1 m 


M 00 


vo •* 












•— ^ 


xr. 










tn 


M 


1-1 












«• r. 


^ « 


























>-i xn 


1-1 CO 






•"T tC 




rooo" 


(4" \ri 


tC cJn 












CO 


c^ 






m 




1-^ 


f<^ 














*s n 


n A 










•% .V 


« ^ 


fT iri 












" s. 


M VO 






i-T xr, 




tv. ON 


PDt^ 


M 












CO 


CO 






n 




lo i-T 




M 0\ 


co^ 










pf CO 


M 1-1 






►h" cT 






ro cf 


C) 












C) 


CO 




"^5 


!* 




" T? 


N 


w vo 


1-1 1-1 


■con" 

CO" — 


— w 




IH »H 

CO 


N cT 


•>? CO 




^ 


00 rC 




ir^ 


r^xr, 


CO 


xr. 






^^^^ 


*« «\ 


t^ 




M* \ri 


i-Tvo 




I-T CO 


r, vv 


xr, hT 


COlO 


CO cfl 


rT CO 


C4 


I-l 1.1 

* — CO 


I-T vo 


1-1 ON 




xr, 


ir, 




N 


OM^ 


M 


1-1 




M 






CO 


CO 




•S o\ 


N lO 




•-T ro 


►h" N 


W 1-1 


" d 


M Cj; 


woo" 




wvo" 


M lO 


" T? 






»-i 




(r> 


ro 


CO 


CO 


M 


M 




N 


N 
































rT i-T 


rT N 




m" -^ 


1-1 m 


i-Tvo' 


w iC 


moo" 


M d^ 


"a 


hH »-t 




1-1 CO 




fo 


m 




ro 


CO 


CO 


CO 


CO 


CO 


•<i- 


"^ 




m 


m 


m 


<T> 


to 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




r<l 


m 


m 


ro 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 






















* 


* 








o 


1—1 


G<J 


CO 


-* 


o 


CO 


t^ 


OO 


Ci 


o 


I— I 


CM 




CM 


G<> 


CM 


CM 


<M 


CM 


CM 


<M 


CM 


CM 


CO 


CO 


CO 




r— 1 


T— 1 


r— 1 


1-H 


T— 1 


I-H 


I-H 


1-H 


I-H 


I-H 


I-H 


i-H 


T-H 




1— 1 


I-H 


I— 1 


1— 1 


T— 1 


^ 


1— 1 


T-H 


I-H 


1-H 


I-H 


I-H 


I-H 



92 



EEPORT 1893. 



O 05 


O 05 


lO -* 


o o 


0^ t- 


(^ -H 


■* lO 


IM ^ 


oo lO 


O rH 


lO tH 


rH in 


t> OH 


o o> 


■* -^ 


O 05 


e-i Gi 


Oi 00 


CO I-H 


CO 


t~ CO 


O I-H 


rH O 


IM (M 


rH CO 


CO lO 


CO CT3 


oo 


lO I-H 


CO 1^ 


<M -*i 


CO t^ 


f-H 


"*< 


IM (M 


o ^ 


05 CO 


CD CO 


IM 


Ui ^ 


CM ^ 


OS «D 


00 o 


CO ^ 


O 00 




(M 


t- lO 


CO IM 


ro o 


to -H 


^^ 


I-H r-l 


lO t- 


f-l lO 


rt C-J 


IM CO 


rH ■* 






Ci IM 


IM r-t 


CO CO 


rH CO 




>n 


t- o 


CO Oi 


t- IM 


to cs 


CO 






CO rH 


00 to 


rH t^ 


in 






O CJ 


CO "^ 


-* 


O 00 








t- r^ 


CD CO 


■* 








T-H «0 


t^ >o 


(M 


C5 CO 








C2 CO 


IM O 










CO 


o t- 

lO ■* 

»— ( 1— < 

CO CO 

o 

rH 

CO 

•"Tvo" 
N 

•- IT) 

CO 
N 
CO 
CO 


•*(o" 


IM tl 

05 O 

rH lO 

CD 

IS 

-fvo" 

IH 

io« 

IH 

iri 

tCoo 

CO 








rH IM 

t~ CO 

O CO 
to 05 
lO CO 
CO IM 
t- (M 

(M t- 

iM in 

CO rH 

lO -* 

OO OS 

CO CO 
CO IM 
Ci 00 
CO t-* 
O CD 

CO CO 

o 

rH 

I-T VO 

CO 

I-T »C 

N 

i-Tvo 

CO 
COlC 

IH 
C^ IH 

N 

hT lo 

VO ro 

J^ 0\ 

CO O 

t^ cT 

cT lO 

N 

i-Too" 

N 

IH OxOO I-^ 
CO^-'^— 


CO — 

I-T cS 


rooo" 

-~^ IH 








'5'5- 


COlo 


« ^ 


>H O^ 


IH CO 
CO 






" CO" r£ 




cT ro 


•H "n" 

^— ' VO 








►^ 


Ovt^ 


p) 






N lO 


oo" tC 


M 






^"^ 


" ox 


fT iri 


fT -^ 


i-T CO 

'~' CO 






„" o" ■<? N 


I-T CO 


•H ^ 






.— s,— s 




•* 


C^ 


M 






^ ." 


ll- 


CO 


VO cR 




VO i-l 


o v^r 


»-» t-l 


rorC 


■^ 'f 






N ,^iH"ro 


pT pT 


►H rC 


" o 




o.^^ 


NvcT 


•"• 


CO 










w 'IJ- 


N 


N 


•^ 




*s *> 


N 


* 


^ 


^ 


^ 






-^ r 










VO ^ 


*< n 


N Ox 


" N 


►H f^ 


corC 






i-Tio" <^ ^ 


lO IH 


«h" tC 


hT lO 




»-l 


t^ On 


M 


CO 


CO 






.^^^-^ 


ro " 


'-' 


CO 


N 


-— ^r. 


w CO 


coin 


■=? ^ 


rT CO 


>-~ pT 


IH IH 




^ lO 


« M* « O^ 


IH t^ 


■<? 'f 


I-T o^ 


lO M 


■>:1- 


*-' 


*^ 


N 


CO 


'I- 


.— ^^^ 


•^ 


CO '^ 


■* 


M 


ro 


- > 


w" CO 


rT cT 


N « 


cTd 


n" o! 


cToo" 


^-^ IH 


covo 


COlO 


CO T? 


•* CO 


T? pT 


VO IH 


CJ 


c^ 


N 


CJ 


•H 


IH 




IH 


•H 


IH 


IH 


IH 


^-' 


1- •^ 


i-T \r> 


M *xr 


"x rC 


i-Too' 


IH On 


•H Cf 


IH IH 


I-T cT 


->" CO 


r »i 

>H T^ 


I-T VO 


rTvo" 


^ 


■* 


•* 


^f 




■>^ 


XT, 


VO 


VO 


VO 


\r\ 


li-> 


in 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


ro 


ro 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


ro 


ro 


ro 


ro 










* 














* 


CO 


'^ 


lO 


CO 


t^ 


GO 


Oi 


o 


I— I 


CM 


CO 


Thi 


iO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


^ 


-*< 


^ 


-^ 


■rtl 


TT 


!—( 


r-l 


1—1 


1— ( 


I— 1 


r— 1 


r— 1 


1—1 


I— 1 


1—1 


rH 


1—1 


J—i 


rH 


I— 1 


T-i 


I— I 


I-H 


T— 1 


I-H 


r— 1 


r— 1 


1—1 


1—1 


r— 1 


1—1 





























ON THE PELLIAN EQUATION. 



93 



. O-t 


CO CX> 


CO t~ 


^ Its 


(M 05 


1-0 


t- t~ 


CO CD 


■* 10 


rH -i< 


r-f ^ 


-* t- 


^^ 


«* la 


•- 


00 


(M Oi 


03 -* 


0^ 


1— 1 l^ 


r^ iO 


CO >o 


CO 


CO 


CO >o 


00 ITS 


CO lO 


•^ CO 


00 00 


CD oq 


IQ tX 


00 00 


»o 


'J 


f-H 






rH 


rH lO 


1-1 t~ 


in c<i 


■* iO 


<?) t- 


lO ■* 


«r- —1 




10 (M 


t— 1 






rH 


IO -tH 


O ^ 


■rj< 10 


:d 


^ 


iM 00 


t- 




l~ t- 










t^ (M 


i-H ■* 


^ 


r—t 


i^ sq 


05 CO 


«0 «D 




00 










10 Tj( 


M 


00 t- 
I- -* 

OS 

•-I kO 




t~ 


CO 00 

i-H 
1— 1 


-n 
OS m 

rH lO 
CO 

ro*— - 




cc CO 
10 M 

<M 



05 •* 
00 
l^ 10 
I— 1 t^ 

-*< 

CO cq 


pH 

CT'ro 
ro 

i-T ro 
--' ro 

rovo" 

ro 

N 
10 ih" 

►h'oo' 

(V) 

hT ro 
N 

ih" pT 
CO 

i-T tC 











00 rH 

CO 10 
00 
oq ^ 

rH 

o: 05 

■* CO 
CD 

rH 

CO ir> 

IH VO 


o"S 


N 






M to 


VO 




ro 














« ro 






N 
















CO LO 


« .v 


(D 








^ 




t^OO 










►H 


IH l-< 


•* ^ 






„ ^ 


fO o^ 




^ ^ 










„ 


■* 


-' t^ 






N i-i 






>H ro 










f) rC 




N 




pT,-^ 


N 


- -s 




lO 










M 


IM lO 






N CO 




N IT) 
















M 


"00 






I-I IH 


N 




VO ON 










N VO 


^ « 


ro 




K 


■* 


•> a^ 




•s »s 










c^ 


►hOO 


n 




m . 


« -V 


c» ro 




IH ih 










^ 


ro 


XT) „ 







*■* 


M 




Tl- 










Tfvn 


rovo 


•^ 


3"5 




H-t 


•H OS 




•h' •^ 










IH 


IH 


" (^ 


I-* 


tC 0^ 


N 




M 










t^ a> 


• « 


rn 


^-' 


. N 


„ „ 






•s r. 












l-< t^ 


A ^ 


" ». 


t ^ 


ro « 


IH 00 




— ro 










N pT 


•* 




CO 




M 


CO 


^ ^^.^ 


•* 


^-^— *» 








M 


\r, o 




^ ^ 


00 . 


CSvO 


fT iri 


I?-S 


hT ro 










hTio 


It 


^ C> 


t^OO 


r^ 


•"• 


IH 


^p.- 


N 










■* 


.« av 


*« n 


•^ •% 


n r. 


■> M 


K fc 


•\ •* 


* r. 


-» ». 


"^G" 
"^2. 


00 IH 


Tj- N^ 


.1 as 


•- »^ 


- 00 


" o\ 


11 


*-« ►-« 


•H P) 


IH m 


►" ■* 


IH 10 


VO '— ' 


ro^^ 


N ro 


U1 


10 


W) 


VO 


vO 


VO 


VO 


VO 


>o 






N 


"- 


• •* 


■ K 


• *. 


• -, 


• •^ 


• •1 


■ •^ 


.» 


■ IS 


• •K 


• •s 


• #> 


CO 


ro 


ro 


ro 


ro 


m 


r*i 


ro 


ro 


ro 


■* 


Tf 


'i- 


ro 


>rt 


ro 


m 


m 


m 


ro 


ro 


to 


ro 


ro 


CO 


CO 














* 






* 






1:0 


t>. 


GO 


Oi 





I— ( 


Ol 


CO 


TiH 





t^ 


00 


Oi 


^ 


-* 


'^ 


-tl 


10 





10 


10 





vO 


lO 


10 


10 


r—l 
1—1 


I-H 
I— 1 


1— 1 


I-H 




I— ( 
I-H 


I— i 
r— 1 


1— 1 

r-H 


i-H 
1— 1 


rH 
I-H 


r— I 
f— 1 


I— 1 

I— i 


1—1 

I— 1 



94 



REPORT 1893. 






t- CO 

o ^ 

•^ 00 
I— 1 «o 

N CO 

in ,-1 

05 



(M CO 
to t- 

CO CD 
CO i-H 

CO CO 



■* O 
lO O 
CO f-l 

in (M 

05 CO 
CO O 
CO CO 



O 05 CO 00 

CO 05 t~ t^ 

OS ^ t- l~ 

■* 00 O --H 

CO IM CO 

t— 05 

CD OS 

00 <o 

Oi 
IM 






r^vO 






o 









t^ On 

oo"©©" 









" O 



CO 



CD 






vo a. 






N CO 



»-t vo 



CO 



CO 



ro^-- 



CO 



CO 



N CO 



1-1 00 
CO 



o ^ 
t-. o 

00 t- 
O t^ 
-* C<1 

CO 'H 

OS o 

rH CD 
CO 



CO CO 

-*i (M 

05 00 
O CO 

CO 



O C5 

in -* 

CD •— t 
CO 00 






CO 



CO 
CO 



M ro 

CO 



CO 



CO 






w 0\ 



w \0 
CO 






11 vo 
CO 



CO 

CO 



M 00 

CO 



t-t CTv 






-* in 

CO CO 
O 05 
OO CO 
IM 00 

00 05 
f-H -^ 

-+I 05 
00 lO 

OO CO 

CO (M 

lO -"ti 
00 



05 

01 OS 
I— I ■* 

CO 






VO O 



CO 



CO 

CO 



►H vo 



lO CO 

vo" i-T 



CO 



CO 



t^ Ov 



N CO 



>Acf 



00 t^ 






1^00 






o 



►1 lO 

CO 



CO 



P) On 



COiO 



Tfvo 
to CO 



CO 



OO 

CO 



■4- 
co 



CO 



CO o 
CO CO 
(M ■-( 
O CO 
CO t- 

-* ^ 

t~ 00 
IM CO 
U3 IM 
rt CM 

to 



O (35 
CTi -* 
OO CO 
Oi O 
>o N 

CO CO 

(M 



vo OS 



CO 



o 



CO N 
CO~^ 






HI O 
CO 



li lO 

CO 



M VO 
M 



PI M 
PI 



I- P) 



CO 



"H CO 
CO 



vo ■♦ 



CO 

covd" 



CO 



cot^ 

■cfvo" 



CO 






ON THE PELLIAN EQUATION. 



95 





-i** t^ 


^ lO 


— < 'X 


O -H 


o ^ 


CO CO 


05 O 


O 05 


lO 00 


IM b- 


.-1 00 


lO l-H 


O —1 




CO 


t^ «o 


O <M 


^ o 


CO lO 


CO 00 


O ^ 


lO 05 


-+i n 


CO 00 


O C-l 


00 O 


O lO 




1— 1 


t~ 00 


O M 


^ 00 


T« CO 


l~ Ui 


CO CD 


05 Oi 


O t^ 


CO lo 


-*< CO 


0<« C-) 


N l^ 






-^ ^- 


(M cq 


■* 


00 to 


rt a> 


o 


00 ■* 


00 CO 


iM N 


CD CO 


lo ta 


CO 00 






l^ C5 


1-1 ■* 




t~ t~ 


lO 


r-^ 


lO 0-1 


CO CO 


05 »0 


OJ l> 


OS CO 


O rH 






CD in 


•4* 




t~ ■* 






o 


00 t~ 


C^ <M 


t~ lO 


t- CO 


(M ■*< 






O CO 






in rt( 






IM 


00 -^ 


t^ 


CO o 


t~ 


7-~* r-^ 






-*( o 






CO o 








t- CO 


IN 


CO 


C) 


•^ 






rH 00 






O 05 








c-l r^ 




r-1 










to C5 






CD CO 








CO CO 














CO !D 






tH lO 








lO ■* 














CO "C 






lO .-H 








CO Oil 














-H to 






CO o 








e<i 














(M O 






00 ^ 








iH 














rH W 






CO o 






















05 OS 






CO (M 






















o t- 






»- 00 






















<M 00 






N ■>« 






















(^ 0-1 






03 






















CD •* 




























CO '^^ 




























!0 0-1 




























CO t- 




























i-H «0 




























■* 




























'i-N 




























n--' 




















































































t^ ON 




























►H tC 




























rD 
























































wo" 




























fl 




























•\ •s 




























N fO 




























N 




























». *s 




























P) ^ 




























N 






^^ 




























VO HH 






















Tj-ii-) 






^^ i^ 






















H4 




























•s •» 






•* _ 






















VO O 






00 oo 






















l-H 






cf rC 






















w" cj; 






N 






















CO 






*> n 






















*s «> 






N Tt 






















>-< r^ 






f) 






















N 






pT ro 








^1.'-^ 














»-t T? 






P) 








CO"! 














ro 






11 (sj^ 








n 




















CO 








ro^ 














•K n 






11 CO 






















« VO 






CO 








w -^ 














•"* 






pT hT 








^ 


^^^-v 












S^ 














«'jr 


O )0_ 












" O 






CO 








VO •* 


I-T rC 






2"^ 






*J^ 






cT .^ 






^— *^-» 


n 


-* 






— 






rotC 






c^ 






N O 


hT^O 


pT o> 






CO d\ 






(— « 






t^ C\ 








to 


'-' 


^-^^^ 




n 






fOiO 












i-T 6\ 


iri 1 


i-T cR 


CO ■* 




pT ^ 






*^ 






COtC 






CO 




CO 


^- 


--^>-^ 


PI 






N o' 






. 






pT " 


CO O 


pT pT 


11 CO 


CT-S 


n n 






n 






"o£ 






N 


PI 


PI 


to 


^^ 


CO 








^ 




•* 






















^ r^l 


U-) w 




•> n 






W H 


CO t^ 


pT CO 


PI CO 


dl tC 


»H lO 






*^ 


l-< 




0\t^ 






CO 


n 


PI 


M 




CO 






*> «s 


n »K 




" ^ 






•* 


•% 




« n 


•S *1 


^ « 






<-.KO 


r) vri 




M CO 






n VO 


H 1 


I-T ■* 


I^ o. 


H ON 


CO NO 






•* 


e^ 


^-^^-^ 


r4 




^--^-, 


CO 


•* 


CO 




^ 








(^ irl 


i-T hT 




i-T hT 


c^ CT 


CON 

CO^-^ 


lO «■ 


pfo 


i-T ON 


"OO' 


CO NO 


H n 






•"• 


CO 




lO 


'~'^ 




n 


M 


N 


CO 


n 


^ 










.< *\ 














•t •% 










>- ro 


" rj- 


N vn 


CO'O 


•* M 


M lr> 


M t-t 


n t^ 


►T CO 


n ON 


M to 


PI « 




'-*»-— ^ 


•* 


ro 


M 


'-' 


On t^ 


•* 


rf 


CO 


CO 


PI 


M 


PI 




^ ^^ 


r^oo" 


ro d\ 


CO o" 


CO I-T 


CO pT 


pT CO 


pT ■* 


pT to 


pTo 


pT rC 


pToo 


pf ON 




— ■ 


•-• 


i-» 


M 


c< 


N 


P< 


N 


c< 


M 


PI 


N 


N 




»m. 


*-. 


■ •V 


• •* 


• *. 


• ^ 


• •\ 


a*. 


• •k 


• •V 


■ •V 


»- 


• •^ 




^ 


3: 


'i- 


•* 


•* 


tl- 


•* 


■* 


^ 


•* 


•* 


^ 


1- 




ro 


CO 


ro 


CO 


CO 


CO 


CO 


CO 


ro 


CO 


CO 


CO 


CO 


















* 












CO 


-* 


»o 


CO 


t^ 


GO 


as 


o 


1—1 


(M 


CO 


•^ 


lO 




t^ 

f_^ 








t^ 


t^ 


t^ 


oo 


CO 

1 


GO 


GO 


GO 


GO 




I— i 




J— 1 


1 1 

1—1 


I— t 


I— 1 


.-H 


1—1 


■-1 


1 1 

r— t 




1— < 


1—1 


1 





























96 



REPORT — 1893. 



IN »o 


lO to 


o o> 


U3 OO 


<M 05 


tN in 


lO 05 


lO 00 


O 05 


!■! C5 


IM lO 


O 05 


O 05 


Cfl Oi 


t^ <M 


-H <35 


^ —1 


«o 


05 t^ 


C<> 05 


O CD 


lO ^ 


CO lO 


rH I-H 


(M OT 


CD 05 


la .-1 


t- ■-£> 


•^ »o 


05 -^ 




1— t 


00 tH 


00 IM 


t- t^ 


■M 05 


-^ 


00 lO 


^ lO 


CO o 


CO lO 


i-H 00 


00 l^ 




CO 


03 (M 


CO ff^ 


CD 00 


CO O 




■* CO 


CO r-l 


CO <N 


^ t- 


■* 


O rH 






CO t~ 


lO 05 


t^ CD 


r-( CO 




t~ CO 


I-H lO 


T-i m 


l- rH 




OS .1 






t- 00 


t- 05 


^ -* 


lO o 




>o 


CO (M 


CD 


^ »o 




^ CO 






CO CO 


^ -* 


CO l- 


-* o 




cq 


CO 05 




CO 05 




(M O 






—1 l^ 


a<) >o 


IM ^ 


CO »o 






-^ lO 




.-H O 




OO ^ 






t— ^ 


00 


CO CO 


t-( CD 






CO CO 




^ 05 




lO CO 






C3 lO 




I-H 


■* 






CO (M 




CO 




00 






CO 
CO 




(M 








00 o 
05 U3 

CO CO 

05 CO 

lo CO 

CnI lO 
«0 (M 

r^ CD 

(M O 

I-H C-l 

co^ — • 

CO >^ 
N 

CO tC 

1-' n" 

N Ov 

i-i 

►-"no" 

no" ol 
•-Too" 

pT CO 
N 

lO 


































no" 






" cf; 




O VO^ 








cf\ tC 








N 






CO 




■ — • 


^-^^^ 


























CJ w^ 










i-H C3^ 




i-i tn 






"00 




« On 








« no 




'i- 




■* 






N 


^-^--^ 


rf 


-^ 






•I 
















1/^ CO 














M 0\ 




^O CT> 






►H >-l 




COJ-^ 


►H ON 






N 0\ 




»-t 










CO 




>~* 


"-) 






C) 




•N *l 




•« * 






.< .s 


lO CO 


■s .v 


-^ -s 






•s n 




" t^ 




•-i r^ 






►H CO 




VO o 


NO 






CO 00 




Tl 




^r, 






CO 


- — 


t-t 


M 






*-* 






























H lO 




\0 •& 






N ■* 


00 00 


hH W 


« ON 






N CO 




CJ 




>H 






N 




'i- 


CO 






P» 




























ro^ — 


»H t-t 




n" ^ 






rOtC 


cf d\ 


« \r, 


« (> 




OO r^ 


moo" 




Tt- 




M 






i-" 


f) 


a 


N 






CO 


.s *. 


•^ "* 




•• •« 






n A 


^ ». 


r^ w. 


r. „ 




•< « 


IN « 


■*io 


0>*s. 




i-< VO 






" On 


COVO 


'-' N 


P) NO 




" ON 


C) w 








tr> 






CO 


•-' 


'J- 


N 




"1 


CS 
























•\ ■% 




►H .^ 


^ 'i- 




N ro 






w 'f 


■-• J^ 


Ov r^ 


1^ On 




NO Tf 


<- Tj- 


rr> 


►H 


^-^^-^ 


CJ 




-— ^>-^ 


c< 


^ 






,^, , 


« 


CO 


i-T CO 


"1 tC 


VO M 


en d' 






cf^tC 


IT) f^ 


rf lO 


CO On 


M CO 
N 


fTrC 


I-T ►^ 


fn 


Tt- 


— ' 


N 








h-t 


" 


t-< 




c< 


CO 


folc 


■^ (^ 


iC ON 


roio 




I-T tJ 


i-T CO 


" cf 


M »H 


"d 


« o; 


hToO 


•1 ■s 
►H t^ 


t-l 


M 




»-t 




m 


CO 


CO 


CO 


CO 


N 


N 


PJ 


N o 


cT i-T 


pT fT 


ti ro 


hT i/> 


i-Tvo 


w rC 


"00 


w <> 


"d 


>-« »-i 


hT n" 


ro 


ro 


CO 


m 




en 


CO 


CO 


CO 


CO 


•<i- 


•* 


^ 


.K 


• •K 


..^ 


• •V 


• fc 


• .V 


• •\ 


■ •k 


.« 


..^ 


>•. 


• •^ 


>K 


■^ 


Tf 


T^ 


■* 


■* 


rf 


■* 


■* 


•* 


•* 


■* 


•* 


Tl- 


n 


ro 


ro 


fO 


to 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


co 


■- 




* 








* 












O 


t^ 


GO 


Oi 


o 


T— 1 


«<l 


CO 


^ 


lO 


CO 


t^ 


OO 


OO 


CO 


GO 


OO 


Oi 


CTi 


G5 


Oi 


Oi 


OS 


Oi 


CJ5 


OS 


T— 1 


1—1 


.-H 


r— 1 


I— I 


I— t 


i-H 


1—1 


1—1 


I— 1 


1—1 


r-i 


1—1 


r-i 


T— 1 


r— 1 


1— 1 


T— ( 


I— 1 


1— 1 


1—1 


r—t 


pH 


I— 1 


rH 


1— 1 









ON THE PELLIAN EQUATION. 








9 


05 O 


0> -H 


lO tM 


N t- 


-H M 


CO "O 


CO OS 


iM O 


t- 00 


CO CO 


CO in 


-^ -H 


U3 -^ 




CO lO 


00 CO 


1—1 r-1 


cq 00 


1-1 OS 


CO 00 


O M 


00 cq 


-* CN 


to CO 


CV) 00 


t>i 




CO 


CO 00 


CO 00 


lO (M 


•^ CO 


■o O 


Ol as 


CO OS 


O «0 


-H CO 


W3 C<I 


1-H 




r-t 




O 


IM -* 


'Jl t- 


CO-+1 


^ lO 


CO OS 


CC CD 


O 35 


3i 35 




t- t- 




fr- -* 


1-1 


1-1 CO 


U5 CO 


O t- 


-*l 


CO lO 


iq l^ 


'^< 'M 


Oi rH 




CO t~ 




o -< 




■* 


lO iO 


(N -H 


rH 


1-H 


1— 1 CQ 


CO O 


O IM 








00 t~ 






CO (M 


t- 




rH 


•^ 


1— I b- 


CO OS 














m Oi 










»o 






■* 




'^l o 
■* >o 

CT> 50 

CO tr- 
io iM 

00 CO 

CO oq 

.-1 CO 

•* 00 

lo CO 

00 rH 

^ O 

'tl 
<N 

tCoo 

■>?iO 

" n" 

CO 
N 

« o" 
pT d? 
•-Too 
CO vn 

« o 






Oi CO 

CO 00 

-H 00 

to 

ss 












1—1 




*^.-** 




■* 






vo 
















r*l W 

-' W 










S'^ 










SS 


vo 'o" 


































►1 in 

CO 
















"^ 


pT^h- 
CO 




-< to 










fod; 










" d^ 


^^' 






























CO 




rj- to 






pT to 

P) 


N to 




CO N 
CO' — 


oo~So" 


cT to 


tZ d\ 




























SrC 








CO N 


pTj;: 


l-t I-H 


CO^-" 


" dv 


pT CO 


COtC 


IH 1.^ 






^-s^^ 








N 


vo 


to 


p< 




•* 




i>o 


roo 






"I 1^ 


»C d; 


vo -i^ 


tf to 


vo dJ 


l-T r? 


•H o 


•H VO 




^■^ 




^-~— , 


>o 




»-l 


P> 




Ti- 


•* 


P) 




1 u-i 




-?^N 


^'~' 


lo 1-1 


-8 


N On 


1-00 
CO 


iH r«. 


OM^ 


pTco 
PI 


" Ov 

CO 




1 vo 
M 


M 




P) rr, 

p« 


p) PI 


P< 


Pio 
M 


P) Oi 


tioo 


CO t^ 

»H 


covd" 


CO to 


^2" 


■" fO 
'J- 


" s 


« m 


«vO 


>-• t^ 


'- 00 


►^ d> 


w O 




IH N 


•H CO 


IH Id- 


1 #1 




■<it- 


■^ 


•* 


^ 


'J- 


to 


to 


to 


to 


to 


vo 


% 


^ 


•* 


■5t 


-S- 


■* 


i^f 


-^ 


■* 


• t 
•& 


■* 


•<1- 


Tt 






CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 






* 






















3i 


o 


T-\ 


(M 


CO 


^ 


ut) 


ZD 


t^ 


GO 


05 


o 


1-H 


ji 


o 


o 


o 


o 


O 


O 


O 


o 


O 


O 


r-H 


<—i 


—1 


oi 


CM 


(M 


(M 


OJ 


CM 


CM 


CM 


(M 


CM 


(M 


CM 


•H 


^ 


i-H 


]— 1 


1—1 


r-i 


I— 1 


I-H 


I-H 


I-H 


I-H 


I-H 


i-H 



1H93. 



98 



EEPoni — 1893. 



O rH 


1:^ '^ 


•* la 


t- ^ 


lO »H 


03 CD 


O 03 


la CO 


•* 05 


(M >0 


(M t- 


in -* 


iH lO 


00 lO 


t-H CO 


o t^ 


•* 


00 o 


CD lO 


rH -*< 


CO IM 


i-H OO 


1-1 OD 


<M O 


CO (M 


CO 


05 >-l 


.-1 t~ 


f-H OS 


IM 


to 00 


05 IM 


CO 


^ CO 


tK 


CO CO 


.-H CO 


IM 




in ^ 


t- o 


0-* 




CO 00 


rH 00 




lO lO 




f— ( 


^ 03 


1— ( 




CD ^ 


(M O 


CO t- 




O -*l 


Oj <M 




OJ lO 




(M 


M O 






crj t^ 


O --0 


cq CO 




to Tjt 


t- CO 




IM 00 






lO ■* 






IM 


<M O 


O 00 




r-H f-H 


t- 




O "*< 






05 lO 






t— 1 


«> 


03 O 

OS la 

O r-< 
IM CO 

N 

M 




Oi 00 

iH CO 
CD 


IM 
CO 




O »0 

t- -*l 

•* IM 

I— 1 t— ( 
03 ^ 
t^ i-H 

-^ r-l 

t- 00 

CO 

(M 

coin 

l-t 

i-T d^ 

«0 CO 

T? lO 






•rti -^ 
IM IM 

rH -S< 

M CO 

m" cT 
NCO 
















»-1 M 
^ 

CO 




in M 

1^ 






CO 
































vo Tf 


w r^ 
























1-4 


-^ N 


CO 




CO 


■1 ON 




to 






1-1 1^ 






" tC 


c^^C 






*-• M 


►^»C 




C?^ t^ 






"OO 






•* 




ro 




fO 


CO 










CO 






N w 


►To" 


ro (> 




ff l^ 


co\o 




t^ On 






COtC 






N 


ro 


t-t 




M 


M 
















N ro 


►^ ro 


\o' o 




'S-lA 


M CO 




I-T rT 






N 0\ 






N 


ro 


*~* 




kH 


•* 




■* 






p« 






>- tC 


•^ ro 


i-T r^ 




<*)tC 


cT d\ 




hT lo 






tC Ov 






ro 


•^ 


■* 




" 






M 




, , , 








N ^ 


« c; 


pT r^ 




"oo" 


i-T tC 




I-T CO 




P) CO 
" — CO 


CO N 






N 


■* 


N 


^^^-» 


■* 


■* 




■* 


. 




N 


^^.— . 




>? r^ 


■* N 


vn i-T 


ir> O 


^' d\ 


rCoo 


00 t^ 


OVO 


N U|J 


VO ■* 


cf CO 


CON 
CO^-^ 




^^ 


•^ 


•^ 


^"^ 










^-' 


•"• 


M 




-^-^ 


«vo" 


•-1 I^ 


"Oo' 


i-Tdi 


" o" 


hH M 


i-T rT 


k-T CO 


I-T T? 


i-T in 


i-T^o 


•-"tC 


•-■ 00 


vo 


VO 


in 


lO 


VO 


VO 


^o 


VO 


VO 


VO 


VO 


VO 


• *. 


• *. 


• •s 


••« 


• K 


-.N 


■ •^ 


• •^ 


• •s 


■ *s 


• •K 


• -S 


■ ■K 


■* 


rh 


'^ 


■<1- 


•* 


11- 


1- 


■* 


T^ 


•* 


■^ 


-^ 


•* 


ro 


ro 


ro 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




* 








* 
















<M 


CO 


TjH 


lO 


«5 


t^ 


GO 


Oi 


O 


r— 1 


0^ 


CO 


-H 


I— t 


1— I 


1— 1 


I— 1 


I— 1 


— H 


I— 1 


1— ( 


Ol 


CM 


'M 


•ri 


<M 


0^ 


G<l 


(M 


(M 


G<l 


CN 


G^ 


CM 


C<1 


G^ 


(M 


G<l 


CM 


t— ( 


1 — 1 


I— 1 


I— 1 


1—1 


I— 1 


I— t 


I— 1 


rH 


1— ( 


I— 1 


I-H 


rH 



ON THE PELLIAN EQUATION. 



99 



CO 



■as CO 





CO o 

— ( 05 

CO ^ 

•— ( 




CD 00 
— 1 7^1 






O CO 

n; 00 






i-H 










o - 






•-* l-l 

ION 









N fO 
M 















CO 



CM 






•1 m 



>o 



»^* ^c:." 



IT" 



to 



O 

CO 
CM 



t- o 

l^ o 

■-H t^ 

lo 00 
t~ -* 

N CO 

O 00 

1— I a 

o o 
Id .-( 
CO o 

CO t- 

O lO 

m (M 

00 rt 

o 












On 
f<1 



fOoo 






ON 

CO 



O. 



" o 

CO 



CO 



^ lO 



fO VO 






'S- CO 



N O 

CO 



t^ ON 



N CO 



>o 



O rH 
-H »0 

CO 



-+I t^ 

00 lO 

Ci CO 

00 -* 

CO C>1 

O -K 

CO lo 

CO lO 

o o 

--lO 
N "*< 



CO 



O t^ 



lO 

CO 



CO 



VO 0\ 
lO 

omC 

m" (?; 

CO 

CO 
tC Ov 

•vjvo 

rOrC 



"I cfv 
00 oo" 



lO 

CO 



CO 
CO 



CO lo 
lo CO 

00 IN 

CO t- 

t- CO 

o o 

CO 05 
(M CO 
O 00 

CO CO 
CO CO 
I— I 00 



CO-— 



CO 



CO 

cooo" 

t-l 
N 
CO 

1-1 d\ 

CO 
ONtC 

N o 

CO 
Tf lO 

1-4 



1-1 f^ 

COl/j 

1^ 

" o" 
tC o? 



CO 



CO 



CV| Oi 

t— -^ 

CI lO 
00 IM 

^ t- 

CO IM 
<M O 

00 (M 

CD 



p) CO 



M On 



N O 
N 



11 CO 
CO 



1-1 «o 

to 



1-1 r^ 



»*■ CO 



O -4 

lO o 

CO lO 
»0 IM 
IM O 

OS 



.*>o 



to 

CO 



CO 



^- rr 



CO 



•00 
M 



N lO 



CO 



CO 



t^ On 

tC o\ 



N CO 



11 CO 
CO 



CO 



t^ •* 



CO CO 






II VO 
CO 



n VO 

CO 






»o 

CO 

co 



Ov 



N VO 
CI 



00 
CO 
CM 



H 2 



100 



REPORT 1893. 



lo CO 


<^ 03 


ta N 


O rt 


in -*< 


O 03 


00 rt 


00 lO 


CO CO 


03 tr- 


CO o 


^ t- 


CO o 


t— 


O rH 


O CO 


CO lO 


t~ i- 


CO O 


CT -i< 


00 CO 


•-' 00 


io rH 


03 •* 


O o 


-* IQ 


1^ 


1— ( t>- 


o o 


t^ i-H 


oo oo 


CO t^ 


>0 <M 


iM t- 


CO »H 


,H CD 


lO (M 


CO 00 


C3 IM 




■^ CO 


lo io 


,-1 in 


tH rt 


O CO 


CO ^ 


t- c» 


CD 05 


lO 


IN CO 


t- lO 


(M CO 




(N •<*< 


CO 03 


f— t rH 


I- 


CO O 


fH CO 


CO ^ 


cq sq 




C3 00 


t- 


03 CO 




CO 


03 OS 
CO 
CO 

00 00 


■* 


1— 1 


o t- 

co t- 

t-o 

lO CO 
-* O 

CO CO 

»— * ^H 

CO o 
rH tr- 
io 

>H VO 

ir, 

•* CO 

•* «t 

CO 
CO lo 

►" lO 

N 

•» _ 

« ro 
■<*• 

oo'oo" 


t-- 


(M 1-H 

^H CO 
CO 03 
^ CO 
lO CO 

t- 03 
lO 00 

rH "* 

co^-' 

« lO 

•* 

►T lo 
p) 

lO" 

cooo" 

COlO 


03 




CO CO 
CO 03 
C3 M 
OO 
CO 03 

CO cq 

O-l CO 

O CO 
Tj( O 

CO tr- 

N CO 

CO lO 
^ lO 
CO CO 

(M IM 

^ LO 

■* lO 

'— ' tH 

M IH 

CO 
COCO 

00 00 

vo 

COlO 

"00 

•* 

'? CO 

"A 

ih' rC 
N 

>-■ 0^ 
CO 

covo 

IH 

r» •. 
IH lO 

cor^ 

*H 

N •* 
d 

IH tC 

CO 
m" vo 


CO 

IH IH 

"•- CO 


rH lO 
N t- 

Ir- 

lof^ 

_ro^ 

lO CO 

IH 




— ' tn 


fo o^ 


fTco 








lO 

vo O 








IH .^ 

CO 


pTfC 

M 






I- in 




CO"^ 


coo" 


i? •* 


m r» 


'w'oo" 




cT ci 


pT vo 


pT vo 




tC d> 


CD 


»i t-i 


^-' M 


N 




t^ &1 


«— lO 




CO 


M 


M 




n" t? 


1^ N 


CO 




N CO 


^ 0\ 


.. lO 






CO lO 


■^^ 


cT ro 




N 


CO 


►Too 

CO 


(^rC 


N 


CO 


■H Tl- 


0>rC 


^-^^•^ 


n 


•H 


N 








*« •« 










t^ Tj- 










w »-i 


N in 


•s ■« 


>H o^ 


" o 


IH »-f 


N N 


lO CO 




1- lO 


*-* IH 


l-l f^ 




•"^ 


N 


r^ 0^ 


•"^ 


■0- 


CO 


N 


tH 


•_^ 


•* 


■* 


ro 




























\r^ ^ 


•<*■ to 


TtVO" 


'frC 


CO 00 


CO d\ 


CO o 


CO" 


CO cT 


CO CO 


N ^ 


cj" vo 


N vo 


•^ 




M 




t-4 




c< 


M 


N 


N 


N 


N 


01 


to 


trj 




lO 


lO 


lO 


lO 


lO 


lO 


lO 


vo 


VO 


vo 


ro 


fO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 






* 














* 


* 




Ol 


O 


I— 1 


(M 


CO 


'^ 


lO 


ID 


l^ 


00 


OS 


o 


,-H 


CO 


'^ 


'^ 


^ 


'^ 


-* 


-* 


^ 


-* 


■•* 


'* 


lO 


lO 


CM 


Gv| 


<M 


G<1 


(M 


C^ 


(M 


G<» 


S<l 


<N 


<>J 


G^ 


<M 


T~{ 


,—1 


1—i 


rH 


rH 


1— 1 


I— 1 


1—1 


I— ( 


I— 1 


\— 1 


i-H 


1— I 



ON THE PELLIAN EQUATION. 



101 



© 05 

00 ■* 

O 30 
0-1 -*l 
OC CO 

cq --I 

» (M 

O OO 

o o 

C5 (M 

to i-H 
Oi 00 

o 00 

(M 

CO 



O I-H 
C^ 1(5 

CO CO 

00 C) 
b- 



CO o 

O O'l 

rH to 

CO 






CO 






t^ o> 



»0 



T^ ro 






r^ a\ 



CO 



t-« OS 









00 OS 

O 00 
h- 00 

CO t- 

«o la 

CO <M 

^ o 

00 o 

00 ■* 
t- ec 

00 i-l 






CM 
(M 



O r~ 



w OS 



N CO 



ITS 

crj 



(M 



K5 Ol 

O ■* 
1-1 (M 
t— i OS 

CO 






►H OS 









fO 



CM 



t-t vo 



►H OS 



N OS 



w in 



•*•* 



ro hi 



»-i VO 



N 1-1 
N 



P) O 



"1 



G<1 



O OS 

CD OS 
00 CO 
IM I-H 

o 



CO OS 
CO to 
IM to 

CO •* 



OS o 

to I-H 

O 00 
i-H (M 

00 CO 

(M OO 

CO CO 

00 .-I 

OS CJ3 

CO o 

.-H Tj( 

CO .-H 






" o 



cs 



rrt 



CO 



N CO 



lO 



CO 



U1 
CO 



(M 






co 

CO 



CO 
CO 



M vo 



t^ OS 



M CO 
CO 



CO 

* 

OO 

<M 



VO o 



woo 
CO 



W lO 






t-i 1^ 



CO 



<N 00 

t~ to 
o t- 

T— I OS 

to o 

•* OS 

o -* 

•* N 

OS to 
to to 



00 CO 

o to 

TJH OS 
O to 

(N to 

»-H lO 
t> 00 



CO 






"— ' CO 



«0 

CO 



O 
CO 
<M 



-I vo 
CO 



vo 

CO 



«Om 



N vo 



I vo 

CO 






CO 



r> rj- 



t^ OS 



CO 

vo 



vo N 



??^ 



O OS 
C <M 



vo 

CO 



I VO 
CO 



vo 
CO 

I-H 
CO 
CM 



CO*-' 



I-l CO 

>o 



cot^ 

HI 



I-l OS 



'S- CO 



1 VO 



CO 



Osr^ 



O OS 
to OS 

CO t- 



CO 



vo 

CO 



CM 
CO 
G<1 



r) CO 



MOO 
vo 



IH CO 
CO 



woo 
CO 



lO 
CO 



CO 
CO 
CM 



'^vo 
'f vo 



I-l P) 

CO 



t-1 OS 
CO 



vo 
CO 



CO 



102 



REPORT 1893. 



O 05 


00 lO 


t~ oq 


O C5 


^ la 


00 1-1 


o o 


CO t- 


CO c- 


Ort 


O 02 


o a, 


>n IM 


<M a 


o to 


(M to 


a -^ 


CD .-H 


rt cs 


(M 03 


o 


t- o 


(M O 


-*l C5 


00 03 


00 00 


OO C5 


t- -* 


»— 1 Ttl 


•* 00 


(M (M 


■-I CD 


05 «r~ 


l-H 


^ 00 


t~ 00 


l-H OS 


m t~ 


(M ■* 


»0 CO 


«D O 


CO •* 


C-. tr- 


CO 05 


CO CO 


(M 




rt -* 


in o 


-* 


(N CD 


IM OO 


o 


CX> ^ 


t- rt 


05 O 


05 <M 


•* l-H 


CO 




la CO 


rH O 




O CO 


■* -ai 


« 


05 M 


IQ O 


lO 05 


■^ 


t- ^ 






00 ,-H 


lO l-H 




t- CO 


t~ OS 




■* CC 


t- lO 


CO OO 


CO 


CO t- 






»0 OO 


rt ■* 




IM MH 


(M t^ 




i-l CO 


l-H <M 


00 t- 




(M CO 






l-H CD 


to 




-* O 


-* CO 




»r3 


SO 


O; CD 
CD 00 




CO 00 
CO 1-1 

l-H 00 






<M OO 

CD O 

^ -+I 
CO ■* 
1-H 05 
■* ■* 
l-H ^ 

»0 CO 

00 

l-H 
m'on 

i-Too" 






t^ OO 

l-H i-H 

CO C5 

CI (M 

CO 

CO 

"23 


o ^ 

l-H 


















tC oi 












































































vo CO 






•» „ 




















I-l 






" CO 




















-s -s 






vo 




















N "S- 






" 




















N 






COu-, 




































VO Tj- 




'd- vn 






•^ •% 
















l-t «*-' 










11 H 






fT^ 














•— ' 






-i- 














., ^ 




r, ^ 






•s *« 






cs 










I-l 1-4 




r~ 0> 






cot^ 






■» 










vo 
















" vo 






^S 




d\t% 




« r? 
lO 






w N 






■cf 


VO ~ 




t-Ti^ 




■<f\o 




vom 






CO 






dvtC 


vd t^ 




iri 




*-« 




»-4 






w d^ 


^_^ 




i-Tvd 


^_^ 




^ ^ 




•* •» 




.» •» 






CO 


'JJ'VO 




CO 


^ 




CO u-i 




N CO 




11 O^ 






•V SN 




n -s 


P) CO 




l-H 




C4 




CO 






CO CO 


*"-' 




11 lO 


P) 






to rf 




' — ' c» 


" d 

CO 






■^vd 


IvT CO 




CO 
tC o> 






^ 


•_^ 


« « 




^ « 






I-l 


•V 




^ „ 


*« -> 




t<itC 


« »\ 


Ul HI 


^ « 


W ON 






•^ - 


"% 




M 00 


r^ rj- 




HH 


COCO 


1— 1 


CO o 


N 






rj i^ 


CO 




N 






^ 


M 


-s A 


M 


„ •» 






N 


" 




•V -N 


^ 




N lo 


« •v 


w 0\ 


^ ^ 


H I-l 






-^ .s 


Nj? 




M lO 


vo CO 




M 


11 i^ 


•& 


»^ c^ 


•* 






N ri- 




M 


hH 






CO 












c^ 










VO « 


t-1 PO 




co\o 


« ►T 


hTvo 


C4 HI 
^-^ CO 






vdS 




cT ■* 


cT cK 


^^_^^ 


CO 


i-T T? 


HH 


•* 


1-1 






I-T i-T 






N 


P< 


^VD 


w .^ 


CO 


I-T tC 


moo" 


coo! 


vd d 




CO 


"? 


N vo 


i-T CO 


corC 


•-I 


CO 


fC On 


CO 


c< 


vo 


»-i 




I-T o; 




CO 


n 












^ 






CO 


*s 




^ 


^ 


toc^ 


ci CO 


cT i-i 


W l-H 


" vo 


" cfi 


n CO 




*« « 


<^« 


cfid 


hT lo 


11 if 


HH 


N 


C4 


CO 


CO 


CO 


•* 


^-..-^ 


00 00 


n 


M 


CO 


1* 


M ►h' 


hT o 


" d\ 


i-Too" 


hT^C 


wvd 


miA; 


I-l ^ 


cT ro 




«i « 


N d 


cf cR 


CO 


CO 


N 


M 


« 


M 


« 


c< 


N 


c< 


" 


»H O 


w j^ 


>-<" rT 


w CO 


i-T ^ 


I-l >o 


i-Tvd 


►H J^ 


►H Oo" 


hTo; 


w o" 


n HI 


>-" cT 


^ 


-i- 


-^ 


'd- 


•* 


Id- 


'I- 


■* 


■* 


-i- 


VO 


VO 


..^ 


IT) 




lO 


lO 


lO 


yr, 


lO 




lO 


vo 


»o 


•n 


vo 


fO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


























* 


lO 


i:d 


t^ 


GO 


Oi 


o 


I— 1 


CM 


CO 


^ 


lO 


CO 


t^ 


ZD 


<a3 


<X> 


«o 


<X> 


t^ 


t- 


t^ 


l>- 


l>- 


t^ 


t^ 


t^ 


<M 


CM 


CM 


CM 


(M 


<M 


CM 


CM 


(M 


CM 


CM 


CM 


(?q 


I— < 


l-H 


l-H 


I— 1 


I— 1 


^ 


rH 


t-H 


1—1 


I— 1 


rH 


I— 1 


l-l 



ON THE TELLIAN EQUATION. 



103 






IT) 



oo 

CM 



1-1 o 

-t< o 

o o 

lO 5D 

t- la 

CO r^ 
C3 to 
Oi I— t 

CO a 
CO 00 

00 05 

t~ oo 

« --I 

00 -^ 
<M OS 
00 O 
oo t- 
t~ 00 

•<*H OS 

o «c 

-* Ui 

OS tH 

00 CO 

00 



VO Cf 






11 o 



l-t 


m 

■^ 






v^ 


^ 






w 


w 
w 














w 
















•I 


^ 






K 


r. 






11 










■* 


.^^ 


, . 


« 


v^ 


lO N 


(^ fo d 




w 




^-^ 




coo<r 


n' 


tc 




n 








^ 


hT 


'f 




IT) 




ro 



MOO " T2 



1/1 









05 rH 

M< 00 

I— t I— I 



oo in 
-*< t^ 

r-t OS 

00 (M 

O CO 
<M O 

(M OS 



t^ ^ 



M 11 






oo CO 
CO o 

■* <N 

IM CO 
lO o 

OS ^H 
CO 






II ^ 












o 
oo 



M VO 



OO 






VD 



rood" 



ti o^ 



I~« OS 



m to 

O <M 

-H 00 

to 00 
N o 



i-H to 



00 



lO 

fo 



OO 






N 0^ 



N VO 



"-1 r^ 



•* T^ 






' VO 



C\f« 



CO 



CO 



< 00 



CO 



CO 
OO 
G<1 



to to 



>0 00 
C-l 1-H 

(M CO 

OS m 

to h- 
W O 

oo 00 

■* to 

00 



w 0^ 
U1 



»o 

CO 



oo 



— CO 



H VO 

CO 






■* 



Tl-lO 

H 



ti C\ 






N ON 



t-t VO 
CO 



"1 >o 
CO 



00 ic 
t- to 

-* o 

to 1-1 

t- CO 

O to 

i^ CO 

lO 



II o 

VO 



CO 

* 

oo 



00 t^ 

oo 



OS CO 

CO 



co- 



ll »o 

VD 



N VO 



CO 



N VO 
M 



Ul CO 

VO d 



VO 



CO 

oo 



VO 



CO 



OO 



n CO 
VO 



CO 



00 
OO 



CO O 
lO o 
oo OS 

CO -^ 
CO (M 

CTS -H 
CO o 
^H CO 

-^ o 
OS la 

ta w 
CO n 
00 o 

o 

CO 



w to 

CO 



•1 o 



N CO 



n to 
CO 



n M 
CO 



n Ov 



od~o<r 



N lO 



II o 



11 T^ 

VO 



* 

OO 
CM 



O VO 



n u-1 

VO 



o 

CM 



104 



REFOET 1893. 



61267 
08410 


00 w 


^ CO 


CD to 


I-H «0 


rt CD 


CO [^ 


-f to 


CO 03 


lO 00 


(M CO 


rt oo 

CO o 

-^ 00 
^ CO 


r-l -* 

CO 


(M CD 

00 


00 03 
<M 

1—1 


CO 


CO 


CO 03 
r- ( 


IM CO 
00 


CO 


O CO 
CO t- 

t— ( 


7—t 00 


a: to 


















(N 




(X> CO 


05 lO 






















OC ^H 


CO -* 






















CD r-H 


-* ^ 






















•f (>. 


Oi t- 






















CO GO 


o t- 






















C3 O 


tO CO 






















CO CO 


CO to 






















^H o 


C5 CO 






















to CO 


l-H O 






















^H CO 


03 ^ 






















CO C-1 


O tr- 
ee lO 






















CD -* 


JO 05 






















C<J CD 


-*< CO 






















I-H to 


t- CO 

t- to 






















o to 

rH CO 


-* CD 






















CO 


t- CO 
























C5 02 
























rt o 
























t- 






















'^« 


























*H 1^ 
























■* 
















































1-. vo 
















































1-1 lO 






















►■T pT 


•. *> 
























J?-' 






















loi-T 

I-H 
















































to 
















































i-Tvo 

»-H 


























N O 
























CO 






















»0 CO 


vo M 






















.- n 
























CO 


























M VO 
























*H 






















r-^ 0\ 
























hToo 


til 






















CO 


























^ CO 






















►- CO 


t-« 






















CO 


























i-< On ro~— 






















CO dv 


CO -12 






















•H 


i-T cT ff CO 






















COOO 


CO CO 






















•-• 


n n •- r> 






















» — 


w « VO O 






















►H ro 


CO >-■ 






















■* 


n n as .- 






















.- n 


I-. »., i-i tr^ 






















N ■- 


CO •<t 






















N 


.»«.«.- 






















■- >- 


COOO N CO 






















►H O 


►H CJ 






















CO 


rT t^ cotC 






















N vo" 


M " 






















P) 


i-T r? m" (D 
CO tj") 
























i-T cotC dl 


















"JT to 




►h"o;« OV 
•* CO 


- ., *to 


















cf to 




pT pT " CO 
PI O 


CO tn 


Co~2 


'JT'co 


CO'^^ 
















CO I-T 
p) 


*"* 


— ' 




**^ 


*— ^ . 


^_^_ ^ 


^-v^^ 


, ^^_^ 


.— ..^-^ 




.--v^^ 




WVO 


m" rC 


i-Too" 


i-T d; 


" o 




VO N 
CO* — 


■* CO 


00 ■>!- 


rf to 


M VO 


o'lC 


\o 


vo 


vo 


vo 










^"' 


^^ 


■"-^ 


" 


to 


to 


to 


to 


to 


vo 


vo 


vo 


VO 


VO 


VO 


vo 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


ro 


CO 


CO 


CO 












* 








* 






I— 1 


<M 


CO 


"^ 


lO 


t^ 


oo 


C5 


o 


r— 1 


(M 


CO 


Oi 


o:) 


OS 


Ci 


Oi 


Gi 


Oi 


OS 


o 


O 


o 


O 


G^ 


(75 


CN 


C<l 


CN 


CM 


G<l 


Ol 


?o 


CO 


CO 


CO 


I— 1 


1—1 


i-H 


T-H 


I— 1 


^H 


r-H 


I-H 


1— ( 


r— ( 


I— ( 


rH 


1 

























ON THE PELLIAN EQUATION. 



105 



(M 



00 C5 

oo 
(M 



en la 
la o 

O lO 



to i-H 

(M to 
to t- 

00 ■—I 



On 00 



VO 

CO 



O 

CO 



00 o\ 



VO 



o 

CO 



►^oo" 



N 

w'vd" 



tCd" 



fo 

* 

CO 

o 

CO 



I— I 00 

>o O 
■* 00 
I-H ■* 

lo in 

05 



ro' — ■ 






ro 



tn 1-^ 






CO 



VO 



o 

CO 



VO N 



VO 

CO 



00 

O 

CO 



•* in 

•* to 
o <» 

00 C-l 

t- o 

■—I ■<*< 

<M t- 

M 1-1 
Oi O 

OJ l- 
.-( ^ 
IN cn 
oq o 
00 



t^ 0\ 









CO <-> 






1-1 CO 
CO 



■H VO 
CO 



CO o> 



11 "^ 

CO 



IH VO 

CO 



IT) CO 



VO 
CO 



O 
CO 



IM — I 

oo I-l 

CO o 

to O 

lO o 

■^ r-t 

CO »o 

(N 



CO c 
»C IM 

CO 00 

m CO 

05 



CO CO 

TtH i-H 

t-H CO 



t~ to 

I-H ■— I 
CO 



VO o 






1-1 ■* 
CO 



CO 



l-l >o 

CO 






.-I o 
lO -* 

CO CO 

■-^ y—t 

t~ >-l 

M 00 

oo 



" 00 

' CO 



M VO 



VO ^ 



O "-1 



VO 
CO 



o 

I— ( 

CO 



i-T d\ 



i^ ■<!- 



1-1 Ov 
CO 



t-i CO 
CO 



VO 

CO 



CO 



•<a-vo 



VO 
CO 



I-H 

CO 



00 >o 
O .-1 

lO to 
CO t- 

CO 



VO 
CO 



* 

CO 

F— I 

CO 



VO 
CO 



I-H 

CO 



Bs^ 


tC dv 




i-Tvo" 





1-1 VO 

1^ 



VO 
CO 



CO 



«oo 



W to 



CO 



CO 



CO 



CO O 



VO 
CO 



CO 

I— I 

CO 



106 



BEPOBT 1893. 



O 1-1 


•* t- 


^O 


CO cr> 


lO (M 


1— ( 1—1 


o ^ 


O 05 


10 (M 


03 


lO -H 


03 t~ 


O lO 


lO rt 


1—1 -^ 


o 


(M CO 


<M lO 


CD O 


rt OS 


00 


t^ -*1 


00 (>! 


CD -* 


lO t^ 


lo >n 


O IM 


1— I 


c; ■»< 


00 OO 


CO ^ 


OO l~ 


I-l 


in 


l^ 


CO -*t 


i-H CO 


^ <D 


^ 03 




Ol CD 


02 


O O 


I* r~t 




<M 


i-hS 


CO 


00 03 


03 t- 


O >0 




CO OS 


<M 


o «o 


i~ oq 






CD 


1—1 


CD O 


l> IN 


-* o 




rt t~ 




rt CD 


CO r— 










O t- 


lO CO 


m CO 




^ (jq 




CO 


-* OO 










CO t^ 


a> t- 


CO >-i 




CO r-1 






^ 05 










C2 O 


CO *— 1 


(M 




03 CD 






00 o 










Ci t^ 


O 00 


i-l 




.-H CO 






CO ^ 










o t- 


TjH cr> 






t^ Oi 






o ro 










lO CO 


la t~ 






(M CO 






lO 1—1 










■* (M 


a> (M 






CO IQ 






■* 00 










CO -"H 


CJi CO 






00 1-1 






(M 1-1 










o >o 


CO IM 






CO t- 






t- •* 










.-H t~ 


05 00 






-H «0 






CO <M 










CO 


t^ CO 

CO ^ 
CO i-H 
CO rH 

00 CD 

CO CO 

i-H 05 

CO CO 

I— t 

i^H 
#t .< 

i-i ro 

CO 
N 

i-T ^ 

CO 






CO (N 
CO OT 
O O 
t- US 

rfl -H 

r-1 CO 

■*^ 

pT CO 

CO 

■>!• 

M 1-1 

CO 

vo" " 






lO r-l 

CO CO 
to t~ 

la I-H 

00 00 
1— 1 CO 
t^ 00 
IM O 

1— ( r-* 

O <M 

lO O 

CD OS 

1— 1 

1-1 VO 

COlO 

w CO 
lO 

00 00 

CO I-T 

pT CO 
N 

1-" lO 












►h" CO 






^4 
















■<*■ ro 


CO 






















N ^ — 














lO Ci 
























" 










o'tC 


M 












fj' in 










t-t 


M cT 






w CO 






N 










fo 1^ 


•* 












w o 










N 


"cK tC 












-& 










t^ ■^ 


« .» 












N I-l >— ' 










i~» 


>-4 )— 1 






■^VO 














^ „ 


u-> 






















1-1 t^ 














w* -^ ^ .^ 










lO 


cooo 






M C^ 






•<^ r^ 










fc « 


t-l 






CO 






#, w. *^ 










■* rn 


•^ n 






(^ ». 






COtC - - 










H4 


t^ c» 






CO CO 






1-1 C>) Tj- 










« " 


•* « 






N 






N 










t-T t-i 


M CO 






« •« 






1-1 in « -^ 










■* 


u^ 


^-^^^ 




>-l to 






CO 11 I^ 










i-Too" 


•>? ■* 


lO N 










hTvO - - 










w 


1^ 




covo 






CO com 










i-T cS 


CO I-T 


m" tC 




I-l 






I-l 
•f in - - 










CO 


C) 


-d- 




>" tc 




1- w 












« (^ 






CO 


*— ^-— ^ 


„ „ vo 










ro a> 


CO t^ 


w iri 




»v ^ 


I-l 1-1 
CO 

^— ' CO 


« « 


CO - - 










iri N 


,"5; co-^ 


i-Tvo 




1-1 CO 
CO 


N cT 


N ^^0^ 
cT tCvo " 










hH 


in — 


•* 




cT 1? 




>^ iC 


N >- 


















P) 




•* 












►-* cK 


CO covo •-< 


coin 






I-T 00 




pT ■>? ff CO 






ION 

CO^-' 


COVO 


Tl- 


Cl I- 






pT dv 


CO 


tC dv 


W CO 






""^ 1—1 


fO t^ 


cT « i-Too 


►T d; 




N 


COt>^ 


cTvo 


M in CO CO 




cTvO 


M I-l 


I-l f^ 


>-* 


CO CO 


m 




00 00 


I-l 


p) 


COM 




in 


^ 


























NOO 


CO cR 


vo d 




I-T m 


I-l I-l 


hT tC 


"T CO 


P) ov 

M 


cT in 


cT ►-" 


CO 1^ 


N 


t— 


M 




«* 


■* 


CO 


CO 


M 


p) 


I-l 


























fO "f 


CO pT 


CO CO 


CO rt- 
* — C^ 


cTin 


cTvo^ 


cTi^ 


NOO 


c< 0^ 


pT 


M •- 


cT pT 


M 


N 


N 




M 


M 


r) 


M 


CO 


CO 


CO 


• •V 


• •V 


• •\ 


• ■s 


• fs 


• ■^ 


• .V 


• •V 


•#1 


• •\ 


..k 


•*. 


VO 


vo 


VD 


vo 


vo 


VO 


vo 


vo 


vo 


vo 


vo 


vo 


m 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 










* 


* 






* 








t^ 


OO 


CI 


o 


1—1 


G<l 


CO 


^ 


10 


CO 


t- 


00 


I— 1 


i-H 


1— 1 


(M 


Ol 


G<1 


CM 


Gv^ 


CM 


CM 


CM 


Csl 


CO 


CO 
1—1 


CO 

T— 1 


CO 
I-H 


CO 
1-H 


CO 
t-l 


CO 
1—1 


CO 

1—1 


CO 

1— 1 


CO 


CO 
I— 1 


CO 

1—1 



ON THE PELLIAN EQUATION. 



107 





o in 


(M Oi 


»^ o 


(M CO 


O rt 


CO in 


in 'ti 


IN 10 


(N t- 


4* CO 


-+i lO 


<N ^ 


rt 




.-H m 


00 OO 


<N Oi 


t- 


•* in 


U3 05 


CO <M 


(N Oi 


t- -*< 


03 I-I 


1^ 


CO CO 


IN 




i-i ^ 


i-H »0 


t~ 00 




I— 1 T— 1 


(M O 


IN 1-4 


CO CO 


IN CO 


^ 00 


f-H 4—1 


era CO 


CO (M 




■^ r-H 


T« CO 


o o 




'S' C-l 


OO IM 


I-I in 


05 05 


t^ 1-1 


CO 00 


rtl 


05 05 


ic 




:c O 


CO -a< 


r-t i-H 




00 CO 


O t- 


■* 


03 r-H 


Oi CO 


«> 


10 


rH IN 


■* CO 




CT5 (M 


IN 


rH O 




CO CO 


-* c: 




05 t- 


CO •'tl 


-# CO 


1— 1 


t- 


CO IN 




O CO 


1— 1 


00 t- 




CD CO 


CO >n 




m CO 


t- t^ 


t- 






CO OS 




lO OO 




t- CO 




r-< 05 


00 »ci 




t- 


CO CO 


1— 1 






t- 00 




CI CO 




CO o 




o ^ 


f-H 




CO CO 


CO 








CO 




m CO 




O (M 




IN CO 


CO 




10^ 


t-H 








00 IN 




CO in 




CO i-H 




Tj< Oq 






-f 










tlQ 




OO ^ 




(^ CO 




O rt 






t^ 00 










10 CO 




00 rH 




C-l C2 




Oi o 






I-I CO 










CO CO 




oq ^ 




05 




CO 






CO 










■«< IN 




<0 t£> 








CO 
















rH (^ 




OS ■* 
























05 OS 




t— c 
























in m 




t^ 
























CO -*l 
CO rt 

CO CO 

CO 
00 Ov 

•<? to 

»H 

>H iC 

CO 

M VO 

CO 

dvtC 

IH CO 




^^^^ 
























VO 




rf- m 
























»N •^ 




M — ' 
























t^-* 




— 
























^-4 
































►^■cS 














00" 00" 










cToo" 




CO 
























N 




•\ •^ 














■4 *4 










•- 4X 




I-I M 














(.4 OV 










r>4 ov 




CO 








^ ^^.^ 






CO 






















N I-I 

»-^ CO 
















h- Ov 




M »0 












I-I CO 










Tl- 




C^ 




lO CJ 










CO 














ff 1*^ 




co^-- 




lO pT 






CO 










N 




M 




•% « 




1-4 






ft 


















I-I CO 










•« ^ 










I-T lO 




« t^ 




lo 




W t-l 






t^ 0\ 










•<1- 




CO 








•^ 
























c^ cR 




•» — r 


O CO 




« 10 










COtC 




i-T d\ 








I-. ON 


'~'S1. 




VO 










IH 




M 








N 




^ 










^ 




•^ •% 




« 0\ 




— "S 


•* •s 




10 N 










►" vd" 




" o 




•* 




I-I VO 


-< >o 




»-l 










CO 




■* 




VO O 




CO 


CO 




T?lO 


2^S 








1-^ to 




•^lO 




I-I 




N t^ 


I-T ^ 




H4 








CO 




■^ 




•\ »^ 




N 


CO 




.1 44 


^^ 








— 44 




^ „ 




►h" t^ 




^ 


^ #s 




I-I •* 


•4 44 








CO OS 




T^IO 




CO 




1^ ■* 


M vn 




rt 


•*VD 












HH 










c^ 






I-I 












n ». 


■?'? 


hT >0 




*, 






fT CO 




M VO 






CO 




M CO 


CO 




I-I 1-4 


fT N 




M 


N " 


^^""^ 






N 




M 








VO 


C4 






CO 














~~' 


•<?■* 










N ■* 




cS t^ 


■* CO 


00 ^ 


n" VO 




I-I 00 


i-T cf; 


>^ 




tC dv 


-"^ 




M 


00 00 


IH 


•^^ 


> 


CJ 




CO 


— ^ 




«i ^ 




r4 VI 


44 1 


^ 


«V #4 


44 44 


4^ n 








>-i CO 




ION 






1-1 OV 


I-I t^ 


N VO 


IH »H 


VO IH 


I-. >£> 




co>o 


1^ I-I 


■<*• 




»-i 


COlO 




CO 


■<d- 


C4 


10 


IH 


CO 




1^ 


CO 






•x •» 


w 


^ 












.4 ^ 




n as 


•* n 


m'io 




1-1 Ov 


•4 as 




cT »o 


N CO 


I-T dv 


>* •* 


" 


IH IH 




t-l t-l 


M o 


N 




lO 


1-1 N 


- . ■ 


M 


N 


to 


IH 


■* 


CO 




VO 


CO 


^ »y 




-1 »v 


VO 


»i ^ 


^ « 


44 44 




** 


44 44 


4, *v 








O t^ 




CO CO 




VO " 


'^ 10 


CO Ov 


cT CO 


N t^ 


IH IH 


M to 




00 00 


►-• M 






M 


ONt^ 






1-1 


r< 


M 


CO 


CO 




»< •» 


■<*• 


— r. 




•s •v 


•, - 


•\ •v 


•4 4, 


•4 44 




•4 44 


44 44 


44 4> 




lO CO 


^ 


T)-\n 




►- VO 


1-4 U-1 


►H •* 


1-4 CO 


1- ej 


I-I 1-4 


IH 


IH ON 


►-00 




•^ 


t^ di 


H* 


^-s^^ 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


f) 


f) 




cT CO 


N ■5? 


cf lo 


M VO 
*""^ CO 


i-T tC 


1-4" oo" 


m" cK 


i-T 0" 


IH I-I 


i-T cf 


w CO 


W T? 


M to 




CO 


CO 


CO 




CO 


CO 


CO 


■* 


■"I- 


■<*• 


'd- 


■* 


•* 




VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 




CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




Ci 


o 


I— ( 


C<l 


CO 


^ 


10 


«o 


t- 


GO 


Oi 





— I 




(M 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


Ttl 


'* 




CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


r-t 


J— 1 


I— 1 


»— 1 


1-1 


I— 1 


I— 1 


I— 1 


i-H 


I-H 


I-H 


I— 1 


T— ( 



108 



REPORT — 1893. 



O Oi 


■-H CO 


la 05 


(M rH 


(M >0 


CO (M 


CD CO 


O rt 


tH 05 


00 in 


t^ CO 


CO CO 


CO in 


cc a 


Gi (M 


eo -+i 


CO -^ 


O i-i 


lO 00 


t- C5 


-*i in 


O tl 


CO t~ 


O TH 


CO CO 


^ CO 


o 


lO l-H 


i-H O 


i-H 00 


Cf5 i-H 


t^ CO 


CO t- 


CO 05 


00 -*< 


T^ t— 1 


rt (M 


in '^ 


CO — 1 


r^ 


O oo 


CD 


•^ 


<M O 


^ CO 


(M CO 


■*! in 


C-] O 


CO 


CO -+1 


oo (M 


^ CO 




rH 00 






OO lO 


CO ■*! 


CO rt 


CO CO 


rt t- 




f-H 


CO 00 


Ol C5 




CO 






05 o 
CO 

ro^-- 


^ o 

CO 


oo t- 
CO IM 

CD CO 

in in 

-* CO 

rt o 

I-H T-H 
(M 00 

CO CO 

m CO 
o 
(M 

t-t *—^ 
»o CO 
i-T o^ 

CO 
CO 

»H ON 

CO 

M oo" 

M CO 

w"io' 
CO 


O CO 

o o 

<M 00 

lO 1-H 

in 05 

lO CO 
o 

pTon 

" pT 
VO 

CO VO 

i-T VO 

VO 


•<*< 




i-^ 


.-1 Oi 
1-4 (M 

■<*< 

N CO 
■ — CO 

oo'oo' 


CO o 

CO 05 

o in 
t~ -^ 

in in 
'^::::| 

CO 

1— I 

pTv?; 

^^ 

►H CO 

CO 

►Too 

CO 

CO rT 










^^^-v 


►-< t^ 


*-* 








■* 


I^ On 
















n *s 


























P) ►- 










►H r^ 










N lo 




ONt>, 


CO 








N 


VO 










N 




















If, M 






HH 1— 1 


■^ 3" 


CO O 








" t^ 


VO O 










I-. ^o 


VO 


« 


N 


^-^ M 






CO 


i-t 




i-T o; 






■* 


to cT 


^^^ 


VO CO 






i^ •*■ 


« pT 


N CO 




lO 






On t^ 


l-< 




»-« 


N On 




- - 


CO 


CO 






























"fen 


t^M- 




>- ILO 


M VO 


t-» KM 


M VO 






1-. o^ 


t-« hH 


►H VO 








W^ 


Tt 


-* 


N 


t^ ON 




■"^ 


CO 


»-l 




























w O 


n fo 


>H r^ 




■* ■* 


M ro 


" M 


w >^ 


w"d" 




W CO 


►- ON 


►- VO 


CO 


■* 


^ 


-^ 




N 


CO 


•* 


VO 


— 


M 


CO 


lO 


-> t^ 


1- VO 


►H li-l 


NtJ 


N CO 


N C) 


N M 


P) O 


C^ CJN 


cooo 


COtC 


covo 


CO VO 


M 


M 


CS 


f) 


Ci 


r« 


M 


M 


*"' 


w 


t-i 


ti 


^ 


►H VO 


•"I t^ 


moo" 


M o^ 


M O 


M m" 


w N 


►H CO 


" •<1- 


11 »o 


MVO" 


>- I~. 


•- 00 


•* 


M- 


^f 


■* 


VO 


iO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


■£) 


^O 


VO 


VO 


«3 


VO 


« 


VO 


"O 


VO 


VO 


vO 


VO 


r<i 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


























* 


CM 


CO 


tH 


lO 


ZO 


t^ 


00 


Ci 


r— 1 


T— 1 


(M 


CO 


"* 


^ 


^ 


'^i 


'tl 


■* 


^ 


-* 


'^ 


lO 


lO 


lO 


lO 


O 


CO 

r— 1 


CO 
r— 1 


CO 

I— 1 


CO 

I— 1 


CO 
1— 1 


CO 
r— 1 


OO 
rH 


CO 
t— 1 


CO 
I— ( 


CO 
I— 1 


CO 

I— 1 


CO 
1 — 1 


CO 

I— 1 



ON THE PELHAN EQUATION. 



109 



(M C5 


O 05 


o ^ 


-* CO 


-H o 


05 O 


35 O 


00 t~ 


>0 CO 


O f-H 


'tl rH 


<M lO 


t^ 00 


90 00 


l^ Oi 


-H m 


O CT 


CO -t< 


-* to 


IM --O 


-*< <o 


05 (N 


CO lo 


00 t- 


-* IM 


CO CO 


lO N 


CO t- 


C3 CO 


-* 00 


IM O 


t~ t~ 


>n c-i 


O O^ 


-f t^ 


c^ o 


CO <M 


O lO 


CO 


C5 OO 


00 ^ 


-H <M 


r-i a> 


00 00 


>>• lO 


00 lO 


t- -* 


CO I-H 


t^ CD 


lO 


-f ro 


I-H 


•^ N 


OS ■*! 


to t^ 


00 a> 


t- -*< 


ao 


lO -*< 


CM 00 


05 lO 


00 c^ 


(N 


CO Oi 




00 


0^ iM 


O CO 


Oi 


00 ,-t 


c^ 


rH CO 


f-H I-H 


-* 


(M CD 




CO OO 




f-H 


.-1 <s> 


CO ^ 


(M 


to 00 




00 00 


t-O 


CO 


o 




<o o 






(M O 


'^ I-H 




■^ (M 




CO I-H 


CO t- 




T-H 




OO ~K 






»0 --H 


CD ^ 




t- 




CO CO 


CO 








•^ >o 






05 


^ C5 




fi 




Oi CO 


r~t 








CD 05 






1-H 


CO t~ 

o •* 
CO CO 
in OS 
to >o 

05 in 

CO 








CO !M 

CO 

f-H 










00 00 

CO •* 
(M I-H 

OO >n 

CO CO 
-H CO 
00 o> 

a 00 

o ^ 

M CD 

f-H ^ 
ftH 00 

t^in 

OO O 

00 CO 
05 O 

-H I-H 

CD 05 




^ 






























N CO 
— ' N 

i-Tvo 
CO 


















NO 
CO 

N CO 
CM 

I-T rT __^ 

"*vO "n" 
ft ft co^-* 






•*>o 

l-t 


M CO 

CO 

??^ 

VO 

ff CO 
CO 

>o C^ 

I-I 

i-T CO 




CO So" 

IH lO 

CO 

" tc 

CO 

1? -* 




IH IH 
CO 

^^ CO 

»0 CO 

IH 

5- 


VO "c? 








N ft ft 

ft ft P) VO 

IH VO P^ 

'*• ft ft 

ft ft i-vo 
Tt lO w 

."ft-tC 

»0 Tf VO 

-"ft -^ro 

•* VO " 

IH ft ft 

- ft I-I OS 
MM •* 

'I- ft ft 

ft ft cooo 

CO ft ft 

ft ft CO OS 
M ft ft 

ft ft "H OS 

^ VO CO 




- 




ll t>. 




w" lO 




I-T c^" 


pT CO 








ft ft "" o 

IH VO f*^ 






»o 


N 




n" CO 




CO 


CO 




2 "" 




CO ft ft 

ft ft " t-N 






lO hT 


w" T? 




N 




N CO 


'f T? 




- . 




M 00 ^ 




rj- lo 


•-• 


•<*• 


VO N 






c< 


IH 




ft ft 




CO ft ft 
ft ft N VO 










CO-— - 


cT >o 










N rr> 






•_^ 


1-1 t^ 


t-» OS 




N 




IH O 


►H OS 




N 




r^ OS PJ 




N vcT 


to 


i-i ^^ 


N " 


w lO 


covo" 

^— ' IH 


Th 


■* 


I-I 00 


ft ft 
IH CO 




i-T VO P^ 'h" 




N 


oozo 


CO 


CO 


CO 


N VO 


CO tC 


—^ VO 


■* 




■* M 
















M 


IH 












M HH 


N VO 


M VO 


N M 


W T? 


#s « 


^ ft 


ft ft 


ft ft 


covo" 




i-Tvo" *^ O 




rt 


M 


CO 


<M 


.'? 


MCV 


■*vO 


•H i^ 

CO 


r^ OS 




--.^-. 


N " 




ro c^ 


i-T -f 


vo" « 


ih" I-C 


N rC 




ft ft 


ft ft 


CO CO 


IH LO 


M VO 


MtC o t-C 




H-t 


■* 


IH 


■* 


M 


T? lo 


'l- 1^ 


IH OV 


N 


lO 


'S-" 




^ 


•N n 


^ 






IH 




CO 










-— *^— ^ 


■*■* 


•* CO 


ION 


VO ^ 


vo" o" 


■\ n 


ft ft 




«vO 


covo 


rC <^ 


CO CO 


VO PJ 

CO^— ' 


•^ 


ll 


IH 


IH 


IH 


t>. Ov 


00 00 


cjv rC 




IH 


IH 


N 




►T cS 


"O" 


•T I-T 


" ci 


I-T CO 


I-T if 


IH lO 


hTvO 


►-" rC 


i-Tod" 


I-T dv 


M O" 


M IM 


to 


VO 


VO 


.^^ 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


r-- 


r^ 


.-, 


• •^ 


.•* 




• «y 


•M 


• ft 


• ft 


• ft 


• ft 


• ft 


• ft 


• ft 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


VO 


\o 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


»o 


CO 


t^ 


OO 


as 


O 


1—1 


Ol 


CO 


'^ 


iC 


CO 


t^ 


^O 


lO 


lO 


lO 


^o 


ZD 


CD 


CO 


CO 


CO 


CO 


CO 


CO 


CO 
i-H 


CO 
1—1 


CO 
1-H 


CO 
I— 1 


CO 

I-H 


CO 
I— 1 


CO 
I— 1 


CO 

T— 1 


CO 


CO 

r— 1 


CO 

T-i 


CO 

I-H 


CO 

1—1 





























110 



REPOKT — 1893. 



CI5 



Ct3 



t- o 

CO t- 

CO 



CO 



GO 
CD 
CO 






* 

o 



CO 



■^ t- 

CO 'M 

to t- 

-* to 

O CO 

CO •* 
to CO 

o o 

<M O 

OS rH 



00 ■^ 



ro o\ 






"-> N 









m 
rTrC 

N 
00 00 

"*■ ro 



CO 



OO 00 

to CO 
lO 



■* >o 

o o 

00 « 

oq CO 

'tl >* 

-* CO 
lO 



CO 



* 

CO 

CO 



CO -ti 

CO c<i 

t^ lO 

O 00 

05 O 
O CO 
-*l CO 
(N OS 

00 






C^ VO 









N lO 
M 



U1 



CO 






CO 






CO CT> 



CO 



CO 



*-* vO 






N vO 



CO 



»0 05 

o -* 
M o 

t- 00 

CO (M 

CO lO 

to to 



o ^ 
00 o 

C<1 O 

to t- 

^ o 

(M O 



I^ Tj- 



N 00 
M 



N VO 



•-1 N 
CO 






CD 
CO 



CO 



COVO 

cocJ\ 
^3^0o" 

CO 

CO 



CO rH to lO 

m o — I cs 

1— 1 OO O 00 
i-H 0-1 to 00 

o to 

00 o 

tO 1-1 
lO 



Oq i-H 

00 to 

to 



00 <?; 



CO 

* 

GO 

CO 



O t^ 



CO N 



COO\ 



CO 



N VT) 



N \0 



N ON 



CO 



M O 






O 

GO 

CO 



ON THE PELLIAN EQUATION, 



111 



00 C<5 
>* O 

eo o 
CO 



1—1 CO 
<M •*< 

00 05 

CO OS 



lO 05 

CD 05 






■<1- 






N CO 



ON 



M 






CO ^ 



t- o 

O 



t^ 03 



«^ Th 






O O 



CO t- 

00 O 

CO 00 

05 lO 

CO (M 

00 CO 
05 O 
O CO 
IM CO 

00 



f^ ON 



o 



ON 









N TJ-i 



00 o> 



l^ 03 

CD "O 



00 ■^ 



fo ro 



"in 



Noo 



M ON 



On tC 



IM 1-1 
00 CO 

lO 05 

O CO 

CO ■* 

T— I lO 

iO 00 

00 J^ 

CO C-1 

m M 

CO CO 

i-H 00 

CO 03 






N ■ — • 



r<i 









On 






r^ On 

NO 



ON 



"*• ■* 



05 O 

tM CO 



<M O 

05 



ON 

ro 






■>!< CO 



CO CO 

a 00 

CO 



CD lO 
CO '*! 
CO lO 



'^ ro 



t-t to 



VO O 



fO 



w On 



"oo 

CO 






■*vO 



O t^ 



VO N 



On 



00 
CO 



UlTl- 



CD 



CO 

oo 

CO 



^ to 






00 
CO 



CI 

IT" 

oo 
CO 



•<i-f^ 



CO 

oo 

CO 



*oo 






OO 

CO 



-o 



ro O 



CO 



C5 
00 

CO 



o 

CO 



CO N 



CO 



as 

CO 



CO ro 
M 



CO 



CO tj- 



CO 

CO 



N to 



CO 



CO 



112 



EEPOET 1893. 



O i-H 


O rH 


O rt 


■* t^ 


33 O 


IM 33 


<M lO 


33 03 


10 CO 


CO 'O 


03 


H 10 


^^ 


IM O 


CO o 


-* la 


lO CO 


-* 'Ji 


T-H rtl 


CO rH 


c-1 


03 0-) 


CO iM 


^ 2: 


i^ 


to 


CO O 


>n ox 


-^ CO 


rH -* 


CO CO 


^ 


33 O 


ira 


cr> t^ 


CD -* 


(M 




rH >-- 


CO 'S* 


O 00 


CD 00 


O CO 


lO 33 




C^ iO 





^ ^ 


<-l <^ 


<M 




CO 


Cv| 


Ttf TtH 


CO -rf 


CO CO 


rH O 




03 00 


00 


t- 


CO 








rH 


>0 CD 

-* C3 

CO 

1-H 

m"iO 
M 

MOO 


a M 

00 CO 

cq CO 

TJH O 
CO 

f-H 

fToo 

CO 

>-i CO 

00 ^ 


r-i 00 

vO^pT 
CO^-- 

lO 

fT CO 
N 


O CO 

-*< -*l 
^ o 

O ■* 

O 33 
CO 33 
'i* 00 

O CO 

CO CO 

rH 00 

CO CO 

03 (M 

rH (M 

I- 

CO^^ 

■<?>o 

n 

" OO 
to 

•<? CO 

n 
CO 

cooo" 

n 
hT CO 

ci to 

N 
•«?to 

« O 

CO 
CO 
N 

►<' rT 
vo 




^ CO 
00 33 
t- (M 
CO oq 

CO r-l 

CO to 

CD tH 

00 o 

•* CO 

CO CO 

CO 03 
00 t- 

•-I t~ 

rH CO 

CO 
^^ 

35 

cf to 

dtC 

n 

'f to 

i-T vo 
to 

00' 00" 

rT (> 
CO 

11 to 
CO 

•^vO 

n 

vd « 

"[€ 

11 CO 
CO 

N 
to CO 

cT •>;? 
M 


03 C- 

CO rH 
00 

■* 

<M CO 

a 

CO 

tC Ov 

pT of 

i-T CO 

CO 

H M 

rTvd 
H 

w CO 
vo 












M^ON 


■*io 

11 


" 5 


CO Ov 


■* to 




n 

'I- 


Ov tC 


« vo 


^CO 








VO « 


CO O 


1-1 a. 


11 oo 


pTvd 




■* to 


" ■* 


CO Ov 


■« n 






N ~— 




M 


w 


CO 


^ 


- 


•-' 


to 


n 


11 VO 


.-^.r^ 






M VO 


IH »-l 




M CO 


N C> 


N to 
— N 


CO r. 


cot^ 


to CO 




Tj-tO 




n t-» 


* 


•* 


CO 


CO 


M 


N 


n 


n 


I^ Ov 


^-^ 


_^ 


CO 


Nvo 


N tC 


NOO 


N cR 


NO 


pT m 


N N~ 


N CO 


N •<? 


pT 10 


cTvd 


N t^ 


rToo" 


M 


N 


N 


M 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




CO 


■ »v 


>., 


• •» 


• .t 


• •V 


• ■^ 


• •s 


• •s 


«*v 


• •\ 


• •k 


• M 


• »s 


r^ 






t^ 


r^ 


t^ 


t~. 


r^ 


r^ 


I^ 


1^ 


r^ 


r~. 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 
















« 












lO 


'^ 


t^ 


CO 


C5 


O 


iH 


CM 


CO 


-* 


lO 


CO 


t^ 


Oi 


cn 


OS 


Oi 


Oi 


o 























CO 


CO 


CO 


CO 


CO 


^ 


-* 


'^ 


^ 


^ 


^ 


'^ 


TjH 


1— ( 


,— ( 


rH 


rH 


rH 


1—1 


iH 


r-t 


>H 


rH 


y-i 


iH 


rH 



ON THE PELLIAN EQUATION. 



113 



to 00 

.-H t~ 

O C5 

•-< t~ 

rH 00 

<M -^ 

CO o 
CM 



CO 

CO 
Oi 
?— I 
o • 



05 ^ 

in 

CO 









■- O 
■:1- 






VO 


►I lO 




o 


r~. o^ 


« •* 


„ 


OM^ 


N 00 


„ « 


N 


l-l -f< 


•s n 


CO 


►H n 




m 


n-«o 










hi o^ 


»» « 


ro 


O\00 






"^kO 


r^ ro 


*"* 


M 



O t^ ^ l-H 



O -H 



m o 

lO 00 

O CO 



00 o 



r-. M 



P) 



' 00 



^ iri 



^ u-j 



N O 



ro cji 



(M CO 

CO CO 
-* UO 
O rt 

CO i-H 

O t- 

o 



O 05 

o — 
CO CO 

^ i~- 

rt 00 
C<J IN 
CO t~- 
(M 00 

•>*< o> 
c-i «o 

i-H CO 



O CT5 
i-H M 



<M O 

CO o 
in 05 
oo w 



CO o lO o 

00 00 (M 

-*" CO w 

CD O 
(M O 

00 ■* 

•* IM 

00 



00 uo 
•a CO 
X o 

CO oo 
U5 



05 CO 
0<) CO 
00 CO 

CO o 
to 



CO Ol 

CO C5 

O oo 












00 On 






00 ■* 



1 o 



CO oa 

CO o 
CO oc 
m ^ 

05 






1-. I^ 









M \0 






^^ 









lo r<i 



N O 






00 ON 
"if to 



I lo 



1* 



i:0 



fO ON 



On 

■5t 



■* ■* 



to 



IT) 

CO 



00 00 



ON 









N ON 
P» 



N On 
— N 



VO 



On 
CO 






<o 



O r^ 
cftC 



I- On 
CO 

CO 

I „ 
i VO i-T 



1 vo 
ro 



On 



ro 



GO 

o 



to 

<o 



to 



l-l fo 
ro 



ro 



O 



to 



O 



ro 



to 



'ctl 



CO 

1-H 



o 
to 



>o 



1—1 



1893. 



On 

CNI 



I NO 



•00 






I-H 



to 



T— I 






■ OO 



I VO 



On 



N VO 



« o 

VO 



to 

1-H 



ro 

* 

OO 
1-H 



CO 









CO 



o 

Sn< 



114 



KEPORT 1893. 



o *— < 


C<1 t^ 


Ci 00 


O i-H 


-4( 1-1 


IM lO 


t- <M 


O rH 


lO CO 


<M iH 


in -*< 


00 t^ 


t^ ■* 


CO O 


Oi as 


ir3 o 


lO o 


in 


CO t- 


05 CO 


Ci o 


O rH 


in rH 


CO (N 


CO 05 


CO IM 


C^ 00 


t^ o 


t— IM 


0-1 o 


r~i 


--H 05 


o t- 


-H 


CO cn 


CO CO 


CO 


CO t- 


(M t^ 








CO o 




rH O 


t~ CO 


CO 


05 in 


CO 


^^ 




CO C3 




l^O 


05 O 


1—1 o 




CD CD 


-* rH 




00 t- 


rH 




CD O 


in M 




r-< o:. 


Cf5 t^ 


lO 




(M CO 


rH C5 




CO 






0-1 CO 


CO CO 




CO o 


CD CO 






CS 


CO CO 




CO 






CO 05 


OJ t- 














^ t~ 












m CO 




?— I 


to '-0 

r-1 7-t 

t~ CD 

.-1 00 
O '-H 

CO CO 
-!K (M 

(M r-l 

M O 

rr, — 

N 
N 

oo" c> 

t-i 








(M CO 










CO in 

1^ CD 


rH t^ 

lO 

•H r^ 
ro 

ih' rC 
-^ ro 

rfvo" 




































M CO 


"^ 










ss 


\r> ro 




°° S 


■sl-OO 
(-1 






•1 ON 
CO 


ro 










•<?rC 


Tt 








■* vo 




" cT 


P> CO 




















' — 




n 


N 




N 'to 






p) 


>- PI 
ro 




ro o 


1-1 fT 


N "^ 


























M 




•* 


■cj- 










— On 










« •>? 




CO J-; 


N >^ 




N ro 






Tf 


ro 






fO 


■* 






P) 










O t^ 


1-1 ro 


■ — 01 




roiC 




►r o 


yr, ro 


N 1-1 
■ — N 


VO 


N VO 
— ' N 




oo" 6< 


oo'oo* 


ro O 


fT d\ 


« co" 


i-t r^ 




■>4- lo 


N 1-1 


1-1 t^ 


00 T^ 


fj On 


— to 


to CO 


rTo; 


N 


N 


ro 


■* 


. , 






"4- 




N 














N O 




CO 00 


CO J-» 


rovo 


tMo 


^Tl- 


■<1- to 


vo pT 


in ■-« 


N 


N 


N 


N 


•~- 


k-4 


•^ 


•^ 


•H 


•^ 


■^ 


•^ 


*~* 








M lo 


»-. lO 


1-1 1-^ 


■-100 


w On 


-1 o 


t-l IH 


•-• N 


" ^ 


" ? 


>0 


"-1 


lo 


VT) 


"1 


lil 


"-> 


<^ 


vo 


NO 


NO 


vo 


vo 


• •< 




• .. 




t>- 


t^ 


t^ 


t^ 


r^ 


»-~ 


r^ 


f^ 


»^ 


m 


ro 


m 


CO 


CO 


m 


CO 


CO 


CO 


CO 


CO 


CO 


ro 


















* 








# 


I— 1 


G^ 


CO 


Ttl 


>o 


CD 


b- 


GO 


Oi 


o 


y-\ 


(M 


CO 


d 


G<l 


G^ 


CM 


C<1 


CM 


(M 


CM 


CM 


CO 


CO 


CO 


CO 


I— 1 


i—t 




r-l 


<* 

t— 1 


rH 


r-l 


I— ( 


r-H 


rH 


T— 1 




I— ( 



ON THE PELLIAN EQUATION. 



115 





o ^ 


00 CO 


O 05 


O OS 


'ti CO 


^ o 


OS i-H 


O OS 


oo CO 


,-1 00 


r-l 00 


CO >o 


CO 00 




O «2 


t- -*< 


-*! OS 


^ OS 


CO -* 


IM CO 


i-H N 


O OS 


CO ^ 


CO 


CO 


CO -"^H 


OS -^ 




(M t- 


CO o 


CO .-1 


O CO 


o t- 


HO OS 


t- 


t- OS 


-^ 






-^ 


O 00 




C5 00 


CO OS 


CD CS 


-* o 


CO t~ 


^H ^tl 




IM ^ 


*— ( 






I-H 






«o OS 


(N OS 


lO 


CO ^ 


O <M 


C-l CO 




OO in 












CO o 


OS 


C<) 


lO (M 


m T-H 


O CO 




3!'=' 










CS 'ti 

00 t- 




»0 OS 






O oo 


"^ 00 


rHO 




O -H 












CO CD 






(M CO 


OS <M 


CD CO 




1-1 C-l 










co to 




to CO 






CO CO 


CO t- 


t- o 




rH in 












-<< to 






CO OS 


oo 


CO O 




CO 00 










I-H T-H 




t~ 






CO in 


IM CO 


t-t- 




CO CO 










OS CIS 




t— t 






O CO 


^ OS 


CO rH 




to o 










(M CO 
00 O 










C<l t— 


lO 


lO »o 




OS CO 


















03 


t— ( 


lO 00 
OS OS 

CO t- 

CO »n 

CO 00 
(M 

rH 

CO— - 
cT lO 

CO 

tC d 




to ~n 

OS CO 

>o (>? 

oo t- 
OS •* 

^ -*l 

lO rt 

^ o 

00 

ci cT 

CO 

•* to 

l-i 

"i 

►4" CO 
CO 

pT OS 
N 

■^ to 

•1 ^ 

i-i r^ 
to 

covd 










(M 1-H 

CO 

ro>— - 

•-<" d; 




























CO 




N \o 






"^CO 




" o" 




to 










"IC 










M -—^ 




lO 






























•<J- to 










CO 










" rC 




^■f? 














pTvd 










Tl- 








CO dv 










*^ 










"oo" 




« to 




« 00 










•Oco 




rj- 






*^ *-t 


1-4 1— t 


CO 




«t •* 










►H M 










cT i-T 


•^co 

C4 


11 t^ 

CO 




CO fr^ 
►^ t/) 










to 

cooo 

I-I 










« (^ 


CO CO 


^'?f 




■<^ 










pTtC 




CO 






to 


cooo 






pT •<? 

P) 

pT to 










PI 

•H <? 

CO 




i- oo" 






^rC 


•^ CO 


t-H 




PI 










iH-d; 










l-H 


lo 






I-T o" 










CO 










cToo" 


tC d\ 


lO CO 

h-t 




pf rC 










corC 




PI 


Ss" 








« vd 




P) 

o^oo' 










tr. 






CO h-T 


^2 


«^N 




^'i? 




oo" cK 










iC d> 




•~< »-i 


N 


— 


•^ 


" tC 


to ■^ 




^ s^ 














rf 


N " 


cT lO 


" CJ\ 


■^ 






PI 












VO c5" 


CO 


CO 


u^ 


i-Tvo 


Tt to 


'^S 


'*CO 


co"pr 

CO- — 








pTvd 




•-• 


tC o\ 


cooo" 


On t^ 




»-* 


■^- 


N 




^-^.— ^ 


^-^*-^ 


.-^^-^ 




►1 iri 


i-Tvo" 


"I r^ 


« oo" 


w cf; 


i-T d 


>S .-T 


« pT 


« CO 




VO « 


00 PI 
CO — 


to CO 

PI 




\o 


vo 


yD 


\o 


vo 


r^ 


r^ 


1^ 


t^ 










.^ 


..s 


..K 


.» 


.* 


••^ 


»ry 


.*. 


■ -. 


• •> 


• •V 


• .» 


••* 




t^ 


t^ 


J^ 


fr^ 


t^ 


t^ 


r^ 


J^ 


r^ 


r^ 


00 


00 


00 




ro 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 
























* 








^ 


o 


O 


t^ 


GO 


en 


o 


I-H 


<M 


CO 


»o 


O 


t- 




CO 


CO 


CO 


CO 


CO 


CO 


^ 


^+1- 


^ 


'ti 


-* 


Tt< 


^ 




-* 


^ 


tH 


'^ 


^ 


^ 


^ 


'^ 


•^ 


^ 


'^ 


^ 


•^ 




1— I 


.—1 • 


I— I 


I— ( 


I— 1 


t— 1 


T— 1 


I-H 


I-H 


rH 


I— ( 


1—1 


rH 



I 2 



116 



EEPOET 1893. 



OS CO 


O 05 


CO CO 


w o 


00 t- 


»o ?.i 


rH lO 


CO rH 


lO ^ 


(M CO 


O r-l 


rH 


00 05 


t-l IM 


o ■* 


CO 05 


O CO 


►^ 00 


O 00 


CO oi 


C<1 CD 


in lo 


-H O 


rH O 


00 in 


05 0^ 


t- 


00 (M 


Oi •* 


t- >o 


CO o 


oo 05 


00 o 


CO 1^ 


oo 05 


CO l^ 


in ■* 


o<t 


00 10 




^ T— t 


rH »— 1 


O 00 


CO o<i 


rH 05 


i-H 00 


CO 


03 rH 


O CO 


lO CO 


CVI rH 


10 10 




00 O 


O 00 


<M (M 


CO 


»0 C2 


CO in 


<N 


iM in 


1- CO 


IM 05 


10 00 


(N rH 




<M CO 


tH 00 


CO CO 


w 


CO o 


as c~ 




I-H 05 


CO 00 


O O 


(N M 


CO 05 




I- 1- 


CO 


CO ^ 




■* 05 


CO t- 




r*4 


in <M 


05 rH 


!>. CO 


CO 




t~ 




la rH 




.-1 o> 


•-H O 






C3 CO 


00 m 


00 


(M 




(M 




^ 00 

CO t- 

O IM 

rH 00 
CO t- 

ta o 

00 lO 

C«l 

CO 

"J- 
CO 

t-l 

« o; 

m 

N « 
CO 




t- CO 

CO (M 

CO rH 
lO ■* 
rH rH 

«Q CO 

rH 05 
CO 00 
CO CO 

CO o 
t- »o 

CO in 

I-H CO 
oo rH 
>0 lO 

CO CO 

rH 
T-H 

i-T^o 

CO 
COlC 

00 -^ 

CO >-r 

N 

i-T rC 

CO 

« vo" 
CO 

rT CO 

■<^ 

N " 
N 

>- pT 
"-) 

o'rC 


CO t- 

05 CO 

CO 

CO 
00 n" 

CO—* 






rH I-H 
05 CO 

OO CO 
I-H <M 

pre 

~— ' CO 


, I, 10, (38) 78 88 
, 62, 7, (2) 3012 27 


(M 10 
Oq rj< 

rH CO 
IM 
rH rH 

00 05 

C5 05 

t~ 

C<> CO 

00 CO 
rH CO 

(M in 

rH Oi 
05 CO 
CO rH 
in rH 
0^ 30 

05 

t^'w" 

CO-^ 
ri- 

M 1-4 

PO 

pT 0" 

CO 

.. .. 

«0 CO 

p) 

10 to 

r?00 
to CO 

►7 CO 

rl- 
" 

CO 

CO 
pT to 

M 

pT rC 
M 










N 




vo C^„,^ 

'-' lO CO 






'tvo 


r^ Ov 


pT CJv 
p) 










l-f in 




- - N 


\r>\r, 




















ro 




CO 0\ . _ 








CO CO 


rj- 


■4;^ to 














" W CO 


•* •» 






M 




IH 










w 00 




- - p) ^ — 


rl- r^ 








W 1? 












CO 












O l-r 


ro 


rT 10 










ro 0> 




» . f» 00 


pT Ov 






1-4 


pT CO 


r^ 


oo"5 












vo P) P< 


PJ 






w CO 


P4 


pTvo 


. 




ss 








- - ->' Ov 
w « CO 


^*J? 




^vo" 


rj- 
►H pT 


„-vO 


00" di 










•V >v 




rl- - . 






>.^ 


ro 




^ .. 


^ ., 




t? rC 




N ro 




. - P< l^ 


« tC 




^ . 


- - 


CO tC 


»^ 


►H to 




n" ^ 


00 ol 




oo ^ 


« CO M 
CO . _ 

. -VO -< 


ro 




■1 lO 

»o 


N OS 
P) 


« d; 


r4*rC 


CO 

rfvd" 




N 


■* 


NH *— ' 


M oo •-< 


CO 




iC eS 


o^oo" 


rl- 


CO 


•-• 












M . - 


















n7 lo 


N iri 


o o 


n — 


„ . " Ov 


t-t ►-* 


■-t vo 


« 00 


vo " 


POOO 


« d^ 


CO 0> 




•* 


N 


•^ 


■-I 0\ 
CO 


lO CO CO 


CO 


^^ 


■* 






CO 


^ 




•*vO 


i-T o; 


IM 1-4 


■« ws 


^ ^ 


i-T CO 


1-7 t^ 


cT lO 


« vo 


pT 1-4" 


cTvo 


« ds 






•<^ 


vo 


1-. «~~ 


M CO 


rt 


vo 


PI 


ui 


CO 


*^ 


^ 










CO 


CO 
















2^-2 


w ir, 


N^O 


o"tC 






tC o 


vo " 


vo pT 


to CO 


10 rf 


to u^ 


r?VO 


— ■ 




»-• 


■-* 


cSoo 


oo" ci 




1-4 


»-• 


*-l 


►H 


^ 


*^ 


.. 


.^ 


.. 


.. 


.> 


.. 


,m. 


.. 


.. 


... 


... 


• « 


— 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


CO 


CO 


ro 


ro 


CO 


CO 


CO 


CO 


CO 


CO 


ro 


CO 


CO 






* 






* 
















CO 


en 


o 


I-H 


<5<l 


CO 


^ 


iO 


ZO 


t^ 


CO 








'^l 


^ 


>o 


o 


lO 


o 


O 


lO 


lO 


»o 


»o 


^ 


ZO 


I-H 


I-H 


T— 1 


1—1 


1— 1 


I— 1 


r-H 


r-H 


r-H 


I-H 


I-H 


1-H 


I-H 



ON THE PELLIAN EQUATION. 



117 



oc to 

C 00 

in C2 



C-l CO 
1^ lO 



* — t^ 

■<foo 



00 



CO 



05 lO 

CO I-- 
(M O 

05 



Tj- OS 



00 



CO 

CO 






N "1 



M C3S 



CO O 



00 



CO 



to e^ 

00 CO 

^H ■* 
N 00 

<M CD 

rt o 

00 



fo 


N 


ro 


N 


n" 




M 


cS 



1^ 0^ 






1— ( 



1-1 0\ 



M li") 






1-1 OS 



M O 






00 
CO 

CO 



U3 CO 
00 rt< 
•-H O 
»0 CO 
O U5 

O CO 
•>*< CO 



lO so 
o o 

CO o 
t^ 00 

5D O 
t— I -^ 









N \0 



»^ o 



N 11 
ro 






00 



* 

CO 
CO 



CO — 



11 OS 






CO N 
M 



CO CO 



c-a 05 

o CO 

UD 1—1 

00 00 
O (M 

CO CO 

l>- -^ 

CO O 
00 (M 
00 lO 
CO CO 

1-1 oq 



00 ■* 






II CO 
CO 






<M 




oo" 


ds 


« 


n 
n 


M 


lO 



11 t^ 

CO 



M OS 

CO 



"1 CO 



N CO 
CO 



n so 
CO 



n OS 
CO 



00 
CO 



CO 



CO ■* 
M 



00 
CO 



GO 
CO 



CO t- 


5D la 


rH -^ 


CO CO 


(M C-) 


00 <M 


in lo 


05 O 


CO oo 


I-H CO 



00 f-1 
CO 05 
t— I <M 



00 1;^ 



co»o 

M 



00 
CO 



as 

CO 



w OS 



N VO 



t- o 

CO CO 

t~ — 1 

CO CD 

CO CO 


»0 CO 

•-1 00 

CD O 

lo CO 


1-1 in 

CO 00 
CO •*! 
<M »n 


CD 00 
t- 00 
<M IM 
l>- GO 


CO b- 

CO ^ 
1-1 CO 
OS t- 

00 CO 


C-l t- 

<-i in 
t- o 

OO 


1-1 Ci 
CO 



"1 CO 



00 OS 



P) »^ 

CO 



n CO 

SO 



VO o 



CJ 


t-H 










rN. N 






rn 






■^ 














moo 


1— 1 


t—l 




hH 




U-1 


r. 


^ 


^ 


„ 


»-l 


lO o 


lo 




CO 




ri 



00 
CO 



o 



•1 1. O t^ 

1^ n 



W VO 1 lO 

1 'l- 



TM^ HI o 

n CO 



N O n t^ 
CO CO 



CO " n n 
M CO 



•>d-io n PI 



n CO 'J-lO 



■>d- 1- P> M- 






PI 



00 
CO 






O iH 


O Oi 


CO in 


<M C5 


1— 1 


IM CO 


rH 


-*l CO 




rH 05 




CD IM 




CO OS 




t- OS 




(M CO 




<Ji 00 




CO in 




CD 




(M 



•<J-CO 



n Os 
"1 



w CO 
"1 



N ro 
•— ' PI 



P) 00 
PI 



00 
CO 



CM 



Osoo 


pf 


c«- 


cT 


P) 


n 


CO 

'J- 


« 


to 
p» 


M 


ro 



CO 



P< OS 

PI 



oo 
CO 



CO 



118 



EEPOET — 1893. 





CO Ci 1 


O "-1 


O 1-1 


^ t- 


lO CD 


a 05 


in 00 


IM t- 


in CD 


•* >n 


00 a> 


00 m 


lO - 


c<i o^ 


So 


tH lO 


rH i-H 


(M t~ 


la lo 


O CD 


t- 


Tt< (M 


1*1 Oi 


<N t- 


C<l CO 


05 C 


ZD t— 


>0 CO 


IM M 


y-l t- 


in CO 


lO oo 


•* -*i 




O IM 


CO 


O 


IM b- 


■* C 


05 Oi 


^*4 ?— t 


00 CD 


(M CD 


CO O 


•* -»i 


>o CO 


rH t- 




00 '-I 


rH 


t—t 


IM -* 


in - 


So 


i-l 05 


P) CC 


T-H 


rH O 


tH 


CO T-l 




CO 00 






C3 l^ 


Oc 


o o 


lO 


o^ CO 


<M 'l^ 


1—* 


rH -*! 


O) 


CO >n 




<=^ zl 






-* O 


IM : 




oc 


CO O 




^ 




rH lO 




CO 05 






CO 


t 






O IQ 








JO CO 




CD r^ 






n 




CXI O 

o «c 






t^ ,-H 








f- (M 




^ O 














-* ^ 








05 t- 




Ttl CO 










,-1 1^ 

tH OS 

CO »o 






.-1 t- 








lO -^ 




O (M 














CT T-H 








■* CD 




t~ Tti 














rH O 








05 (M 




lO 03 














<M 00 








rH CO 




OO 














t- t- 








O <N 




l-O 
















CO CO 








1-1 <J> 




00 CT> 














CO Ttl 








CO 




(M 00 














CD O 












C5 00 
















^ lO 












o m 
















CD O 












O) 03 
















N o 












rH CO 
















o 












^ OO 
















f— 1 












in 

CO' 

VO 

CO d\ 
pTio" 

HI 




































j 








o ^ 












I-T CO 
















Nvo" 












I-T CO 
















CO 








^^ ^ 




CO 
















\r, CO 








l-H lO 

CO 




pTvo 
















M 












p^ 
















vo" " 








I-T VO 

~— CO 




pT cfi 








i 








l-H 


















1 




























f 


00 N 
CO 






hT CO 








" pT 




cooo" 
















VO 








CO 




•^ 










V. (^ 






r. at 








n n 




•^ «• 










toiri 






00 •>!- 








»-l *-* 




hi CO 








L 


1-4 






hi 








■* 




VO 








1 


•« n 






« •• 








r, r. 




•V « 








f 


O »^ 






N r^ 








CO t-» 




VO " 










►-t 






N 








»H 




i-t 










hT lo 






i-T T? 








wvo" 




■*tC 










M-) 






Tf 








lO 




IH 






































ClOO 






corC 








O t^ 




P) l'^ 










t-t 






n 












P) 










n m 






^ « 








«. •N 




*% av 










« "-) 






►J" CO 








■*VO 




hi t^ 










N 






ir, 












CO 








1 


r. -. 






•\ •% 








>s X 




n -< 








I 


•-. \o 






"^ N 








M 1^ 




hi ^ 








1 


^ 














•* 




CO 








r 






























rt-\r, 






i-i CO 








P« CO 




hi CO 
















•* 








M 




CO 






































C4 O 














i-i »0 




hi Ov 










to 




.-^-— * 


CO 




t-i Tt 




CO 




CO 






^pT 


r>. f 






00 o^ 






' — CO 














ro^ 


CO-, 


N m 






I-l VO 








►H O 




p) PJ 










N 




«v * 


CO 








^ 




PJ 






„ ^ 


^ 


•. #* 




pdO 


»- •^ 




►^ «o 




»< *t 




« ». 






CO hi 


hi ( 


■H O 




w 


•-I CO 




CO 




lO CO 




hi hi 






PI 


1 


lO 




M >^ 


CO 




tH CO 




IH 




m 






I-i" i-T 


CO I 


«C di 


■<*• 


1-^ rC 




CO 




pfin 




tC d^ 






•^ 


^ 






„ 


CO 








PI 




» « 






„ 


„ 


►H iC 


i-T rf 


N fO 


^ ^ 




iH od" 




^ ^ 




n 00 






" O 


f 


trt 


tn 


M 


N 00 
M 




CO 




-§: 




VO 






CO 


' 


■^ "f 


t-i M 


i-T tC 


^ ^ 




pT »A 




^ ^ 




VO CO 






rT ro 


rTl 

( 


t-« 


■* 


m 


00 o\ 




M 




00 00 




hi 






•0- 






























M Im" 


vo "-T 


tTvo" 


\0 N 


00 N 
CO" — ' 


pT d 


0\ ^ 


w lO 




VO PO 


O t-l 


vO_ hi 


■^ VO 


CO( 


■* 


■^ 


CO 






CO 


»— t 


VO 




PI 


— 


^^ 


►1 


1 


>-" CO 


N d^ 


N un 


CO I-T 


^rC 


lO CO 


^ „ 


■^>o 




hi" 00 


hi t^ 


rTvO 


hi lO 


hH 1 


ro 


N 


C4 


P) 




l-l 


00 0^ 




^^^^ 


CO 


CO 


ro 


CO 


1 


pT o" 


pT i-T 


m" C^" 


N CO 


rT rf 


pT lA 


pTvo 


pTrC 


P) 00 
^^ CO 


S 6^ 


-" o" 


hT hl^ 


rT fT 


I-T' 


m 


PO 


CO 


CO 


CO 


CO 


CO 


CO 




CO 


■<t 


■>i- 


■* 




•.. 


• •s 


• *. 


• r. 


••I 


• •. 


• •V 


• >v 


• n 


■ •v 


• -. 


• K 


• •« 


•«. 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


OO 


CO 


m 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 
















* 














'^ 


»o 


zo 


l>- 


GO 


en 


O 


I— 1 


CN 


CO 


<* 


»o 


CTJ 


t- 


b- 


t^ 


t>- 


t^ 


t^ 


l>- 


GO 


GO' 


OO 


GO 


GO 


GO 


OC 


OC 


1—1 


r— I 


r-i 


J— t 


I— 1 


T— ( 




I— 1 


1—1 


l-H 


1— ( 


I— < 


T— 1 


"* 































ON THE PELLIAN EQUATION. 



119 



10 ^H 


in (M 


>0 CO 


t- o 


O 05 


lO (M 


^ lO 


CO to 


t- lO 


oq t- 


-+I t^ 


en O 


rH rH 








to CO 


t^ ^ 


(M 00 


rt to 


I-H 


00 to 
















t- <N 


(M 00 


cq .-1 


Ol lO 


I-H 


CO 


S ■-< 


CO 02 




00 t^ 




CO ^ 




.-1 00 


to b- 


I-H O 


in o) 




CO 


O I-H 


oo C5 


o o 


n O 


i-H 


t- 00 




to 


lO 00 


■* O 


OO 






CO lO 


I-H O 




l-H t- 










n CO 


-* I-H 


O 05 






■* t- 


on to 


t- CO 


00 ^ 










I-H (M 


05 t- 


■* O 






I-H 00 


I-H o 




I-H b- 


( 


Oi 






lO 


tO '^ 

to 








I, 8, I, (24) 68 196 
51, 8, 67, (3) 2251 671 


^ o 

CO t^ 

00 I-H 

CO 
"o r^ 


O 05 

CO to 
"* (M 

Oi to 

CO lO 
CO to 
in -* 

O 05 

(M to 
lO t- 

lO lO 
t- <M 

t~o 

O 
CO 

CO~— 

>1 •% 
n lO 

VO 

(O" |i 
n 

cTvd" 

M 

-? 
o"t^ 

i-T lo 

CO 

« oo' 

CO 

fT CO 
N 

."VO 


i-H lO 




-~^^— K 


















CO 


-, * 






"-* CO 
















N CO 


«• »\ 


CO a. 






CO 
















N 


woo 


NH 
































J:!. CO 

CO 








O ^^ 








CO 


00 cfl 


PI m 


00 _^ 






























"^ 






00 _^ 


O »5 








VO hT 


N VO 


1-1 1^ 


U-) 




CO o^ 






i-T &; 


i-T rC 








n to 


i-T tC 


^'^ 


cT lO 








^__^ 


M- 


VO 


^„_^ 






Tj- 


lil 


n 


N 




pTJ- 






w tC 


CO ■* 


00 C) 






" N 


cot^ 


►1 IT) 


VO " 




ro 




M 










CO 


►H 




l-* 




■<t in 




CI in 


». 00 


cT '-' 


lOu-1 






i-H rr, 


11 M 


lO CO 


►H ON 




M 




o 


tl- 


CO 


M 






CO 


'J- 


n 


tr 




























"1 N 


'-' t>. 




N VO 


o'tC 


N 00 


lOlO 






»-« I-I 


M H 


t^ O 


N •* 


— 


•t 




c^ 




N 


•^ 






-si- 


CO 


*"* 


c^ 


11 o> 


tf •<? 




►< j^ 


C) 00 


CO Ov 


l^ o 






<^>o" 


(H ON 


n n 


M lO 


■* 


N 


--^— . 


CO 


N 


n 








•"* 


CO 


^J- 


M 


N ro 


N »^ 


CO 


t-l U1 


t-i a\ 


HH CO 


"-< r>. 




O^00 


"^M^ 


M VO 


w in 


" Tl- 


N 


CJ 




CO 


CO 


■* 


■* 


.— .^— s 




*-* 


M 




■* 


►H fO 


1 N 




>-< o 


« t> 


■H 00 


•I i-N, 


" VO 


C) m 


M 'I- 


M CO 


N M 


M " 


CO 


CO 




CO 


cs 


N 


w 




N 


M 


O 




N 


■1 ■.^ 


<-l til 


I-.VO 


" I~« 


"OO 


« oI 


« o" 


I-T I-T 


>H M 


1-1 CO 


" ■* 


►H m 


w VO 


■* 


'i- 


'd- 


Tl- 


■4- 


■* 


u-1 


lO 


lO 


lO 


lO 




m 


M 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


00 


to 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 




CO 




* 


* 






* 
















oo 


en 


O 


r— 1 


fl<l 


CO 


■^ 


lO 


CO 


t^ 


oo 


as 


O 


oo 


oo 


OS 


Ci 


as 


O 


CI 


Ci 


OS 


as 


Oi 


o:> 


O 


i-H 


I-H 


1— ( 


r-i 


T-t 


.—1 


I— 1 


I— I 


1—1 




1—1 


I— 1 


1—1 









120 EEPOET— 1893. 

In connexion with the subject we have a paper, 'A Table of the 
Square Roota of Prime Numbers of the form 4to+1 less than 10000 
expanded as Periodic Continued Fractions,' by C. A. Roberts, with Intro- 
duction and Explanation by Artemas Martin, the 'Mathematical Magazine,' 
vol. ii. (No. 7, for October 1892), pp. 105-120. This extends, in fact, to 
numbers up to 10501, but only the denominators of the continued frac- 
tions (that is, the first lines of Degen's and the present table) are given : 
thus the entry for 1009 is 31 ; 1, (3, 3). 

The paper just referred to notices errors in Degen's tables for the 
numbers 853 and 929. For 853 the first line should be 

29,4,1,5,1,2,4,1,1,15,19,(2,2) 

(l5 instead of Degen's 14). For 929 the first and second lines should be 

30, 2,11, 1, 2, 3, 2,7, 5, (2, 2) 
1, 29, 5, 40, 19, 16, 25, 8, 11, (23, 23) 

The values of a', y in Table I. and those in Table II. (for the solution 
of ?/2=aa^ — 1) are correct for each of the numbers 853 and 929. 



On the Establishment of a National Physical Laboratory. — Report 
of the Committee, consisting of Professor Oliver J, Lodge 
{Chairman), Mr. E. T. Glazebeook {Secretary), Lord Kelvin, 
Lord Rayleigh, Sir H. E. Eoscoe, Professors J. J. Thomson, 
A. W. Eucker, E. B. Clifton, G. F. FitzOerald, G. Carey 
Foster, J. Viriamu Jones, A. Schuster, and W. E. Ayrton. 

The Committee hoped to have been able to present a report dealing with 
the work done at the Reichsanstalt in Berlin and the Bureau Inter- 
national at Sevres. They have not, however, been able to prepare this 
report in time for the meeting, and they desire to be reappointed to 
continue their investigations. 



The Best Means of Comparing and Reducing Magnetic Observa- 
tions. — Interim Report of the Committee, consisting of Professor 
W. Getlls Adams {Chairman and Secretary), Lord Kelvin, 
Professors G. H, Darwin and G. Chetstal, Mr. C!. H. Carpmael, 
Professor A. Schustee, Mr. G. M. Whipple, Captain Cbeak, The 
AsTRONOMEE EoYAL, Mr. WiLLiAM Ellis, and Professor A. W. 

EiJCKEE. 

The Committee have considered and reported to the Admiralty on plans, 
submitted to them by Mr. Gill, for a Magnetic Observatory at the Cape 
of Good Hope. In conjunction with Mr. Gill, they have drawn up a 
scheme embodying their recommendations as to its establishment and 
maintenance, which has been laid before, and is under the consideration 
of, the Admiralty. 

The Committee desire to be reappointed, with the addition of Mr. 
Charles Chree in the place of the late Mr, G. M. Whipple. 



ox ELECTRO-OPTICS. 



121 



On Electro-optics. — Report of the Committee, consisting of Dr. John 
Kerr {Chairman), Mr. E. T. Glazebrook {Secretary), Lord 
Kelvin, and Professor A. W. Rucker. 

The Comraif.tee report that Dr. Kerr's experiments have been continued, 
and that he hopes sLortly to have further results ready for publication. 



Magnetic Work at the Falmouth Observatory.— Report of the Com- 
mittee, consisting of Mr. Howard Fox, Professor A. W. Eucker, 
and Professor W. G-. Adams. 

Magnetical Observations. 

[Made at the Falmouth Observatory, latitude 50° 9' 0" N. and longitude 
5° 4' 35" W., height 167 feet above mean sea level, for the year 1892, 
by Edward Kitto, Superintendent.] 

The results in the following tables, Nos. 1,2, 3, 4, are deduced from 
the magnetograph curves which have been standardised by observations 
of deflection and vibration. These were made with the collimator 
magnet marked 66a, and the declinometer magnet marked 66c in the 
unifllar magnetometer by Elliott Bros., of London. Table No. 5 is 
deduced from these observations. 

The inclination was observed with the inclinometer by Dover, of 
Charlton, Kent, No. 86, and needles 1 and 2, which are 3| inches in 
length, the results of which appear in Table No. 6. 

The declination and horizontal force values given in Tables 1 to 4 
are prepared in accordance with the suggestions made in the fifth report 
of the Committee of the British Association on Comparing and Reducing 
Magnetic Observations. 

The following is a list of the days during the year 1892 which were 
selected by the Astronomer Royal as suitable for the determination of 
the magnetic diurnal variations, and which have been employed in the 
preparation of the magnetic tables : — 



January . 






. 2, 9,20,22,30. 


February 






. 3, 8, 17, 18, 22. 


March . 






. 10, 14, 17, 18, 23. 


April 






. 5, 6, 17, 20, 22. 


May 






. 12, 13, 15, 23, 26. 


June 






. 8, 9, 12, 14, 15. 


July 






. 5, 6, 8, 20, 23. 


August . 






. 11, 14, 15, 19, 30. 


September 






. 4, 5, 9, 12, 25. 


October . 






. 9, 17, 23, 26, 28. 


November 






. 8, 11, 12, 16, 27. 


December 






. 3, 9, 18, 26, 27. 



122 



KEPOET — 1893. 



Table I. — Hourly Means of Declination at the Falmouth 
Five selected quiet Days in each Month 



Hours . 


1 


2 


3 


4 


5 6 


7 


8 


9 


10 


11 


Noon 


Winter. 


1892 






















' 




Months 


f 


r 


/ 


/ 


t 










' 






January . 


15-5 


15-3 


151 


150 


15-2 


15-4 


15-3 


14-9 


150 


16-4 


17-9 


20-7 


February . 


13-8 


13-1 


13-2 


14-2 


13-8 


150 


14-9 


152 


15-2 


15V 


IV -6 


20-0 


March 


14-5 


14-7 


14-8 


14-9 


15-3 


14-4 


13-4 


12-3 


12-8 


13-9 


16-6 


20-2 


October . 


10-5 


10-6 


10-5 


10-6 


10-9 


10-6 


10-4 


91 


8-4 


9-2 


11-9 


15-5 


November 


9-8 


101 


9-9 


10-2 


9-7 


9-7 


9-3 


9-4 


87 


8-9 


10-1 


12-4 


December 


9-4 


9-9 


9-7 


100 


9-8 


9-3 


9-2 


9-2 


9-4 


106 


12-2 


13-6 


Means . 


12-3 


12-3 


12-2 


12-1 


12-5 


12-4 


12'1 


11-7 


11-6 


12-5 


14-4 


171 


Slimmer. 


1892 
























' 


Months 


t 


1 


1 


t 


t 


/ 








' 


' 




April 


13-7 


13-3 


13-2 


12-9 


12-5 


12-2 


10-7 


9-6 


9-4 


11-4 


14-4 


17-9 


May . 


12-8 


12-9 


12-4 


11-7 


10-3 


8-9 


7-7 


7-7 


8-8 


11-5 


14-9 


18-4 


June 


12-1 


12-1 


121 


11-2 


9-5 


7-4 


6-9 


70 


8-2 


11-0 


13-7 


17-4 


July 


11-3 


10-7 


10-4 


9-9 


8-2 


6-4 


5-8 


5-6 


6-4 


8-6 


11-4 


14-8 


August 


100 


10-4 


9-6 


9-3 


8-5 


71 


5-9 


5-8 


7-0 


100 


13-7 


17-1 


September 


10-2 


9-9 


9-2 


91 


8-6 


7-9 


7-1 


6-9 


8-2 


11-6 


14-6 


17-8 


Means . 


11-7 


11-6 


11-2 


11-4 


9-6 


8-3 


7-4 


7-1 


8-0 


10-7 


13-8 


17-2 



Table II. — Solar Diurnal Range of the Falmouth 



Hours 


1 


2 


3 


4 1 5 


6 


7 


8 


9 


10 


11 


Noon 


Summer Mean. 




' 1 ' 

-0-7 -0-8 


-1-2 


-1-0 


-2-8 


-4-1 


-50 


-5-3 -4-4 -1-7 


+ 1-4 


+ 1-8 


Winter Mean. 




-1-4 


-1-4 


-1-5 


-1-6 


-1-2 


-1-3 


-1-6 


-2-0 -21 


1 

-1-2 


+ 0-7 


+ 3-4 


Annual Mean. 


' « ' ' ' 
-1-1 -1-1 -1-4 -1-3 -2-0 


-2-7 -3-3 


1 
-3-7 


1 1 1 
-3-3 -1-5 +1-1 


+ 41 1 
















No 


IE.— W 


hen the 


s sign is 


+ the 


magnel 



ON THE MAGNETIC WORK AT THE FALMOUTH OBSERVATORY. 



123 



Observatory, determined from the Magnetograpli Curves on 
during the year 1892. (19° + West.) 



4 


6 


6 


7 


8 


9 


10 


11 



Mid. 



Winter. 



21-7 
20-6 
22-0 
17-6 
13-4 
14-6 



18-3 



t 


/ 


p 


/ 


f 


; 


/ 


/ 


/ 


t 


21-2 


19-9 


18-8 


18-0 


17-3 


16-8 


15-8 


15-5 


15-1 


150 


20-8 


20-1 


18-1 


16-7 


16-8 


16-3 


15-4 


14-5 


14-2 


13-8 


21-8 


20-7 


19-0 


17-1 


]61 


15-3 


15-4 


14-8 


14-3 


15-2 


18-7 


17-5 


15-6 


141 


12-7 


11-9 


11-6 


11-3 


10-8 


10-5 


13-9 


131 


12-7 


11-9 


111 


10-7 


10-4 


9-8 


9-7 


9-5 


13-7 


13-3 


]20 


11-7 


ir8 


10-9 


100 


9-5 


8-7 


8-5 


18-4 


17-5 


160 


14-9 


14-3 


13-7 


13-1 


12-6 


12-1 


121 



15-2 
13-6 
16-4 
101 
9-7 
8-9 



12-2 



Summer. 



t 

19-9 


20-1 


f 

18-8 


f 

17-4 


t 

15-8 


t 

15-2 


t 

15-1 


15-0 


14-6 


14-8 


146 


20-1 


19-5 


180 


16-2 


14-4 


12-9 


12-3 


12-6 


12-8 


13-2 


13-0 


19-7 


19-9 


181 


16-8 


15-3 


140 


130 


12-7 


12-6 


12-9 


12-6 


17-3 


18-5 


17-6 


15-3 


13-6 


121 


11-5 


11-3 


11-6 


11-8 


11-6 


19-2 


18-5 


16-4 


13-6 


11-5 


10'5 


10-4 


10-3 


10-4 


10-6 


10-1 


18-6 


17-9 


160 


13-7 


11-8 


11-0 


10-9 


10-6 


101 


10-6 


10-5 


191 


191 


17-5 


15-5 


13-7 


12-6 


12-2 


121 


120 


12-3 


121 



14-3 
12-9 
12-5 
11-6 
9-4 
100 



11-8 



Declination as derived from Table I. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


10 11 


Mid. 




Sumvier Mean. 




+ 6-7 


+ 6-7 


+ 51 


+ 3-1 


+ 1-3 


1 

+ 0-2 


-0-2 


-03 


-0-4 


-01 


-0-3 


/ 

-0-6 




Winter Mean. 




1 

+ 4-6 


+ 4-7 


+ 3-8 


+ 2-3 


+ 1-2 


+ 0-6 


0-0 


-0-6 


-1-1 


-1-6 


-1-6 


-1-5 




Annual Mean. 




+ 5-7 


+ 5-7 


+ 4-5 


+ 2-7 


1 

+ 1-3 


+ 0-4 


-0-1 


t 

-0-5 


-0-8 


-0-9 


-10 


1 

-11 



point-s to the west of its mean position. 



124 



REPORT 1893. 



Table III. — Hourly Means of the Horizontal Force ^ at Falmouth 
{corrected for Temperature) on Five selected quiet Days in each 



Hours . 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


Noon 




Winter. 




1892 




























Months 




























January . 


444 


446 


444 


448 


450 


450 


451 


447 


439 


426 


420 


422 




February . 


410 


408 


404 


405 


407 


406 


413 


413 


407 


397 


385 


385 




March 


430 


432 


433 


434 


436 


438 


433 


427 


417 


407 


402 


401 




October . 


452 


454 


455 


455 


456 


457 


457 


449 


435 


425 


422 


420 




November 


460 


460 


463 


464 


465 


467 


466 


462 


453 


447 


445 


445 




December 


452 


453 


453 


456 


457 


460 


461 


457 


452 


444 


442 


440 




Means 


441 


442 


442 


444 


445 


446 


447 


443 


434 


431 


419 


419 




Summer. 




1892 




























Months 




























April 


462 


460 


460 


460 


459 


458 


455 


450 


438 


427 


425 


430 




May . 


446 


443 


443 


440 


443 


438 


429 


417 


408 


407 


405 


413 




June 


456 


45S 


454 


454 


454 


448 


438 


429 


421 


420 


429 


437 




July . . . 


453 


449 


448 


447 


445 


440 


435 


429 


419 


412 


409 


410 




August 


456 


454 


455 


453 


452 


451 


444 


432 


417 


411 


411 


420 




September 


460 


457 


458 


458 


457 


454 


446 


436 


427 


423 


425 


439 




Means 


456 


453 


453 


452 


452 


448 


441 


432 


422 


417 


417 


425 





Table IV. — Dmrnal Range of the Falmouth Horizontal 



Hours 


1 


2 


3 


4 


6 


6 


7 


8 


9 


10 


11 


Noon 


Summer Mean. 










+ •00009 


+ •00006 


+•00006 


+•00005 


+ ■00005 


+•00001 


—•00006 —•00015 


—•00026 


—•00030 


-•00030 


—•00022 


Winter Mean. 




+ •00001 


+ ■00002 +^00002 


+•00004 


+•00005 


+ •00006 


+ •00007 


+•00003 


—•00006 


—•00009 


—•00021 


—•00021 


An7ival Mea7i. n 




+ •00005 


+•00004 


+ ■00004 


+ •00004 


+•00005 


+ •00004 


+ ■00001 


—•00006 


—•00015 


—•00020 


— ^00026 


—•00022 1 



* Approximate values. Note. — When the sign is + the 



ON THE MAGNETIC WORK AT THE FALMOUTH OBSERVATORY. 



125 



Observatory as determined from the Magiietograph Curves. 
Month during the year 1892. O'lSOOO + (C.G.S. units). 





1 


2 


3 


4 


5 


6 7 


8 


9 


10 


11 j Mid. 




mnter. 




429 
890 
407 
431 
446 
443 


435 
396 
418 
438 
453 
446 


438 
402 
429 
440 
459 
448 


441 
407 
429 
444 
462 
451 


442 
410 
427 
447 
465 
457 


446 
420 
431 
451 
465 
458 


448 
415 
444 
454 
466 
459 


449 
421 

444 
458 
467 
460 


448 
421 
439 
458 
469 
456 


448 
414 
440 
459 
469 
454 


450 
4] 7 
443 
459 
467 
454 


451 
419 
443 
458 
470 
452 




424 


431 


436 


439 


441 


445 


448 


450 


449 


447 


448 


449 




Su7U7)ier. 




433 
421 
442 
418 
431 
450 


444 
430 
449 
429 
439 
457 


453 
440 
456 
440 
449 
457 


460 
447 
454 
447 
456 
455 


459 
453 
458 
452 
459 
455 


464 
454 
462 
458 
462 
459 


465 
457 
466 
461 
464 
465 


465 
453 
467 
460 
468 
465 


464 
456 
466 
460 
468 
465 


467 
454 
466 
456 
466 
462 


463 
452 
462 
455 
467 
463 


462 
452 
461 
454 
463 
462 

459 




433 


441 


449 


453 


456 


460 


463 


463 


463 


462 


460 



Force as deduced from Table III. (C.G.S. units.) 



1 


2 


3 


4 5 


6 


7 


8 


9 


10 


11 


Mid. 


Summer Mean. 


—•00014 


—•00006 


+•00002 


+•00006 


+•00009 


+ •00013 


+•00016 


+•00016 


+•00016 


+•00015 +^00013 


+•00012 


Winter Mean. 


—•00016 


-•00009 


—•00004 


—•00001 


+ •00001 


+ •00005 


+ •00008 


+•00010 


+ •00009 


+•00007 


+•00008 


+ •00009 




Annual Mean. 


-■00015 


—•00008 


+•00001 


+ •00003 


+•00005 


+•00009 


+•00012 


+ •00013 


+•00013 +^00011 


+ -000U 


+ •00011 


reading 


is abo\ 


e the n 


lean. 



















126 REPORT — 1893. 

Table V. — Magnetic Intensity. Falmouth Observatory, 1892. 



1892 


C.G.S. Measure 








X or Horizontal Force 


Y or Vertical Force 


January 


0-18426 


0-43691 


February 












0-18405 


0-43624 


March 












0-18444 


0-43734 


April 












0-18435 


0-43727 


May 












0-18448 


0-43673 


June 












0-18465 


0-43694 


July. 












0-18453 


0-43706 


August 












0-18447 


0-43702 


September 










0-18424 


0-43683 


October . 










0-18437 


0-43689 


November 










0-18450 


0-43691 


December 










0-18439 


0-43619 


Means 


0-18439 


0-43686 



Table VI. — Observations of Magnetic Inclination. 
Falmouth Observatory, 1892. 



Month 


Mean at 

10 A.M. 


Month 


Mean at 

10 A.M. 


January 29 . 

30 . . . 

February 25 . 

,. 27 . . . 

March 28 . 

29 . . . 

30 . . . 

April 27 . 

29 . . . 

30 . . . 

May 27 . . . 

28 . . . 

June 28 . 

29 . . . 

30 . . . 


O t 

67 9-4 
67 6-7 


July 28 

29 . . 

30 . . 

August 27 

31 . . 

September 28 

29 . . 

October 27 

28 . . 

29 . . 

November 25 

„ 26 . . 

December 21 

22 . . 

23 . . 


6°7 7-8 
67 6-8 
67 5-1 


67 8-0 


67 6-6 


67 71 
67 7-8 


67 6-1 

67 7-7 


67 7-5 


67 6-9 


67 7-9 
67 90 
67 7-0 


67 7-3 
67 8-6 


67 80 


67 7-9 


67 8-4 
67 80 
67 8-7 


67 7-7 
67 6-7 
67 7-1 


67 8-4 


67 7-2 


67 6-2 

67 5-8 


67 6-6 
67 6-2 


1 67 6-0 


67 6-4 


67 7-4 
67 7-3 
67 5-7 


67 6-1 
67 4-7 
67 4-6 


67 6-8 


67 6-1 







ON STANDARDS FOR USE IN ELECTRICAL MEASUREMENTS. 



127 



Experiments for Improving the Construction of Practical Standards 
for Electrical Measurements. — Report of the Committee, con- 
sisting of Professor Carey Foster {Chairman), Lord Kelvin, 
Professors Ayrton, J. Perry, W. G. Adams, Lord Kayleigh, and 

0. J. Lodge, Drs. John Hopkinson and A. Muirhead, Messrs. 
W. H. Preece and Herbert Taylor, Professor J. D. Everett, 
Professor A. Schuster, Dr. J. A. Fleming, Professors G. F. 
FitzG-erald, Cf. Chrystal, and J. J. Thomson, Messrs. E. T. 
G-LAZEBROOK {Secretary), W. N. Shaw, and T. C. Fitzpatrick, 
Dr. J. T. Bottomley, Professor J. Viriamu Jones, Dr. Gr. John- 
stone Stoney, Professor S. P. Thompson, and Mr. G. Forbes. 

APPENDIX . ^■*-*^^ 

1. Siij>/>le>iie»fari/ Report of the. Electrical Standards Committee of the 

Board of trade . ' 129 

II. Experiments on the Effects of the Heating produced in the Coils hy the 

Currents used in Testinrj. By R. T. GlAZEBEOOK .... 136 

III. On Standards of Low Electrical Resistance. By J. Viriamu Jones . 137 

The work of testing resistance coils at the Cavendish Laboratory has 
been continued. A table of the coils tested is given. They have 
all been ' ohms,' as defined by the resolution of the Committee given in 
their last report, and since adopted by the Board of Trade Committee on 
electrical standards in the following form : — 

The resistance offered to an unvarying electric current by a column 
of mercury at the temperature of melting ice 14-4521 grammes in mass, of 
a constant cross-sectional area, and of a length of 106-3 centimetres, may 
be taken as 1 ohm. The relation between the B.A. unit and the ohm is 
the following : — 

1 B.A.U.=-9866 ohm. 





Table I. 






Ohms. 




No. of Coil 


Value in Ohms 


Temperatui-e 


Nalder, 3717 . 


^^ No. 361 


1-00025 


17°-7 


Nalder, 3874 


. !^ No. 362 


9-9926 


14°-9 


Nalder, 3059 ' . 


. 3p, No. 326 


1-00000 


16°-5 


Nalder, 3033 


;^ No. 363 


100000 


170-2 


Nalder, 3637 . 


;^ No. 364 


100-000 


17°-05 


Nalder, 3635 . 


$^ No. 365 


1000-00 


17°-3 


Nalder, 3872 . 


^ No. 366 


9-9947 


14°-9 


Nalder, 3873 . 


^ No. 367 


9-9919 


14°-8 


Nalder, 4085 . 


"^^ No. 368 


•99889 


14°-8 



' This coil had been tested before. 



128 



REPORT 1893. 



Table I. 
Ohms — continued. 



No. of Coil 


Value in Ohms 


Temperature 


Nalder, 3263 . . • [^ No. 369 


•99895 


14°-2 


Warden, 1866 






'^^ No. 370 


100080 


l4°-5 


Warden, 1918 






$, No. 371 


100011 


14°-3 


Nalder, 3715 






^ No. 372 


•99944 


13°-5 


Nalder, 3719 






^^ No. 373 


■99907 


13°-3 


Nalder, 3720 






^^ No. 371 


•99898 


13°-3 


Nalder, 3633 






|:^ No. 375 


9-9910 


15°-3 


Nalder, 3876 






^ No. 376 


•99932 


15°-2 


Nalder, 3981 






^ No. 377 


10-0001 


15°-7 


Nalder, 4086 






$ No. 378 

• ^ No. 379 

* No. 380 


•99978 


15°-9 


ElUott, 303 






1^00054 


18°-2 


Elliott, 301 






1^00052 


18°-1 



The resolutions adopted by the Committee at Edinburgh were com- 
municafced to the Electrical Standards Committee of the Board of Trade. 
After consideration the Board of Trade Committee drew up an amended 
report, in harmony with the Edinburgh resolutions, for presentation to 
the President (see Appendix I.). 

The resolutions were accepted at Edinburgh by Dr. von Helmholtz on 
behalf of Germany, while in France an official committee decided last 
June to adhere to the propositions of the Board of Trade. Austria and 
Italy are connected by treaty with Germany for telegraph purposes, and 
in consequence adopt the same units. 

The Committee have learnt with pleasure from Mr. W. H. Preece, 
one of the English delegates to the International Congress of Electricians 
at Chicago, that the Congress has accepted a series of resolutions defining 
the fundamental units practically identical with the Edinburgh resolu- 
tions. 

Thus these resolutions have now been accepted as a basis for legisla- 
tion throughout the British Empire, the whole of Western Europe, and 
the United States of America. 

The Committee are also informed that the Chicago Congress have 
adopted the name ' Henry ' for the unit of self-induction ; while looking 
with favour on this suggestion, they think it desirable to postpone definite 
action until the ofiicial report of the Congress has been received. 

In March last M. Mascart wrote to the Secretary asking the opinion 
of the Committee as to a name for the standard of resistance defined at 
Edinburgh. A circular letter was issued inviting members of the Com- 
mittee to express their views on four names which had been suggested, 
viz.: 'International,' 'Normal,' ' Btalion,' or 'Ohm de 1893.' After 
receiving replies to the circular from twelve members of the Committee, 
the Secretary wrote to Professor Mascart to the efi'ect that the number 



ON STANDARDS FOR USE IN ELECTRICAL MEASUREMENTS. 129 

of members who expressed a preference for the name ' International ' was 
greater than the number declaring in favour of any other name, but that 
he thought that the Committee would accept whichever of the first three 
suggestions commended itself to the French Committee appointed to deal 
with the matter. 

During the year Dr. Muirhead has remeasured his standard condenser. 
He now finds as the capacity of a condenser constructed twenty-three 
years ago to represent '1 microfarad (B.A.U.) the value "09998 micro- 
farad. 

Tests have been made during the year on the 1-ohm and 10-ohm 
standards of the Association. These are still being continued. The 
100-ohm and 1000-ohm standards have now been delivered, and the 
tests will be shortly proceeded with. Some experiments were made as 
to the amonnt of heating in the coils produced by the current used for 
testing. These are detailed in Appendix II. Further valuable informa- 
tion on this point is contained in Mr. Griffiths' paper on ' The Value 
of the Mechanical Equivalent of Heat.' ' 

The Comruittee think it desirable that they should be in a position to 
complete the set of resistance standards of the Association, and recom- 
mend, therefore, that they be reappointed, with a grant of 25Z., that 
Professor G. Carey Foster be Chairman, and Mr. R. T. Glazebrook 
Secretary. 



APPENDIX I. 

Supplementary Report of the Electrical Standards Committee of the 

Board of Trade. 

To the Right Hon. A. J. Mundella, M.P., 
President of the Board of Trade. 

Subsequently to the presentation of our former report to Sir Michael 
Hicks-Beach, in July 1891, we were informed that it was probable that 
the German Government would shortly take steps to establish legal 
standards for use in connection with electrical supply, and that, with a 
view to secure complete agreement between the proposed standards in 
Germany and England, the Director of the Physico-Technical Imperial 
Institute at Berlin, Professor von Helmholtz, with certain of his assistants, 
proposed to visit England for the purpose of making exact comparisons 
between the units in use in the two countries, and of attending the meet- 
ing of the British Association which was to take place in August in 
Edinburgh. 

Having regard to the importance of this communication it appeared 
desirable that the Board of Trade should postpone the action recom- 
mended in our previous report until after Professor Helmholtz's visit. 

That visit took place early in August, and there was a very full 
discussion of the whole subject at the meeting of the British Association 
in Edinburgh, at which several of our number were present. The meet- 
ing was also attended by Dr. Guillaume, of the Bureau International des 
Poids et Mesures, and Professor Carhart, of the University of Michigan, 

' Phil. Trans., 1893. 
1893. K 



130 REPORT — 1893. 

U.S.A., who were well qualified by their scientific attainments to represent 
the opinion of their respective countries. 

It appeared from the discussion that a few comparatively slight 
modifications of the resolutions included in our pi'evious report would 
tend to secure international agreement. 

An extract from the report of the Electrical Standards Committee of 
the British Association embodying the results of this discussion was 
communicated to us by the Secretary, and will be found in the appendix 
to this report. 

Having carefully reconsidered the whole question in view of this 
communication, and having received the report of the sub-committee 
mentioned in resolution 14 of our previous report, we now desire, for the 
resolutions contained in that report, to substitute the following : — 



Resolutions. 

1. That it is desirable that new denominations of standards for the 
measurement of electricity should be made and approved by her Majesty 
in Council as Board of Trade standards. 

2. That the magnitudes of these standards should be determined 
on the electro-magnetic system of measurement with reference to the 
centimetre as unit of length, the gramme as unit of mass, and the second 
as unit of time, and that by the terms centimetre and gramme are meant 
the standards of those denominations deposited with the Board of Trade. 

3. That the standard of electrical resistance should be denominated 
the ohm, and should have the value 1,000,000,000 in terms of the centi- 
metre and second. 

4. That the resistance offered to an unvarying electric current by a 
column of mercury at the temperature of melting ice 14'4521 grammes in 
mass of a constant cross-sectional area, and of a length of 106'3 centi- 
metres, may be adopted as 1 ohm. 

5. That a material standard, constructed in solid metal, should be 
adopted as the standard ohm, and should from time to time be verified 
by comparison with a column of mercury of known dimensions. 

6. That, for the purpose of replacing the standard, if lost, destroyed, 
or damaged, and for ordinary use, a limited number of copies should be 
constructed, which should be periodically compared with the standard 
ohm. 

7. That resistances constructed in solid metal should be adopted as 
Board of Trade standards for multiples and sub-multiples of the ohm. 

8. That the value of the standard of resistance constructed by a com- 
mittee of the British Association for the Advancement of Science in the 
years 1863 and 1864, and known as the British Association unit, may be 
taken as '9866 of the ohm. 

9. That the standard of electrical current should be denominated the 
ampere, and should have the value one-tenth (0"1) in terms of the centi- 
metre, gramme, and second. 

10. That an unvarying current which, when passed through a solution 
of nitrate of silver in water, in accordance with the specification attached 
to this report, deposits silver at the rate of O'OOlllB of a gramme per 
second may be taken as a current of 1 ampere. 

11. That an alternating current of 1 ampere shall mean a current 



ON STANDARDS FOR USE IN ELECTRICAL MEASUREJIENTS. 131 

such tLafc the square root of the time average of the square of its strength 
at each instant in amperes is unity. 

12. That instruments constructed on the principle of the balance, in 
which, by the proper disposition of the conductors, forces of attraction 
and repulsion are pi-oduced, which depend upon the amount of current 
passing, and are balanced by known weights, should be adopted as the 
Board of Trade standards for the measurement of current, whether 
unvarying or alternating. 

13. That the standard of electrical pressure should be denominated 
the volt, being the pressure which, if steadily applied to a conductor 
whose resistance is 1 ohm, will produce a current of 1 ampere. 

14. That the electrical pressure at a temperature of 15° Centigrade 
between the poles or electrodes of the voltaic cell known as Clark's cell, 
prepared in accordance with the specification attached to this report, may 
be taken as not differing from a pressure of 1-434 volt by more than 
one part in one thousand. 

15. That an alternating pressure of 1 volt shall mean a pressure 
such that the square root of the time-average of the square of its value at 
each instant in volts is unity. 

16. That instruments constructed on the principle of Lord Kelvin's 
quadrant electi'ometer used idiostatically, and, for high pressures, instru- 
ments on the principle of the balance, electrostatic forces being balanced 
against a known weight, should be adopted as Board of Trade standards 
tor the measurement of pressure, whether unvarying or alternating. 

(Signed) Courtenat Boyle. Kelvin. 

P. Cardew. W. H. Preece. 

Ratleigh. Gr. Carey Foster. 

R. T. Glazebrook. J. Hopkinson. 
W. E. Ayeton. 



November 29, 1892. 



T. W. P. Blomefield, Secretary. 



Specification referred to in Resolution 10. 

In the following specification the term silver voltameter means the 
arrangement of apparatus by means of which an electric current is 
passed through a solution of nitrate of silver in water. The silver volta- 
meter measures the total electrical quantity which has passed during the 
time of the experiment, and by noting this time the time-average of the 
current, or if the current has been kept constant the current itself, can 
be deduced. 

In employing the silver voltameter to measure currents of about 
1 ampere the following arrangements should be adopted. The kathode 
on which the silver is to be deposited should take the form of a platinum 
bowl not less than 10 centimetres in diameter, and from 4 to 5 centi- 
metres in depth. 

The anode should be a plate of pure silver some 30 square centimetres 
in area and 2 or 3 millimetres in thickness. 

This is supported horizontally in the liquid near the top of the solu- 
tion by a platinum wire passed through holes in the plate at opposite 
corners. To prevent the disintegrated silver which is formed on the 



132 REPORT — 1893. 

anode from falling on to the kathode the anode should be wrapped 
roand with pure filter-paper, secured at the back with sealing-wax. 

The liquid should consist of a neutral solution of pure silver nitrate, 
containing about fifteen parts by weight of the nitrate to eighty- five parts 
of water. 

The resistance of the voltameter changes somewhat as the current 
passes. To prevent these changes having too great an eiFect on the 
current some resistance besides that of the voltameter should be inserted 
in the circuit. The total metallic resistance of the circuit should not be 
less than 10 ohms. 

Method of mahing a Measurement. 

The platinum bowl is washed with nitric acid and distilled water, 
dried by heat, and then left to cool in a desiccator. When thoroughly 
dry it is weighed carefully. 

It is nearly filled with the solution, and connected to the rest of the 
circuit by being placed on a clean copper support to which a binding 
screw is attached. This copper support must be insulated. 

The anode is then immersed in the solution, so as to be well covered 
by it and supported in that position ; the connections to the rest of the 
circuit are made. 

Contact is made at the key, noting the time of contact. The current 
is allowed to pass for not less than half an hour, and the time at which 
contact is broken is observed. Care must be taken that the clock used 
is keeping correct time during this interval. 

The solution, is now removed from the bowl and the deposit is washed 
with distilled water and left to soak for at least six hours. It is then 
rinsed successively with distilled water and absolute alcohol and dried in 
a hot-air bath at a temperature of about 160° C. After cooling in a 
desiccator it is weighed again. The gain in weight gives the silver 
deposited. 

To find the current in amperes this weight, expressed in grammes, 
must be divided by the number of seconds during which the current has 
been passed and by -001118. 

The result will be the time-average of the current, if during the 
interval the current has varied. 

In determining by this method the constant of an instrument the 
current should be kept as nearly constant as possible, and the readings 
of the instrument taken at frequent observed intervals of time. These 
observations give a curve from which the reading corresponding to the 
mean current (time-average of the current) can be found. The current, 
as calculated by the voltameter, corresponds to this reading. 



Specification eefeeked to in Resolution 14. 
Definition of the Cell. 

The cell consists of zinc and mercury in a saturated solution of zinc 
sulphate and mercurous sulphate in water, prepared with mercurous 
sulphate in excess, and is conveniently contained in a cylindrical glass 
vessel. 



ON STANDARDS FOR USE IN ELECTRICAL MEASUREMENTS. 133 

Preparation of the Materials. 

1. Tlie Mercury. — To secure purity it should be first treated with acid 
in the usual manner and subsequently distilled in vacuo. 

2. The Zinc. — Take a portion of a rod of pure redistilled zinc, solder 
to one end a piece of copper wire, clean the whole with glass-paper, 
carefully removing any loose pieces of the zinc. Just before making up 
the cell dip the zinc into dilute sulphuric acid, wash with distilled water, 
and dry with a clean cloth or filter-paper. 

3. The Zinc Sidphate Solution. — Prepare a saturated solution of pure 
(' pure recrystallised ') zinc sulphate by mixing in a flask distilled 
water with nearly twice its weight of crystals of pure zinc sulphate, and 
adding zinc oxide in the proportion of about 2 per cent, by weight of 
the zinc sulphate crystals to neutralise any free acid.' The crystals 
should be dissolved with the aid of gentle heat, but the temperature 
to which the solution is raised should not exceed 30° C. Mercurous 
sulphate treated as described in 4 should be added in the proportion of 
about 12 per cent, by weight of the zinc sulphate crystals, and the solu- 
tion filtered, while still warm, into a stock bottle. Crystals should form 
as it cools. 

4. Th& Mercurous Sulphate. — Take mercurous sulphate, purchased as 
pure, and wash it thoroughly with cold distilled water by agitation in a 
bottle; drain off the water and repeat the process at least twice.' After 
the last washing drain off as much of the water as possible. 

Mix the washed mercurous sulphate with the zinc sulphate solution, 
adding sufficient crystals of zinc sulphate from the stock bottle to ensure 
saturation, and a small quantity of pure mercury. Shake these up well 
together to form a paste of the consistence of cream. Heat the paste, 
but not above a temperature of 30° C. Keep the paste for an hour at 
this temperature, agitating it from time to time, then allow it to cool ; 
continue to shake it occasionally while it is cooling. Crystals of zinc 
sulphate should then be distinctly visible, and should be distributed 
throughout the mass ; if this is not the case add more crystals from the 
stock bottle, and repeat the whole process. 

This method ensures the formation of a saturated solution of zinc and 
mercurous sulphates in water. 

Contact is made with the mercury by means of a platinum wire about 
No. 22 gauge. This is protected from contact with the other materials 
of the cell by being sealed into a glass tube. The ends of the wire 
project from the ends of the tube ; one end forms the terminal, the other 
end and a portion of the glass tube dip into the mercui-y. 

To set up the Cell. 

The cell may conveniently be set up in a small test tube of about 
2 centimetres diameter and 6 or 7 centimetres deep. Place the mercury 
in the bottom of this tube, filling it to a depth of, say, 1'5 centimetre. 
Cut a cork about '6 centimetre thick to fit the tube ; at one side of the 
cork bore a hole through which the zinc rod can pass tightly ; at the 
■other side bore another hole for the glass tube which covers the platinum 
wire ; at the edge of the cork cut a nick through which the air can pass 

' See Notes. 



134 KEPOET— 1893. 

when the cork is pushed into the tube. "Wash the cork thoroughly with 
warm water, and leave it to soak in water for some tours before use. 
Pass the zinc rod about 1 centimetre through the cork. 

Clean the glass tube and platinum wire carefully, then heat the ex- 
posed end of the platinum red-hot, and insert it in the mercury in the 
test tube, taking care that the whole of the exposed platinum is covered. 

Shake up the paste and introduce it without contact with the upper 
part of the walls of the test tube, filling the tube above the mercury to a 
depth of rather more than 2 centimetres. 

Then insert the cork and zinc rod, passing the glass tube through the 
hole prepared for it. Push the cork gently down until its lower surface 
is nearly in contact with the liquid. The air will thus be nearly all ex- 
pelled, and the cell should be left in this condition for at least twenty, 
four hours before sealing, which should be done as follows : — 

Melt some marine glue until it is fluid enough to pour by its own 
weight, and pour it into the test tube above the cork, using sufficient to 
cover completely the zinc and soldering. The glass tube should project 
above the top of the marine glue. 

The cell thus set up may be mounted in any desirable manner. It is 
convenient to arrange the mounting so that the cell may be immersed in 
a water-bath up to the level of, say, the upper surface of the cork. Its 
temperature can then be determined more accurately than is possible 
when the cell is in air. 

In using the cell sadden variations of temperature should as far as 
possible be avoided. 

Notes. 

The Zinc Sulphate Solution. — The object to be attained is the pre- 
paration of a neutral solution of pure zinc sulphate saturated with 
ZnS04,7H20. 

At temperatures above 30° C. the zinc sulphate may crystallise out in 
another form ; to avoid this 30° C. should be the upper limit of tempera- 
ture. At this temperature water will dissolve about 1-9 time its weight 
of the crystals. If any of the crystals put in remain undissolved they 
will be removed by the filtration. 

The amount of zinc oxide required depends on the acidity of the solu- 
tion, but 2 per cent, will, in all cases which will arise in practice with 
reasonably good zinc sulphate, be ample. Another rule would be to add 
the zinc oxide gradually until the solution became slightly milky. The 
solution when put into the cell should not contain any free zinc oxide ; if 
it does then, when mixed with the mercurous sulphate, zinc sulphate and 
mercurous oxide are formed ; the latter may be deposited on the zinc, and 
affect the electro-motive force of the cell. The difficulty is avoided by 
adding as described about 12 per cent, of mercurous sulphate before 
filtration : this is more than sufiBcient to combine with the whole of the 
zinc oxide originally put in, if it all remains free ; the mercurous oxide 
formed together with any undissolved mercurous sulphate is removed by 
the filtration. 

The Mercurous Sidphate. — The treatment of the mercurous sulphate 
has for its object the removal of any mercuric sulphate which is often 
present as an impurity. 

Mercuric sulphate decomposes in the presence of water into an acid 
and a basic sulphate. The latter is a yellow substance — turpeth mineral — 



ON STANDARDS FOR USE IN ELECTRICAL MEASUREMENTS. 135 

practically insoluble in water : its presence at any rate in moderate quan- 
tities has no effect on the cell. If, bow ever, it is formed the acid sulphate 
is formed also. This is soluble in water and the acid produced affects 
the electro-motive force. The object of the washings is to dissolve and 
remoVfe this acid sulphate, and for this purpose the three washings 
described in the specification will in nearly all cases suffice. If, however, 
a great deal of the turpeth mineral is formed it shows that there is a 
great deal of the acid sulphate present, and it will then be wiser to obtain 
a fresh sample of mercurous sulphate rather than to try by repeated 
washings to o'et rid of all the acid. 

The free mercury helps in the process of removing the acid, for the 
acid mercuric sulphate attacks it, forming mercurous sulphate and acid 
which is washed away. 

The cell may be sealed in a more permanent manner by coating the 
marine glue, when it is set, with a solution of sodium silicate and leaving 
it to harden. 

Appendix. 

Av!/vd 12, 1892. 

Dear Sir, — T am desired by the Electrical Standards Committee of 
the British Association to communicate to the Electrical Standards Com- 
mittee of the Board of Trade the enclosed extract from their report 
made to the Association on August 9, 1892. 

I remain, yours faithfully, 

(Signed) R. T. Glazebrook, 

Secretary, Electrical Standards Committee 

of the British Association. 

To Sir Thomas Blomefield, 

Secretary, Electrical Standards Committee 

of the Board of Trade. 

Extract from the Report of the Electrical Standards Committee of 
THE Association, August 9, 1892. 

The following resolutions were agreed to : — • 

1. That the resistance of a specified column of mercui'y be adopted as 
the practical unit of resistance. 

2. That 14"4521 grammes of mercury in the form of a column of 
uniform cross-section 106"3 centimetres in length at 0° C. be the specified 
column. 

3. That standards in mercury or solid metal having the same resist- 
ance as this column be made and deposited as standards of resistance for 
industrial purposes. 

4. That such standards be periodically compared with each other, 
and also that their values be redetermined at intervals in terms of a 
freshly set-up column of mercury. 

It was further agreed that these resolutions be communicated to the 
Electrical Standards Committee of the Board of Trade. 

With regard to the units of current and electro-motive force it was 
agreed that the number -001118 should be adopted as the number of 
grammes of silver deposited per second from a neutral solution of nitrate 
of silver by a current of 1 ampere, and the value 1'434 as the electro- 
motive force in volts of a Clark cell at 15° C. 



136 REPOET— 1893. 

Dr. von Helmholtz expressed his full concurrence in these decisions, 
which are, as he informed the Committee, in accord with the recommenda- 
tions which have already been laid by the Curatorium of the Reichs- 
anstalt, as well as by himself before the German Government. 



APPENDIX II. 

Experiments on tie Effects of the Heating produced in the Coils hy the 
Currents used in Testing. By R. T. Glazebeook. 

Various circumstances (notably the experiments of Mr. Griffiths ') 
had made it appear probable that the heating effect in the coils produced 
by the current used in making the resistance test might be sufficient to 
affect the results of the tests. Some experiments were made to examine 
the point directly. 

The resistance of a coil of 100 ohms (nominal value) was measured in 
the usual way, i.e. by making a Wheatstone's bridge of four coils whose 
nominal values were "l, 10, 10, and 100 ohms. If the coils had been 
accurate there would have been a balance ; as it was, one of the 10-ohm 
coils needed to be shunted, and the adjustment was made by determining 
the value of the shunt when no current passed through the galvanometer. 

As the current in the battery circuit was increased by varying the 
number of cells this shunt decreased in value, showing that the effect of 
the heating was to produce an apparent diminution of the resistance of 
the 1000-ohm coil. This, of course, is as would be anticipated ; for \S^ of 
the current goes through the 1-ohm and one of the 10-ohm coils ; the re- 
maining yV goes through the 10-ohm and the 100-ohm. The rise 
of temperature will clearly be greatest in the first 10-ohm coil, and to 
counterbalance the increase in resistance produced thereby it becomes 
necessary to reduce the shunt. 

The following readings were obtained : — 



Current in Amperes 


Shunt in 1000 Ohms 


Correcting Factor 


•05 
•09 
•12 
•14 
•15 


3.5^5 
32^5 
230 
30-5 
29^5 


1 - -00028 
•00031 
■00033 
■00033 
•00034 



The true value of the 100-ohm is given by taking the product of the 
values of the two 10-ohm coils at the temperature of the observations, 
dividing by the value of the 1-ohm and multiplying by a factor repre- 
senting the effect of the shunt. 

During the above observations the temperatures remained steady, 
the factor changed from 1 — ^00028 to 1 — -00034. Thus the resistance of 
the 100-ohm coil changed by -034 -•028, or -006 ohm. 

The ajiparatus was not sensitive with a smaller current ; the effect, 

' PMl. Trans., 1893. 

2 Only one observation at this current was made ; the others are the mean of 
several. 



ON STANDARDS FOR USE IN ELECTRICAL MEASUREMENTS. 137 

however, will vary as the square of the current ; and, since treblingr the 
current produces so small a change, we may infer that the total eflPect is 
itself small. 

Another coil gave the following results : — 



Current in Amperes 


Shunt in 1000 Ohms 


Correcting Factor 


•05 
•09 

•12 

•u 

•15 


48 
45 
43 
41 
40 


1 - ^000208 
•000222 
•000233 
•000244 
•000250 



indicating a change in the measured I'esistance of •0042 ohm on 100 
ohms. 

It is clear, thei'efore, that the effect of heating is small, though appre- 
ciable when currents approaching •IS ampere are used. 



APPENDIX III. 

On Standards of Loiv Electrical Resistance. By J. Viriamu Jones, 
Principal and Professor of Physics in the University College, Cardiff. 

The preparation of standards of low electrical resistance of from 
•001 to '0001 ohm seems to be a matter of some importance at the 
present time. These standards are already in request among engineers, 
and it becomes of interest to consider how they may best be measured to 
a percentage accui*acy comparable with that with which the standard ohm 
is known. 

Such standai'ds of low resistance may be derived by potentiometer 
methods from the standard ohm by a series of downward steps. But this 
is from one point of view roundabout. The method of measuring the 
ohm that seems in all its details most accurate is that of Lorenz. In 
this method the ohm itself is derived from the measurement of a small 
resistance. It is simply going up and down again to prepare from the 
ohm so derived the required small resistance standards, and it is more 
direct and more accurate to measure the latter directly in absolute 
measure. 

' In Lorenz's method a metallic disc is made to rotate in the mean 
plane of a coaxial standard coil. Wires touching the centre and circumfer- 
ence of the disc are led to the ends of the resistance to be measured, 
and the same current is passed through this resistance and the standard 
coil. The connections being rightly made, we may by varying either the 
rate of rotation of the disc or the resistance measured so arrange matters 
as to have no change of current in the circuit of the disc and wires joining 
it to the ends of the resistance, when the direction of the current through 
the resistance and the standard coil is changed. When this arrangement 
is effected there is a balance between the electromotive force, due to the 
motion of the disc in the magnetic field of the current in the standard 
coil, and the difference of potential at the ends of the resistance, due to 



138 EEPORT— 1893. 

the current traversing it. If this adjustment be made we will say that 
the apparatus is in an equilibrium position.' ' 

If M=coefEcient of mutual induction of standard coil and circum- 
ference of disc, 
w=rate of rotation of disc (number of revolutions per second), 
R=resistance, 
y=current through standard coil and resistance, 

then in an equilibrium position 

M??.7=Ry, 
or E=Mh. 

I do not think that electricians have as yet realised the accuracy and 
ease with which absolute measurements of resistance may be made by 
this method. The absolute measurement involves measuring first the 
coefficient of mutual induction of the standard coil and the circumference 
of the rotating disc, and secondly the rate of rotation of the disc. 

Now it lies well within the resources of modern mechanical engineer- 
ing to make a standard coil and disc of dimensions known to an accuracy 
considerably greater than 1 in 10,000, the coil being constructed of a 
single layer of wire wound in a screw thread cut on a cylinder of large 
diameter ; and the measurement of the rate of rotation to equal accuracy 
is a simple matter. There is difiiculty in maintaining a rate of rotation 
constant to this figure for four or five minutes, but with the closest 
attention to the lubrication of all the bearings this also might be accom- 
plished. Such constancy is well worth striving for, as the ease with 
which measurements of resistance can be made by the method largely 
dependu upon it. 

I do not propose on this occasion to enter into the details of the 
method I have adopted in making the measurements, the results of which 
I have now to bring before the Section. But it will perhaps be of 
interest if I say a few words about the time-measurement. 

In measuring a resistance we have to find the rate of rotation corre- 
sponding to an equilibrium position. It is easiest in practice to determine 
this by interpolation from two determined rates of rotation (near together, 
and respectively slower and faster than the required rate) and the 
galvanometer deflections corresponding to them, so that each determina- 
tion of resistance involves two determinations of galvanometer deflection 
and the rates of rotation corresponding to them. 

In order that the galvanometer deflection may be obtained with 
sufiicient accuracy from a limited number of reversals (in my observations 
the number has been almost uniformly thirty-three, taking about four 
minutes in each case) the brush at the circumference of the disc needs 
to be perforated and to be supplied with a constant stream of mercury. 
Such a brush in its best condition almost entirely eliminates the continual 
jerking of the galvanometer needle consequent on thermo-electric changes 
at the point of contact of brush and disc. A multiplication of such 
brushes at three or four points of the circumference would do this even 
more completely. 

During the four or five minutes' run the rate of rotation is referred by 

' Vide Phil. Trans., 1891, A, p. 2, ' On the Determmation of the Specific Eesistance 
of Mercury in Absolute Measure.' 



ON STANDAEDS FOR USE IN ELECTEICAL MEASUREMENTS. 139 

a stroboscopic method to a suitable tuning-fork provided with riders and 
maintained in vibration electrically. The observer at the fork can shunt 
more or less current through the electromotor driving the disc, and in 
this way maintains the rate of rotation as constant as he can. But 
though the electrically maintained fork is laseful for purposes of control 
it cannot be relied on to give us the rate of rotation. Its vibration period 
is not within my experience constant to the degi-ee of accuracy required. 
If stopped and set going again it may start with a period different 
by several parts in 10,000. No previous determination of the period 
of the fork can therefore be relied on to give us the rate of rotation, 
though once stai'ted the fork goes sufficiently uniformly to give us a 
means of control. 

Accordingly it is necessary to measure the rate of I'otation during 
each run while the galvanometer observations are being made. The 
rotating disc is, by means of an eccentric attached to its axle, made to 
record its revolutions on the tape of a Bain's electro-chemical telegraph 
instrument side by side with the record of the standard clock. We have, 
then, a time record exactly corresponding to the period of observation 
of the galvanometer deflections. During the run the observer at the 
galvanometer calls out the galvanometer readings, while the observer at 
the tuning-fork controls the speed, and the Bain's instrument records it. 

I have made in this way a number of measurements daring the 
months of July and August of a standard resistance of approximately 
■0005 ohm, prepared last year l)y my assistant, Mr. Harrison, and a 
student in my laboratory, Mr. Parker, with the following results : — 



July 17, morning- 
„ 17, afternoon 
,, 19, morning 

Aug. 2, afternoon 
„ 3, morning 
„ 4, „ 
„ 4, afternoon 
,, 5, morning 
q 

,, 9, afternoon 



Mean 



00050016 
00050016 
00050015 
00050020 
00050021 
00050016 
00050013 
00050019 
00050021 
00050018 

00050017 



The maximum divergence from the mean is -00000004, or about one 
part in 12,000. Mr. Crompton has recently been issuing standards of 
low resistance made of manganine sheets, and he was kind enough, at my 
suggestion, to send me one for measurement towards the end of July. 
It was prepared in his laboratory as a derivative from the Cambridge 
ohm by means of his potentiometer. Its value so given was -00050175 
at 23° C. Its temperature coefficient appears, from the measurements 
made in Mr. Crompton's laboratoi-y, to be so small that we need hardly 
consider it for our present purpose. My measurements of this standard 
were as follows : — 



July 29, 

Aug. 1, 

„ 1, 


morning 
afternoon 


»1 


ii, 


morning 



•00050219 
■00050225 
•00050219 
-00050226 



Mean . . -00050222 
■which differs from Mr. Crompton's value by something less than one part 



140 KEPOET— 1893. 

in 1000. Mr. Crompton's resistance is a rectangular sheet of manganine, 
and the potential terminals are two screws inserted at a suitable distance 
apart in the median line. The screws are not soldered. I thought it 
would be of interest to unscrew them, screw them up again, and re- 
measure the resistance. The results were — 

August 10, morning -00050328 

,, 10. afternoon -00050322 

„ 10, „ -00050327 



Mean . . -00050326 



indicating a variation of about one part in 500. I unscrewed them again, 
and after screwing them made a new measurement with the following 



results 



August 11, morning -00050398 

„ 12, „ -00050403 



Mean . -00050401 

which, compared with the first value "00050222, shows a variation of, 
approximately, one part in 280. 

We may therefore conclude that if an accuracy of yV^'^ P^^' cent, is 
required of a standard so constructed its potential terminals ought not 
to be meddled with after its resistance has been determined. 

In making these measurements my direct object has been to obtain an 
accurate and ready method of measuring standards of low resistance. 
But I think something more than this comes out of them. It would be 
possible in the light of our present experience to constract a Lorenz 
apparatus considerably more accurate and easier to use than that in my 
laboratory at Cardiff. Such an apparatus placed, let us snppose, in the 
National Laboratory, of which we have heard a good deal at recent 
meetings of the British Association, might with advantage be kept in 
constant use, not only for the calibration of low resistances, but also as 
embodying in concrete form a proper ultimate standard of electrical 
res-istance. We have not in our electrical standard legislation given full 
credit to the mechanical engineer for what he can do for us ; and I think 
that a coefficient of mutual induction arranged, as in the Lorenz method, 
80 as to be easily combined with a time would afford a more satisfiactory 
standard of resistance than any wire coil or coils, and one easier to use 
for purposes of ultimate reference than any mercury column. 



The Application of Photography to the Elucidation of Meteoro- 
logical Phenomena. — Third Report of the Committee, consist- 
ing of Mr. Gr. J. Symons {Chairman), Professor E. Meldola, 
Mr. J. HoPKiNSON, and Mr. A. W. Clatden {Secretary). [Drawn 
up by the Secretary.) 

Your Committee beg to report that their work has progressed slowly 
during the last year, though it has been greatly hindered by the appoint- 
ment of their secretary as principal of the new Technical and University 
Extension College at Exeter. The large amount of work involved in the 



ON PHOTOGRAPHS OF METEOEOLOGICAL PHENOMENA. 141 

organisation of so novel a type of institution has left little opportunity 
for carrying on the work of the Committee. 

Having been thus obliged to postpone much of the work they hoped 
to carry out, they have not drawn last year's grant. 

Nevertheless, considerable progress has been made. The number of 
persons who have sent in their names as willing to contribute has been 
added to, the photographs in your Committee's collection have in- 
creased from 861 to 467, and the objects of the Committee have again 
been brought before some of the most important photographic societies. 

The result is that the secretary is continually receiving letters asking 
for directions for the photography of clouds, for the loan of lantern slides, 
and general instruction, the furnishing of which your Committee consider 
by no means the least useful part of their functions. 

A fairly exhaustive trial has been made of the comparative merits of 
the Sandell plates, and slow plates of the photomechanical type ; from 
which it appears that the double film does not possess for cloud photo- 
graphy any advantage over the older type of plate. Since also the 
management of the latter after exposui-e is the easier, your Committee 
adhere to the decision given last year, that the black glass mirror and 
slow plate really provide the easiest means of securing good cloud 
pictures. 

Attention must be drawn to the excellent pictures of clouds on the 
High Alps which have been received from Mr. Greenwood Pim, who has 
expressed his willingness to turn his attention to the photography of 
high clouds. 

With regard to cload photographs generally, your Committee feel 
that their collection already includes suflBciently good examples of all 
the commoner varieties of cloud which are capable of being so repre- 
sented, and therefore think that there is no scientific object to be served 
in simply multiplying prints. Consequently, during the past year they 
have not sought such contributions, but in soliciting aid have invited 
observers to study especially the changes of high-level clouds. This is 
a work of considerable difficulty, and there are probably few persons who 
possess at once the requisite skill and sufficient leisure. 

The records of cloud forms may thus be said to have been secured, 
and the next question is, How may they be utilised ' for the elucidation 
of meteorological phenomena ' ? 

Upon what problems do they bear ? This is easily answered. They 
should give first the means of settling precisely what connection there 
is between particular cloud forms and other atmospheric conditions, 
and in the next place they should give a clue to the explanation of their 
own forms. 

In order to attack the first problem the great want is an efficient 
cloud atlas of the higher clouds, such as was undertaken some time ago by 
the International Committee. This atlas has not yet been published, and 
in it, moreover, it is proposed to arrange clouds under the names suggested 
by Messrs. Hildebrandsson and Abercromby, a system which English 
meteorologists have not yet adopted. Indeed, as your Committee have 
observed in a previous Report, the system of nomenclature should follow 
and not precede the study of the two problems stated. 

The varieties of the lower clouds are pretty well understood ; it is 
with the higher clouds that all difficulties arise. Your Committee there- 
fore suggest that they should be empowered to arrange for the publica- 



142 REPORT— 1893. 

tiou of a provisional cloud atlas, or one section of it, under the following 
conditions. Divide all clouds into the three great groups, Cumulus, 
Stratus, and Cirrus. Publish volumes dealing with each of these great 
groups, not naming the subordinate varieties, but assigning merely num- 
bers. Thus, supposing there are ten varieties of Cirrus — call them 
No. 1, No. 2, &c. ; then, if there are ten varieties of cirro-cumulus, let 
these be numbered from eleven upwards. 

It seems that if such an atlas were distributed to a number of ob- 
servers who are in the habit of making eye-estimations of the quantity 
of cloud, it would be quite easy for them to record also the numbers of 
the respective types of cloud visible. Since these observations would be 
made by meteorologists, and at the same time as records of temperature, 
pressure, &c., the results could not fail to be of real importance. 

Again, a meteorologist armed with such an atlas would be able to 
note changes of form from one type to another almost as well as the actual 
photographer. 

Lightning Photographs. 

Not many new photographs of lightning have been received, but 
they all agree with the others in the Committee's collection in showing 
what has been called the narrow ribbon structure. There has not yet 
been any opportunity of ascertaining whether this structure is shown in 
negatives on paper, but it is visible in negatives taken on thin films. 
This fact confirms the opinion already expressed by your Committee, 
that it represents the true form of a lightning flash. Moreover, it cannot 
be caused by reflection from the back of the plate, because if so it would 
be most evident in the brighter parts of the flash, whereas it is most 
evident in the fainter ; also, it would be more pronounced in the margins 
of the plate than in the centre, and the apparent orientation of the 
ribbon would vary according to the position on the plate. None of these 
things are noticeable. The major thickness of the ribbon seems to set 
itself in a particular direction, which is constant for all parts of a 
branched or other flash, whatever may be the position of the image on 
the plate. It is also not a whit more obvious in the margins of the 
plate than in the centre. Lastly, it is almost invariably shown more or 
less plainly ; why, then, should it be supposed to be due to some error of 
observation ? 

It has lately been suggested that it is produced by marginal deforma- 
tion of the image. Let us put aside for a moment the fact that the 
phenomenon is not marginal at all. Now, if a lens be used which will 
not cover the plate properly, so that the margins are out of focus, or if 
the camera be purposely put out of focus, it is quite true that the 
image of an electric spark may be expanded into a broad ribbon. But 
this is characterised by both the margins of the ribbon being brighter than 
the centre, while in the true narrow ribbon structure, as shown by light- 
ning, the whole is equally bright, or one margin is bright and the other 
the faintest part of the image. The explanation is clearly incorrect. 

It may be useful here to draw a definite distinction between a light- 
ning ' flash ' and a lightning ' discharge.' Flashes last only a short time, 
a mere fraction of a second, though probably a considerably larger frac- 
tion than was at one time supposed. The eye is not conscious of any 
variations of brilliancy during the flash, and a camera moving with con- 
siderable velocity does not resolve it into a number of components. 



ON PHOTOGRAPHS OF METEOROLOGICAL PHENOMENA. 143 

Discharges may consist of a single f3ash, but they frequently consist 
of a series of flashes following one another with considerable rapidity 
along the same or related paths. The eye is often able to detect alterna- 
tions of brilliancy during a discharge, and may resolve it, as a moving 
camera will, into a series of flashes accompanied by a persistent luminosity, 
which it has already been suggested is probably the flame of burnin» 
nitrogen. 

Last year your Committee referred to a photograph taken by Mr. Glew 
at Brixton. This was taken in a camera the lens of which was attached 
to the hammer of an electinc bell and kept in oscillation during exposure. 
The object was to deduce from the known rate of movement of the lens 
the duration of the discharge. Unfortunately, however, there is nothino- 
to show in which direction the lens was travelling at the moment of each 
component flash. 

There is one very simple method by which it is quite possible to make 
a rough measurement of the duration of a discharge. Let two observers 
A and B, agree that A shall carefully notice the seconds hand of his watch 
while B looks at the sky to be sure that A does not confuse two separate 
discharges. If the night is otherwise dark, A will see the hand only when 
the face is illuminated by the lightning. The secretary to your Com- 
mittee has, with the aid of Mrs. Clayden, made many such observations, 
and has found that a lightning discharge often lasts as much as two or 
thi-ee seconds, and may extend further, the longest time hitherto observed 
being no less than seven seconds. During these times, though the 
brightness of the light varied considerably, it was quite possible to watch 
the hand moving steadily, and not in a series of jerks, as must have been 
the case if the continuity of illumination had been an illusion due to per- 
sistence of vision. In a similar way it is quite possible to follow the 
movements of swaying tree-tops and other objects. It was noted with 
some surprise that the light, as far as the eye can see, is often perfectly 
steady for as much as a couple of seconds. Since beginning these observa- 
tions not a single discharge has been noted of suSicient brevity to prevent 
any movement of the watch hand from being seen. 

Now, although such observations are rough, their bearing upon light- 
ning photography is important. 

An argument commonly advanced to prove that all photographs of 
reduplicated flashes are due to movement of the camera is that the track 
to be followed by successive flashes in a given discharge is marked out 
by the first, which creates a path of minimum resistance in the form of a 
partial vacuum. 

But it seems to be forgotten how far this tube of rarefied air must 
be moved, and how far the discharging point of the cloud (so to say) 
may be displaced by the movement of the air. We know that the wind 
is often quite strong during a thunderstorm. 

Now, a movement of one mile an hour corresponds to 176 inches a 
second. 

Suppose, therefore, we take the first seven values of the Beaufort 
scale and see how far such a tube of minimum resistance would be dis- 
placed during the existence of a discharge. 

Hence it appears that if a dischai-ge lasts as long as three seconds, the 
path of minimum resistance marked out by the first flash might be dis- 
placed as much as fifty yards by a strong breeze. Moreover, since the 
clouds would be moving at the same rate as the upper part of the vacuous 



144 



KEPOKT 1893. 



Force 
Beaufort 

scale 


Miles per 
hour 


Inches 

per 
second 


Displacement in feet (discarding 
fractions) 


Displacement 
in metres 


1 sec. 


2 sees. 


3 sees. 


1 sec. 



1 
2 
3 
4 
5 
6 


3 or less 

8 
13 
18 
23 
28 
34 


53 
141 
229 
317 
405 
493 
598 


4 
12 
19 
26 
34 
41 
50 


9 
23 
38 
53 
67 
82 
100 


13 
35 

57 

79 

101 

123 

150 


1-3 

3-6 

5-8 

81 

10-3 

12-5 

15-2 



track, there would be no disturbance of its relation to the discharging 
point. 

It is frequently observed in photographs of reduplicated flashes that 
the various components do not follow absolutely similar paths, and it is 
often seen that the departure from similarity is near the ground. 

Surely this is exactly what would be expected if the path of least 
resistance were swept along as suggested. The movements of the wind 
are not uniform, and the tube would frequently get bent or broken, such 
an event being most probable to occur within reach of eddies from the 
ground. It may be pointed out that the reduplicated flash photographed 
by the secretary to your Committee in a stationary camera was taken at 
right angles to that in which the storm and wind were travelling. 

Movement of the camera or lens or plate would necessarily exaggerate 
the reduplication where it might not otherwise have been detected, but 
there can be no doubt that a single discharge often lasts for several 
seconds, and therefore that any path of minimum resistance created by 
the first component flash must be moved to an extent quite sufficient to 
reveal the multiple structure to the eye and to the camera. 

It seems, moreover, that the narrow ribbon structure may be attri- 
buted to much the same cause. 

In conclusion, your Committee have to state that their scheme of an 
atlas of typical clouds cannot be carried out without considerable expen- 
diture, and they suggest that they be reappointed with a grant of 501. 
As they did not draw the 161. voted last year, this is really an application 
for only 35Z. for that which they believe would be a valuable piece of 
work. 



The Best Methods of Recording the Direct Intensity of Solar 
Radiation. — Ninth Report of the Committee, consisting of 
Sir Gr. Gr. Stokes (Chairman), Professor A. Schustee, Mr. G-. 
Johnstone Stonet, Sir H. E. Koscoe, Captain W. de W. Abney, 
Professor H. McLeod, and Mr. Gr. J. Stmons. {Draivn up by 
Professor McLeod.) 

During the last year Mr. Casella has constructed for the Committee a 
thermometer with a lenticular bulb similar to that described in previous 
Reports, but consisting of colourless instead of green glass. As stated in 
the last Report, there are great difliculties in constructing an instrument 
with a green-glass bulb, and it was believed that there would be little 



ON THE INTENSITY OF SOLAR RADIATION. 145 

difference in the readings obtained with a thermometer of ordinary white 
glass. 

On May 22 three sets of observations were made, two with the green, 
glass and one with the white-glass thermometer : those with the green 
were made between X.17 and X.50 and between XI.35 and XI.53, 
that with the white-glass instrument between XI. and XI.25. 

The observed excesses of temperature of the green-glass thermometer 
above the temperature of the case were 48°'3 F. and 49°"3. The observed 
excess of the white glass was only 32°'8. The corresponding calculated 
excesses obtained by the method described in the last Report were 
respectively 50°-29, 49°-24, and 33°-30. 

It is thus seen that the white- glass bulb rises to about two-thirds .of 
the excess indicated by the green-glass bulb. This, however, is no dis- 
advantage, for when the temperature of the insolation thermometer is 
much above that of the case the simple law which for smaller excesses 
connects the rate of cooling with the difference of temperatures is no 
longer a sufiBciently near approximation, and the reduction of the observed 
results becomes more difl&cult. 

As the simultaneous reading of the three thermometers is not an easy 
operation, an attempt has been made to replace them by two thermo- 
electric junctions. A copper disc, 20 mm. in diameter and about "75 mm. 
thick, was soldered at its centre to a piece of iron wire. The wire was so 
bent that when the centre of the disc opposite to the soldered joint is 
exactly behind the hole in the copper cube, the other end of the wire 
makes contact with the copper cube midway between the front and back. 
To the edge of the disc a thin copper wire is soldered, which passes 
through a glass tube in the central opening of the cube, and is thus insu- 
lated from it. The experiment being only preliminary, the iron wire has 
been fixed in a hole drilled in the copper plug which usually holds the 
insolation thermometer, the glass tube carrying the insulated wire being 
passed through the hole in the same plug. The other terminal from the 
copper cube is made by fixing a piece of copper wire in the plug which 
closes the hole of the case thermometer B in front of the cube. In a per- 
manent instrument a binding screw should be attached to the cube in the 
plane of the disc. To increase the absorption of heat by the copper disc, 
it was blackened by being placed for a short time in sulphuretted 
hydrogen. The black surface thus obtained does not, however, com- 
pletely absorb the radiation, for, on throwing a beam of sunlight on it, it 
is observed that some of the light is scattered. The surface thus obtained 
may, in addition, be not permanent. 

The terminals of the thermo-couples were connected to a reflecting 
galvanometer of "97 ohm resistance, and the disc exposed to the raj's of 
the sun, the lens of the instrument being used. The deflection of the 
galvanometer became steady after an exposure of from five to eight 
minutes, whereas twenty minutes were required when the green-glass- 
bulb thermometer was used. 

In order to determine the value of the deflections a double thermo- 
couple was made by soldering to two stout copper wires a bent piece of 
thick iron wire. Close to the junctions delicate thermometers were tied, 
and the apparatus was so arranged that the thermo- junctions and thermo- 
meter bulbs could be plunged in test tubes containing paraffin oil : one 
of these test tubes could be heated, and the connections were so made 
that the current produced by the heated junction opposed that from the 



146 REPORT — 1893. 

actinometer. "Whilst the disc in the actinometer was exposed to the solar 
radiations, one of the thermo-junctions was heated, and when the galvano- 
meter indicated that no current was flowing the thermometers were read. 
In one case, in which a deflection of 172 divisions was obtained, the 
current was balanced by a difference of temperature of the two junctions 
of 8°-27 C. 

If an instrument of this kind could be made photographically self- 
recording it would constitute an excellent sunshine-recorder, giving not. 
only the time of the shining of the sun, but also a measure of its intensity. 
An ordinary reflecting galvanometer would not be very suitable for this 
purpose, for variations of the earth's magnetism and the possible movement 
of magnetic bodies in its neighbourhood would vitiate the results. An 
instrument on the principle of the D'Arsonval galvanometer would be 
more appropriate, but a few experiments made with such an instrument 
have not given satisfactory results. Another source of error must be 
mentioned, namely, the variation of the resistance of the long conducting 
wires by changes of temperature. 'No doubt all these difficulties might 
be overcome in. a properly appointed observatory. 



On the Present State of our Knowledge of Electrolysis and Electro- 
chemistry. Report by W. N. Shaw and T. C. Fitzpatrick. 

Table of Electro-chemical Properties of Aqueous Solutions, compiled bij 

T. C. Fitzpatrick. 

The comparison of the numerical results of electrolytic observations 
is rendered difficult from the fact that the data are scattered in various 
periodicals and expressed by different observers in units that are not com- 
parable without considerable labour. The following table has been 
compiled with the object of facilitating the comparison. 

In the table are included all the observations, as far as they are known 
to the compiler, for the metallic salts and mineral acids ; but amongst the 
solutions of organic substances ai'e not given all those for which Ostwald 
has made observations, as it was thought that they would add unneces- 
sarily to the size of the table. Observations for a number of additional 
substances will be found in Ostwald's papers in ' Journal fiir Chemie,' 
vols, xxxi., xxxii., and xxxiii., and in the ' Zeitschrift fiir physikalische 
Chemie,' vol. i. With this restriction it is hoped that no important 
observations have been omitted, and that in the reduction of results, 
expressed in such varied units, the table is sufficiently free from mistakes 
for it to be of service. The data included refer to the strength and 
specific gravity of solutions, with the corresponding conductivities, 
migration constants, and fluidities. The several columns are as follows : — 

I. Percentage composition, i.e. the number of parts by weight of the 
salt (as represented by the chemical formula) in 100 parts of the solution. 

II. The number of gramme molecules per litre, i.e. the number of 
grammes of the salt per litre divided by the chemical equivalent in 
grammes, as given for each salt. 

III. The specific gravities of the solutions : in most cases the specific 
gravities of the solutions are not given by the observers, and the numbers 



ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 147 

given have been deduced from Gerlach's tables in the ' Zeifcschrift fiir 
analytische Chemie,* vol. viii. p. 243, &c. 

IV. The temperatures at which the solutions have the specific 
gravities given in the previous column for the given strength of solution. 

V. The conductivity, as expressed by the observer. In the cases iu 
which the observer has expressed his results for specific molecular con- 
ductivity no numbers are given in this column. 

VI. The temperature at which the conductivities of the solutions have 
been determined. 

VII. The temperature coefficient referred to the conductivity at 18° 

i.e. 1 f^iO- 
k^^\ ct J 

VIII. The specific molecular conductivity of the solutions at 18° in 
terms of the conductivity of mercury at 0° ; specific molecular conduc- 
tivity is the ratio of the conductivity of a column of the liqaid 1 centimetre 
long and 1 square centimetre in section to the number of gramme 
equivalents per litre. 

In some few cases in which no temperature coefficients have been 
determined the results have been given for the temperature at which 
the observations were made. 

The numbers given in the column are the values for the specific 
molecular conductivity x 10^. 

IX. This column contains the values for specific molecular conduc- 
tivity at 18° in C.G.S. units : they are obtained from those in the previous 
column by being multiplied by the value of the conductivity of mercury 
at 0° in C.G.S. units. This factor is 1-063 X IQ-^. 

X. The migration constant for the anion ; for instance, in the case of 
copper sulphate (CUSO4) for (SO4). 

XI. The temperatures at which the migration constants have been 
determined. 

XII. The number of gramme molecules per litre, as defined for 
column II., for which the fluidity data are given in the following columns. 

XIII. The fluidity of the solutions of the strength given in the 
previous column. 

Most of the results given for the fluidity of solutions are expressed in 
terms of the fluidity of water at the same temperature : to obtain the 
absolute values for the solutions they have been multiplied by the 
value for the fluidity of water at the given temperature. The values used 
for this purpose have been taken from Sprnng's observations for the 
viscosity of water given in ' Poggendorfi^s Annalen,' vol. clix. p. I. 

To obtain the values for fluidity in C.G.S. units the numbers in this 
column must be multiplied by the factor '1019. 

XIV. The temperature at vrhich the solutions have the fluidity 
given in the previous column. 

XV. The temperature coefficient of fluidity at 18°, that is, - ( s *)• 

XVI. In the last column are given the references to the various papers 
from which the data are taken : against each reference will be found a 
number, which appears also against the first of the data which have been 
taken from the paper in question. 



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ON ELECTROLYSIS AND ELECTEO-CHEMISTBT. 



153 



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154 



REPORT 1893. 







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vol. 






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1 (M lO 1 CO (M "O 
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1 . . 1 . 1 . «> \ ^ \ 1 W CO ^ 1 



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rt^rtcqcqiMiM^cococococo 



ON ELECTBOLTSIS AND ELECTEO-CHEMISTKT 



155 











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156 



REPORT — 1893. 



-«• 









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°l 1 1 1 M 1 1 1 1 1 1 1 1 1 M 1 1 1 M 1 1 M 1 M 1 


1 1 1 1 1 1 1 1 1 1 r- 1 1 1 1 1 9 M 11 llilllli 



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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



157 



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OSt-O It— OC^>Ot-0>OOtOCD 

pioeM oopi^t- coi^ioioioo 

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h-. (M ^H I-H 
O -H (M lO 

oooo 

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OOOOt— O3O0O3COC31O^Ht— OlO 

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158 



REPOET — 1893. 



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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



159 



el 

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rt <M M CO U3 to 

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cococococococococococoeo 



CO 



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a)c;t--coco-*0505:o^^-t< 

t^codjoosoidob-tbiocbo 
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■tH 00 CO 

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160 



KEPORT 1893. 



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oocsoiOiCs Iosco 



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ON ELECTEOLYSIS AND ELECTRO-CHEMISTRY. 



161 



■^5 

t*S o 



as . 



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Kohlrau 
Annal. 
195. 


torf, 
I. vo 


3 -^i 


ieni 

emie 
5. 


8^ 




^§^S 













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to 



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fa 

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o o p p p 


llllll II1II<mc^im(M(mII(mIIIIII 


05 t- C-1 to «D «0 

lOiOOOTHoOlltollllll 

llllll lllllooooosllollllli 

1— 1 rH »— ( r-t T-H 


1— ( f— 1 O Cs b- 

'lllll IlllllOrtCpr-lClllollllll 

' .^ N tH 1J3 ^ 


MINI 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 


1 ! M M 1 1 1 1 1 1 1 1 1 1 1 i MS Is 1 1 



O O 0><M'i<lOiN«0 
o aj 1— looiosQOiio 
M "o CO<MC^(M^i-l 



COCOCOCOi— (lOCiCOO-*"^C<I^O 
C005CT50^CiGOt— t— lOCOG^t^COO 
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inininoioom»(3 

dsos6scios?-HOsoa 



1-0058 


1-0117 
1-02.30 
1-0453 


1 


M M M 


00dC0^OTt<OO 

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1 1 1 1 1 1 1 1 1 1 Ippp'Ti'Tidcpip 


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p p p p 


in 

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t- in 

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1893. 










M 



162 



REPORT 1893. 



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in o in o in 

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Cl -+I OS 

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ON ELECTEOLTSIS AND ELECTRO-CHEMISTRY. 



163 



.-to:* d( 

t^3 >1> 



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•931 

114 

1192 
1'258 


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CO lO C5 — < lO CO t- 

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164 



KEPOET — 1893. 



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ON ELECTROLYSIS AND ELECTRO- CHEMISTEY. 



165 



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166 



REPORT — 1893. 



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167 



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168 



REPORT — 1893. 



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r IM C5 CO CD -M O 
IM O <M m cn Oi 

CO lO -* CO <M rH 



N (M O 00 

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O O O OJ 



00 10 

IM I CO 
t- I CO 



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o 



t^ CO 

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CM 
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oo 05 1^ 
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aio "O r^ 00 CO rt 
CM OJ CM CM CM -H 
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CO 00 00 00 



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CM 1—1 CO 00 CO CO CO 
CO CM O 00 I lO CM oo 
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30 -t< IQ 

35 t- C35 

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oo -H 
^ I— 1 1— 1 


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CO 00 t^ CM -rtl 

»0 t^ O ^H GO 
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o 



CO 

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f— ( lO ^H 1— t CD ^ 
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O O t-< —I CM CO 



oo m in 

O^HCOt^Oiriin CM ''i^ 

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oo OOOOOO O O O rH rt 
CO no 



in >*< t- N 

^ in 05 ■* 

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o o o o 



1^ 05 00 O 05 O 
05 CM O -* CM C2 
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fl< .^ CM <M -^ 



t- CM « in 

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1-1 CM in 1—1 t- in 
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CO 



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lb cz> in o ih in 

1-1 ^ (M N CO 



00 CO 1*1 t~ 

1-1 b- O -*< 
03 O CO t— 
O 1— I -H CO 

O o o o 



170 



REPORT 1893. 



O > 



t-o '^ XI 

O N O 



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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 III 


°l 1 I^SS 1 ISS 1 1 II 1 1 1 III 


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|||QOI:~-l<l|coco|l||||| III 
lllooollososlilllll II 

i-H I— ( t— t 


|||iM>a ||94ta|ii||i| III 

IJlTHtNOJI-^lMlllllll III 


°l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 III 


1 1 1 1 1 1 1 1 1 1 1 il lii 1 III 



l|CT 



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00 



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t— icMt^cotooo f— (com tot^Oi 

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ppppppoppi— lcOtrit-<M(--00IM OpO 

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oo CO ■* t^ 

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CO b- •* O to 

.-H in (M 



ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



171 












Zi SS 



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fics. 






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sc s- -; i5 -g 

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K 



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Grotian, Wied. 
nal. vol. xvii 
194. 


N Z ■ 


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a 

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o o o o 



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a> la r-i ip t>- 
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CO OO 00 00 00 

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00 

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I-H f-H 




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OS OS O IM CO 

OS en o O O 
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1-0070 
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CO N in 

lO I-H C-l lO 
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OOOOOOi-H(M 



00 OS CO ^ CO 

i-i •*! c-l lO -* CO 

•^XCOi-HOSrH CD-^O 

OOC-ICOOO OOtJHCO 

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lO I-H (N CO t- ■* 

(Muoooo^ c-icce-i 

pp-TlC-l-^CppprHCO 

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CD e-1 o 

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05 OS •* C-l 

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-H d Ir- 

O O O 



172 



KEPORT 1893. 



■^1 






o 



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8 

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bo. 



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b- CO 05 CO 
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CO N l-H rt 



(M ■* 00 00 
^H »-H C<1 lO 

C-l IM IM (M 

o o o o 



rSO 00 00 00 



poop 

o^ »^ 1^ b» 

t- 05 Tj< CT> 

t- 00 00 CO 



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CO ■* 05 ■* 

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b- U5 t- O 

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Q 







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o o o -H eq 
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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



173 



S.-S 



i&.: 



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M 1 1 1 1 1 1 1 1 1 1 1 M 1 1 


1 1 1 1 1 M 1 1 1 1 MINI 


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 


1 1 1 1 1 1 1 1 1 1 1 MINI 


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 


64 

1 1 1 1 1 1 li 1^ 1 1 1 1 1 1 1 



05 ■— ( O 'O O 05 t- 
t- W CO CO (M CO CO 

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in 

CO 



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IS 



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O CO CO O >— CO 
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00 00 30 00 00 00 00 



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■—I I.-1 (M(M<M(M(M<N 





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uo 

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CO CO 

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o I o 



CO 

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o o o o o o o 



CD 

C5 as 05 00 CO o^ 
o — J CO t~ »o .— I 

O O O O -H CO 

oo o o o o 



CO 

Oi OS OS 00 CO d 
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o o o o o o 



CO 

C5 OS 05 00 CO Oq 

o ^ CO t- >o ■-( 

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o o o o o o 



«5 CD 

.-O C-1 LO O CD 

>-lM-*CO(Nt-.05 lO CO <M-H00COr-l(M 

Orl^Jt-CqCOOCD-ie^O rt(M-*SSS 

=> OOrtC0cO00l>qcoa> OOOOrHCO 

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t* »0 1— 4 (M in 
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O O O O >-< (N 



174 



BEPOET — 1893. 







»!i » e CO 

•■g ^ «5 |^..H- 
t| :S =° ftn S 






itsohrift 
.Chemie, 
5. 
















gf^'". 


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ON ELECTEOLTSIS AND ELECTRO-CHEMISTRY. 



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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



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ON ELECTROLTSIS AND ELECTRO-CHEMISTRY. 



181 



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ON ELECTKOLTSIS AND ELECTEO-CHEMISTET. 



183 



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184 



KEPORT 1893. 



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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 185 



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186 



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ON ELECTEOLTSIS AND ELECTRO-CHEMISTRY. 



187 



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CO CD 00 

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(M 00 

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05 (>. ei oo 

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188 



REPORT — 1893. 



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MM 



ON ELECTROLYSIS AND ELECTRO-CHEMISTET. 



189 



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190 



KEPOKT — 1893. 



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d >o o O o> 00 >o 

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ON ELECTKOLYSIS AND ELECTRO-CHEMISTRY. 



191 



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pop 
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192 



BEPORT 1893. 



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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



193 





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194 



REPORT — 1893. 






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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



195 




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196 



REPORT — 1893. 



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ON ELECTEOLYSIS AND ELECTBO-CHEMISTBT. 



197 






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198 EEPOET— 1893. 



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t^ lO 

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o o o o o o 



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in 

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M'«»(00t~->XC500100000C<« 

oooi— leococot^ioooicn 
pppoppf-Hc^in-Hi-ico 



200 



REPORT 1893. 



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to to to to in ifl 



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(M ■* 00 in 

CI ■* 00 b- lO O 
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o o o o o o 



ON ELECTROLYSIS AND ELECTEO-CHEMISTEY. 



201 




i I I 



1 1 «n «s >o ic. 
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t^ to 

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0000000.-1 



202 



EEPORT — 1893. 



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CD OO O CO t~ 

(M O c; t- lO 



COOOOOO rHT*l<35CO.— I 

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iMi— la; t- oooocDinco 

r-l r-t (M i-H I— ( f-H I— t 



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lO lO >0 lO lO 
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o o o o 

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t-C0.-l«O OOTtH(Mi-l-H 

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ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



203 



5: « 




« > 

8 


^1 




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- s 00 


wald, 

emie, 
340. 


thelot 
iii. p. 





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'73 ■^'^ 
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t- t~ t~ t~ t- t~ 



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0100C010->S<CO<Ni— I'— 1 



in 10 00 05 05 t- 

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in 10 lO 1(5 10 



I I I I 



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in 10 »c in in 10 in 

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204 



REPORT — 1893. 



'JE 




11 






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to «n 10 -ifi CO IM rt 


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ON ELECTROLYSIS AND ELECTEO-CHEMISTKT. 



205 



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-* 00 t- lO 
(M ■^ OS OS OS 00 to 
O O O -H CO t~ >o 
O O O O O O -H 

o o o o o o o 



rf( 00 to 
■* 00 b- u-5 
(M -* OS OS 
O O O — I 

o o o o 
o o o o 



00 eo (N 

O -H CO 
■-H N ■* 



00 lO 

CO ■* OS 00 
.-H CO «D CO 
O O O r-l 



o -H ^1 in 

-*00«OC<l»OOO^H 
00-HC050COCO<M 
O0000.-H(M10 



o -H cq in 

-f 00 CO c) in o o 

O O i-H CO CO CO «> 

o o o o o rH eq 



in 

o -H N in 

^ 00 CO N 
O O •— ' CO 

o o o o 



206 



REPORT — 1893. 



^ 


■a 




K 


kl 




S 


• 




»^ 


? 




Ti 


•^ 


, 




Si 


P 


S; tm 


is 

CO 


S 




o 










.fe>« 












K M 




§ _J 




= 1> 










, 






03 to a, 


■p 


O 


<1 


- 


W 






•§^ 



I' 



S 03 



J 8 







CM 



0) o 

^ > 



3 



I I I I 



I I I I 



I I I I I 





to 














to 


















■* 


1 


1 


1 


1 1 


1 




^ 


1 


1 


1 


1 


1 








«o 


1 


1 


1 


1 1 


1 




CO 


1 


1 


1 


1 


1 






















f— t 














CO 




td 


°l 


1 


1 


1 1 


1 




a 


1 


1 


1 


1 


1 




CO 

in 




o 














o 
















n 


o 












Q 
5 
< 


o 














O 


< 


6 


1 


1 


1 


1 1 


1 


u 
5 


1 


i 


1 


1 


1 


w 








N 


— 







— 




W 


c5~ 


— 


— 








i 


qT 


o 


o 


to -^ 


.— t 


CO "f5 


CO 


c; 


I— 1 


t- 


CO 


^H 


CO 


P5 


s 






-* 


05 


Cf5 


-H O -*l 






h^ 


t- ■* 


C-) 


on 


U 




^s 


o 


o 


t — f 


O O IM 


n 


(1) 


a 


in 


35 


05 CO 


>* 




s 





CO 


M 


I^ 


(M rt 


1— 1 


"3 

o 


f-H 


r- 1 








a 


o 


o 

•w 

o 
o 

a 






















1 


1 


1 


1 


1 1 


1 


P3 
O 

K 




1 


1 


1 


1 


1 


o 


lU 

a 


1^ 












y 


Oi 












H 


it; 


;5 


1 


1 


1 


1 1 


1 


-■1 


8 

1 

C5 


1 










O 


C! 


o 


1 


1 


1 


1 




a 














Id 














Si 






























°s 


in lo in in 


in 




O 


in in 


IC 


in 


lO 




s 




a 


« IM S<1 N N 




rrl 


oq 


0) <M 


IM IM 








> 
•3 














> 














w 
















S 


















a" 














n< 


















,W 


^ 












w 


- 


















•* 05 00 


t- in 


to 






•^ 05 05 •* 


*— ( 










t- 


f-H 


CO 'J* in t- 






CO -* o o in 










«> 


!D 


in 'ti CO (M 






Ttl 


CO 


(N 


IM 


rH 










°l 


1 


1 


i 1 


1 






1 


1 


1 


1 


1 







I I 



IM O 

■* CO 



05 
CO 



'tlOOt^iO— •"OCOlOCOa035-*lr^ t- CO 

05a5CDC5f— <0-+t^b-iCOt^'— I I [in I'M 

t^ooiot-OC-ieawciiMoq.— I— I 1^^ loo 

•— —IC^JOC^CMIMIM^MIMIM ■-< ^ 



t-in-^oiM'^OO'— i-*comco 

■*-t<t~30C5r^^-*-^lMt^-*IOO 

t-00'*'"O00O"-lf-l'— li— lO'~>CJ3 

i-ii-(.--lMIMNIM(MlMOJrt 



C5 



t— I oo 

■<J> I -H 

CO I t- 



00 I oo 



^ OOODOOODOOOOOOOOOOOOOOOOCO 
.^ t— tt— It— I^^T-Hr-(^H^Hl— (rHi—t— «l— I 



MINI 



03 t- 

o o 
o o 



o 

CO 

-M 

o 



•* 00 CO 

-»< 00 t- in 

(M -* C5 C5 05 00 

O O O ^ CO t- 

o o o o o o 
o o o o o o 



Tj( 00 CO 
•* 00 t— in 

N '^ CJ5 05 05 
O O O — I 00 

o o o o o 
o o o o o 



-H iM CO 

O O O .^ « CO 

OOOOOOrttMCO coo -H 

ooooooosoi-Hcoin oc5 o 
ocooocoooooooTHrHi-Hinoo 



00 cc N in 

CO t- in O r-l IM 
O O ^ CO CO IM 
O O O O O --I 



00 CO M in 
CO t^ in o ^^ 

O O -H CO CD 

o o o o o 



«0 IM CO t-l 

m r-H CO CO n CO -H 

O-— iCOtOr-^COCOC-lCO^-l 

oooo^-^coin^Hcocoooooo 
ooooooo— icoincooom 
ocooooosoo-^s^iin 



CO I CO 
-f I t- 
r~ CO 



ON ELECTROLYSIS AND ELECTRO-CHEMISTKT. 



207 



*« ft 












K 


o 




' 


> 




S 


•S 


>rs 


ca 


-51 


U5 


& 


9J 


CO 



'■« Ci ft 



! I 



i~ e^ o 

O". 'o la 

n '-Z: ^ 



I— I^H^H^H — ^H^^OOO 

(M C^ (M <M N <M IM (M <M .-H 



C5 O (M O lO 00 -^ 
CD ;0 «5 <M O !M 05 
O O 1-1 O — ( O QO 
C<J M N !M (M IM rH 



•* O « 

— C5 M 

ec 33 i<n 



«S 00 05 O O 00 IM 

-f en CO o 00 o CO 

C3 Oi O OS O^ OS t— 
f-H *-< C<l r-H 1-H f-H T-H 



i-H •* CO 

o; o b- 

-- ?M ^ 

oo o 



I I 



lO lO lO lO IC lO o lO «) 1/5 



00 00 00 00 00 00 00 





-* 




o 




o 




-* 








W 




o 




m 




^ 


P3 


A 


5 


-3 


M 


o 


Q 




t« 


o 


w 


g 


n 


m 


1— ( 

o 


a 


CO 


a 




cb 




-tJ 




fl 




o 








a 




> 








^ 




rr 




W 






t^ 1-1 O O t- CO (M 

CO 00 o «:- ^ o; o 
t^ lO CO o 00 to (>1 



O CO 00 rt 00 eg 00 

CC 1— ( (M ^H 00 t^ f— I 
0^0000050 
f-l IM (M <M i-l .-I i-l 



-* 00 CC t^ to (N O 
CO 00 CT O -H lO C5 
to -*< IM O OO 50 rt 



1^ OS O ^H ^H to Cq 

03 crj o iM -* to lo 

^H 1— ( <M (N (M .?:» T)< 

o o o o o o o 



GO GO CO 00 00 CC 00 
1— ( i-H r— .— ( ,W ,— ( rH 


»0 lO lO »0 IC lO ITS 
(M W C'l (>» G-1 C^ -M 



oceqrHtot-oicoeitO'rtt 
oOi^coiNOooibo-iftb 

<MCOOOCO?0(M(»c-).-lO 
<N(Mcq0^iMC<l(MIMCg(M 



IM 00 O N 00 to o 
00 o »-H o^ O 00 (>- 

■-( (M IM -* t- T*< 



t^ CO t^ o -^ * to 

1— I 00 -*< N to lO 05 

00 -* •* o eg (M 00 

rt Ol M CO CO -H 



«0 O lO 



to lO lO o 



lO lO O LO >o 



to rH t-- N -* 1-- O 

A( lis to lb <N o lb 

»— I f-H ^H ^^ r-^ ^^ O 

!M I?) !M (N (M iM iM 



lo lo in lo lo lo lo 



-* m -H 

:t~ O OS 

<N — 1 O 

^H C-1 '«!t4 



to 1-1 1-1 o 
<M to 5^ CO 
O O 1-1 (M 
O O O O 



OS t* ^H ^H b» 
•^ t^ O OS to 

O O 1— I rH CO 

O O O O O 



lO >-l O ■^ OS to o 
M ■* m ei to OS Ki 

CM •ti 00 C-) lO 00 CO 
O O C " -H 1— I CO 



CO 

o 

© 



lO 

t- lO o 

OS OS Oi 00 to CvJ lO 

o-<cot-iCrt(Mm 

OOOOi-HCOtO(MlO 
OOOOOOOrHNlO 



■* to b- 

IM 1-1 CO CO to N O 
-* 00 O lO O 1-1 (M 
O O i-l 1-1 <M •* 00 



lO 

OS cs c. oo to eg lO 
O 1-1 CO t~ lO ^ M 
O O C O — 1 CO to 

o o o o o o o 



rH ei CO 1* o o 



ro b- CO 

3S 1— 1 00 
Vf* CO OS 

ei CO 



lo OS OS 00 lo 

loo—icor^uoof-toco 

o^-iei^oot-usosoo^ 

oopooi^cotocot- 

fH eg 



00 t- in t- to ei (— 

CO lo t~ in -^ t^ to 

e<i -*< m 00 1— c eg ■>!< 



-i* 00 to 

lo el to oo -^ OS 

OS 00 CO CO CO t;- 

1^ M t- O « to O 

I— I F-4 rH CO 



00 t- lo 1— I eg 
CO b- lo rH eg ■* oo 
o o rH CO to eg r« 
o o o o o r- e» 



208 



EEPOET — 1893. 



^ > 



CM __^ -to 

^-4 



5* a 
■Si 00 
^ IM 

■IS & 
'^ _: 



a> o 

^ > 



3 

M 



5- -^ 


'^ di 


<-3 


.§ . 


^^ 


^•p 










S P 


J3 o 


* > 


o > 




M 


-o .» . 


3 ,^^- 


■S sS 


gg . 


^ ^ 00 

■4-3 r*' . 


3 Ss 


«Oc^ 


w"^- 



a< 



:S « 



o 






S oo 



o 
o 
■* 



'^^ 


g 




OS 


_?; 


tz; 


-K> 






0> 


j^ 


-3 




o 




a> 


H 


t; 


H 
■«1 


g 


« 


<i> 


Q 


a 




u 


o 


C5 


o 


-k3 


o 


a 


Oi 


^ 




c« 




> 




• ■-4 




P 




o* 




W 



1 1 1 1 1 1 llllllll 


°l 1 1 1 1 1 llllllll 


1 1 1 1 1 1 llllllll 


11 1 1 1 1 llllllll 


°l 1 1 1 1 1 llllllll 


m.iOil^ llllllll 
O0''0O'0O llllllll 



ifS t- 


^^ 


'JD CO 


1 o* 


00 1- 


1 «D 



o;-HO?0Ot-00i— I 
COt^COCO— iC3t— 00 

cooooooo-ot-to-^ 












OOOOGOOOOOODOOOO 





(M 




O 




•^ 




(M 








a 




o 






H 


wi 




a> 


P 


3 
o 

(D 


H 




w 


a 


a 


a) 


p 


H 


M 

EC 


Q 




2 

C5 




-^ 




a 




0) 








ert 




> 








3 




a- 




W 



1 1 1 1 1 1 1 1 1 1 1 1 1 II 










llllllll|f~"^ 11® 

iiiiiiiiIqOOO ''oo' 



eo^irit^i^ioo-^mt- 

rt CO CO oa C5 "J -H ■* t~ 

a505a5C50O0000t-CO 



13 ff-l 

t- CO 

Tj< CO 



c 

CI 



oo CO 

CO IS 
CO IM 



I— ( 

o 



-H to 
05 O 



lo m 1.0 iQ 13 >o in o i.o 1 

(M(M(M<NIMMC^(MC<1 1 


1 00 CO 


12 



OJ .-I 



GO 



tocot-t^-+ioo(Mia 

»00'-COiM-*NO 
.-I (N IM ■* "5 O 00 



■*C000O5««:o0ip(N I I 

ocooooimoot- 

(MIMlMNMi-Hi-li-ii-l 



-* CO 
CT: in 
to <M 



GO 

c 



" I .-H l-H I l-l 



inioioioioioioio 



lO o ic 

lO N <M 

O — I <N 

O O I O 



<M to ■* -H O to «0 
(M lO t~ C>1 lO 00 t- 

O O O — I — I (M lO 
O O O O O O O 



00 u; lo ■^ ^oic — •^cot-'^ 
O^^moo 00 co:oc^toioci-*05 

.-lr-((MNiOO 00.-Hi-i<MCO;0(M 



to 
t- in 

cr. 05 C5 00 tc N lo 

O-HCOt-lO^iMin -HIM 
OOOO^COtO(NiOOO 
COOOOOO'-<<M<M-* 



lO 

Ci 

in _ •* 





















CO t- ^ 


00 in 






1 in 


rn 


1 ■* 1 


t- c 


,_H 


fM 


<^1 


Tj< in CO 


iM •* o: 


oo(~inooiii llll 


1 05 oo 


1 m 1 


<M 




o 




^H 


t~ rt 05 


oo o 


1-H CO t^ 


>o 


O 1 1 1 III 


-Tt< 


cr. 


05 


I— 1 


(M 


lO 


to 


o 


ci in 00 


o o o c o o 


.— 1 


CO 






i-t 










»— 1 


rt N T*< 





































ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



209 



I 



O 



o 



■c 


'm 


, 


M 


fe 


M 


►? 




'6 


^ 






a 


<?■ m 


.,^:^" 


CO 

o 


"-J a 



o 

Ui 



f. 


•f-j 




< 


"H 




^ 


M 




^ 


"o 

> 




'« 


•S 


, 








cS 




ira 


^ 


r«* 


CO 


a 


<;:> 


ft 






oo 



w 

O 

03 



o 

to 



w 

o 



(Mm<MO>coco-*iiQm 

eococoMcM — ooioo 



EH 

Q 



■?; 


'> 




g 


K 






^ 






o 
> 




VI 






% 


"^J 


t-^ 




s 




o 
W 


^ 


Gi 


- 







05 

a 
a 









tH 


3 


w 


o 
IP 








o 


1?; 


0) 

a 


o 


Fl 


Ph 


n^ 


H 


u 


CQ 


o 




4J 




d 




<i) 








nS 




> 








E! 




O' 




H 



■* CD O <M CO 05 i-H 
IM »0 lO CT lO OC IM 
<M (N M <>J rt O O 
<M iq C*) (M SO Ol (M 



(NOJOONCqiMi-lrHi-l 



>o lo lo lo in lo in 
<N c^ oq <N (M oq (M 



CO c« t-- p in >o T^ 

6» »q "^ OS M «b o 

© I— 1 1— I O O a: 03 

CO CO (M (M cq rt rH 





(-^ 


1 


1 


1 1 


1 


1 






CO 


























^^ 






















w 


1 


1 


1 1 


1 


1 






O 






























^^-/ 
















cd 
















O 


1 


1 


1 1 


1 


1 




















<l 


CJ 












m 




O O 00 lO 


00 


in 


, 


W 




CD 


02 


CO CO 


IN <M 


■< 




ot 


(N 


<M (M 


T— ( 


o 


1— 1 




04 


OJ 


(M <M <M 


CO 


|2i 


1 

a 
a 












o 


3 

o 


1 


1 


1 1 


1 


1 


< 


<1 


cS 














o 


o 




























-^ 


1 


, 


1 1 


1 


J 






a 


1 


1 


1 1 


1 


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<[> 
































n 






























3 
^ 


»n 


in in in 


lo in 






(M IM 


CO 00 CO <M 






















(M -*< •* M (M 


lo 








CO >n CO 05 O O 








1— ( 


»-H 


^0005 








(N 


C>) 


CO C^ <N ^ 





o 






!3 




O 




<u 


in -* CO 




OS ■* CO 


s 


in t- t- 


o 




a 


« 


a 


ooo 


to o as 


^ 

s 


lO t- CD 



a 

<D 

> 





00 00 oo 



I I 



I I I 



I I 



CD 

t~ in 

05 o: C5 CO CO CO in 

o^coi—io^coin 

Qooo^cococqin 

OOOOOOO--1C0 



CO 
t- in 

05 05 02 00 CO (M lO 

o ^ CO t~ in 1— I CO 

O O O O "-H CO CO 

o o o o o o o 



CO 

t- in 

OS CS OS 00 CD CO 
O rH CO t^ lO 1— I 
O O O O .-H CO 

o o o o o o 



.-( CO CD 

ooo 
ooo 
ooo 
ooo 



CO CD c-1 in 

00 CO CO CO CO CO CO 
O 1— ( CO CO CO CO CO 
O O O O •— I cq lO 



OS 00 CD (M in 

in r-i CO t- -* OS oo 

O ■— I CO ■* OS 00 t- 
O O O O O •-■ CO 



CO (M •<*< 00 m 

CO t- -^ 00 t~ in 
o o <— I c-i in t— I 

O O O O O r-( 



t- ■* CO 

i-H CO O 
O O .H 

O c o 

OOO 

ooo 



1893. 



210 



BEPOBT — 1893. 



1^. 



■— < ^ 00 



o 



5- .J 




<=s 




1 ^ 








so 




stwald, 
Ckemie, 
p. 360. 


o 
■J* 


O 


< 


- 


N 






o 






1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 1 1 1 1 1 


ol 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 IJ_ 


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 


1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 


°l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 


1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 M 1 1 1 1 


t- a> la la la " 'P 


■* M ThI lO 



o 


M 


s 


2 


s 


!i5 


■<< 


-^ 




rt 




<1) 








OJ 




t> 



OOOOO-^C-IOCC-HIMOOMIM 
1— lOCOtDOSi— lOtO-^COt— ( 
to U3 CO « 1— I rt 



^ 



-00 oooocooooooocooooooooooooooo 



lomioioioioioioinio 



o 
a 

a* 







1 


1 


1 


1 1 




■* 












9 












00 


1 


1 


1 


I 1 






1 


1 


1 


1 1 




W 






















;z, 












W 


1 


1 


1 


1 1 














14 


w 








Yt 




oo O as 


-H lO 


tH 




-^ 


^. 


n^ 


•M QO 




Ol 


I—* 


C5 o iri CO 








K 


a) 












a 


1 


1 


1 


1 1 


s 













lO lO »0 »0 lO 

(^^ o5 (M <M o<i 



'* CO r~ -H o to 

t^ibt*cfQciDcbTtHcoc^?-i 

CO ^1 1-1 i-H 



p «-- 00 o cq 

OD •*! ■^ C5 O 

O OD to ■* CO 



00 to 



I I I 



I I 



.-I <M to 

O O O -^ M to 

000000»-HCOW5 

ooooooooo»— tlO 



■-H CO lO O 



05 OV 05 00 to IM lO 

o— <cot-io.-iiMm 

0000>— (C0tO(M»O 
OOOOOOO.— IIMIO 



to 

t- lO 

Oi 03 C^ 00 to 

o —I CO t- lO 
o o o o — 

O O O O O 1 



r^ ^ N 

.-I ^ O t *< !M 

OO^'HCOOt^'^lO 
OOOOO'-Hf— (iO00t-»Or-t(M 
OOOOOOOOOi-IOOt-IM 

fH lb 



<o 

to CO to IN U3 
r-lCOtOCOtOCOtOWlrt 
OOO^-cqioOf— iC<liO 
OOOOOO^HN-^OO 



O --I IM lO 
CO to CJ ■* 05 
O O -^ (N ■^ I 

o o o o o 



ON ELECTROLYSIS AND ELECTRO-CHEMISTRY. 



211 



> 
r3 S O 



to 




(M 







o 



us 



I I 



rH -^ -^i^ ^^ 00 
OO O ■^ O «D 
IM (M I— I 1— I 



05 
US 

w 

w 

o 



a 
o 

w 



»o in to »o 

©^ IM IN iM 


lO 




>p ip tH 

CO OS «b 


Mill 



o 

'o 

a 
a 

O 



IP 



O CO rH CO CO IC »Q 

OS CO ^H CO OS oc o 
^H OS t— lO CO W C<l 



"^ OS 
■* 05 



jcioio»oioio»oio»a»o 

(MN(M(M(M(MC<1<M(M(M 



►J 
o 

M 

PL, 



OOose«osooeoioco>-( 
Noocboiitboscodscb 

t-IOOtOU5CO(Mi— (.-I 



INI 


MM 


MM 


304. 


tl 1 1 1 1 


w! 1 II 1 



3 
o 

0) 

"o 

a 
a 

C 

ID 

"cS 

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KEPOET — 1893. 



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ON ELECTROLTSIS AND ELECTRO-CHEMISTRY. 213 



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COOO'-ilM'^OS OOOOO.-lC0t~ OOOOr-icOtO 



214 



BEPOKX 1893. 



Investigation of the Earthquake and Volcanic Phenomena of 
Japan. Thirteenth Report of the Committee, consisting of 
the Et. Hon. Lord Kelvin, Professor W. Gr. Adams, Mr. J. T. 
BoTTOMLEY, Professor A. H. Green, Professor C. Gr. Knott, 
and Professor John Milne (Secretary). {Draivn up by the 
Secretary.) 

The Geat-Milne Seismogkaph. 

The first of the above seismographs, constructed in 1883, partly at 
the expense of the British Association, still continues to be used as the 
standard instrument at the Central Observatory in Tokio. 

I am indebted to Mr. K. Kobayashi, the Director of the Observatory, 
for the following table of its records : — 



Catalogue of Earthqvakes recorded at the Central Meteorological Observatory in ToMo 
ietween May 1892 and Ajnil 1893. 















Maximum 


Maximum 
















Period and 


Period and 
















Amphtude of 


Amplitude of 
















Horizontal 


Vertical 


Nature 


No. 


Month 


Dat« 


Time 


Duration 


Direction 


Motion 


Motion 


of 
Shock 


sees. 


mm. 


sees. 


mm. 










1 


B92. 














H. M. S. 


M. S. 












1,241 


V. 


3 


1 18 53 A.M. 


1 3 


B.-W. 


0-9 0-2 


— 


— 


slow 


1,242 


»» 


5 


3 10 49 P.M. 


— 


— 


feeble 


— 


— 


— 


1,243 


»» 


11 


6 48 51 A.M. 


45 


W.N.W.-E.S.E. 


0-1 0-2 


sli 


ght 


quick 


1,244 


1) 


12 


2 36 54 r.M. 


— 


slight 


— — 


— 


— 


— 


1,245 


»» 


18 


7 41 1 P.M. 


— 


— 


very slight 


— 


— 


— 


1,246 


»» 


20 


7 17 42 A.M. 


— 


— 


very slight 


— 


— 


— 


1,247 


T» 


24 


9 1 10 P.M. 


— 


— 


very slight 


— 


— 


— 


1,248 


VI. 


3 


4 23 46 A.M. 


— 


— 


slight 


— 


— 


— 


1,249 


>l 


" 


7 9 57 A.M. 


7 30 


E.S.E.-W.N.W. 


2-0 28-4 


0-8 


4-4 { 


very 
quick 


1,250 


» 


3 


1 35 P.M. 








shght 





— 




1,251 


»» 


5 


1 10 3 P.M. 


— 


— 


very slight 


— 


— 


— 


1,252 




8 


9 3 12 A.M. 


— 


— 


slight 


— 


— 


— 


1,253 


»» 


10 


2 52 44 A.M. 


— 





slight 


— 


— 


— 


1,264 


)) 


15 


45 33 P.M. 





^_ 


slight 


— 


— 


— 


1,255 


»> 


19 


7 37 P.M. 


— 


_ 


slight 


— 


— 


— 


1,266 


11 


28 


11 29 36 P.M. 





— 


slight 


— 


— 


— 


1,257 


»» 


30 


6 13 20 P.M. 


— 


— 


slight 


— 


— 


— 


1,258 


VII. 


3 


1 9 26 A.M. 


— 


— 


very slight 


— 


— 


— 


1,259 


» 


»» 


7 20 56 P.M. 


— 


— 


slight 


— 


— 


— 


1,260 


a 


6 


2 58 16 A.M. 


1 30 


E.-W. 


slight 


— 


— 


Blow 


1,261 


)> 


20 


3 10 6 A.M. 


1 30 


N.N.W.-S.S.E. 


0-9 0-4 


— 


— 


,» 


1,262 


»» 


» 


6 11 10 A.M. 


3 20 


N.N.W.-S.S.B. 


0-8 0-7 


— 


— 




1,263 


it 


») 


8 29 41 A.M. 


— 


— 


very slight 


— 


— 


— 


1,264 
1,265 






11 31 44 A.M. 
2 9 52 P.M. 


1 

2 30 


S.-N. 
S.-N. 


slight 
slight 


— 


:! 


slow 
very 
slow 


1,266 


»> 


21 


56 46 A.M. 


— 


— 


very slight 


— 




— 


1,267 


)) 


23 


9 19 39 r.M. 





— 


sUght 


— 


— 


— 


1,268 


)) 


24 


11 21 A.M. 


— 


— 


slight 


— 


— 


— 


1,269 


}) 


26 


9 22 25 A.M. 


— 


— 


very slight 


. — 


— 


— 


1,270 




27 


10 20 42 A.M. 


1 30 


N.N.W.-S.S.E. 


0-8 0-8 


very 


slight 


slow 


1,271 


yy 


29 


7 3 P.M. 


— . 


— . 


sUght 


— 


— 


— . 


1,272 


VIII. 


20 


2 29 29 A.M. 


— 


— 


slight 


— 


— 


— 


1,273 


,, 


28 


10 19 1 P.J[. 


1 30 


E.-W. 


slight 


— 


— 


slow 


1,274 


IX. 


4 


10 7 43 A.M. 


— 


— 


very slight 


— 


— 


— 


1,275 


n 


7 


6 11 57 A.M. 


3 SO 


S.B.-N.W. 


1-7 


11 


— 


— 


Blow 



ON THE EARTHQUAKE AND VOLCANIC PHENOMENA OF JAPAN. 
Catalogue of Eabthquakes — continued. 



215 















Maximum 


Maximum 
















Period and 


Period and 
















Amplitude of 


Amplitude of 




No. 


Month 


Date 


Time 


Duration 


Direction 


Horizontal 
Motion 


Vertical 
Motion 


Nature 

of 
Shock 


sees. 


mm. 


sees. 


mm. 








H. M. s. 


M. S. 












1,276 


IX. 


11 


9 31 47 P.M. 


— 


— 


very slight 











1,277 


» 


13 


11 29 42 P.M. 


2 


E.S.E.-W.N.-W. 


0-4 2-6 


0*3 


0-3 


quick 


1,278 


JJ 


15 


2 57 28 P.M. 


— 


— 


very slight 








1,279 


»> 


17 


11 51 40 A.M. 


— 


— 


very slight 








. 


1,280 


„ 


18 


1 34 17 A.M. 


— 


— 


very slight 











1,281 


X. 


1 


2 6 31 A.M. 


— 


— 


very slight 











1,282 


J> 


» 


9 21 36 A.M. 


— 


— 


very slight 








. 


1,283 


»» 


6 


60 32 A.M. 


— 


— 


very slight 











1,284 


»» 


7 


23 37 A.M. 


— 


— 


very slight 











1,285 


)» 


8 


1 35 54 P.M. 


20 


E.-W. 


0-3 0-2 








quick 


1,286 


n 


14 


7 54 46 P.M. 


— 


— 


very slight 










1,287 


)» 


19 


53 9 P.M. 


— 


— 


very sUght 











1,288 


*) 


21 


7 28 26 P.M. 


— 


— 


slight 











1,289 


11 


22 


7 9 54 P.M. 


— 


— 


slight 











1,290 


1) 


25 


10 11 38 P.M. 





. — 


slight 


. 







1,291 


i» 


27 


3 14 P.M. 


— 


— 


slight 


— 





__ 


1,292 


XI. 


5 


1 48 53 A.M. 


40 


E.-W. 


1-2 0-4 








slow 


1,293 


11 


15 


11 6 2 P.M. 


— 


— 


feeble 










1,294 


»> 


16 


4 25 44 P.M. 


— 


— 


feeble 


, 





„ 


1,295 


M 


21 


10 37 53 P.M. 


2 30 


S.E.-N.W. 


0'3 0-7 


0-2 


0-2 


quick 


1,296 


XII. 


6 


3 30 22 A.M. 


— 


— 


slight 








1,297 


11 


») 


4 22 38 P.M. 


1 30 


N.-S. 


1-0 0-6 








slow 


1,298 


»» 




7 19 P.M. 


1 30 


S.-N. 


slight 










1,299 


11 


9 


8 11 A.M. 


1 30 


S.E.-N.W. 


0-4 OS 


sli 


ght 


quick 


1,300 


If 


11 


10 43 57 A.M. 


2 40 


E.S.E.-W.N.W. 


1-5 1-5 






slow 


1,301 


11 


10 


10 46 AM. 


— 


— 


slight 










1,302 


tl 


11 


1 34 39 A.M. 


2 30 


W.S.W.-E.N.E. 


1-1 1-1 








slow 


1,303 


1> 


12 


2 56 57 P.M. 


— 


— 


very slight 










1,304 


»1 


24 


2 12 31 P.M. 


— 


— 


slight 


— 


— 


— ' 



1893. 



1,305 


I. 


3 


1,306 




8 


1,307 




16 


1,308 


)» 


20 


1,309 




23 


1,310 


n. 


11 


1,311 




17 


1,312 




19 


1,313 




21 


1,314 


III. 


6 


1,315 




17 


1,316 




24 


1,317 




26 


1,318 




„ 


1,319 


IV. 


4 


1,320 


jj 


5 


1,321 




9 


1,322 


n 


19 



35 

5 40 

10 37 
8 10 

1 7 

6 46 

7 13 

1 39 

2 48 

8 52 

9 6 

6 4 

7 47 

8 27 

7 33 
1 8 

8 21 

11 22 



25 P.M. 


1 30 


27 P.M. 


2 30 


18 P.M. 


— 


21 A.M. 


_ 


62 P.M. 


— 


31 A.M. 


1 


59 A.M. 


50 


52 A.M. 


— 


3 A.M. 





18 A.M. 


3 20 


31 A.M. 


1 


52 A.M. 


3 30 


21 P.M. 


— 


52 P.M. 


— 


11 A.M. 


— 


46 P.M. 


1 


6 P.M. 




26 P.M. 





N.W.-S.E. 
W.N.W.-E.S.E. 



E.-W. 
E.-W. 



E.S.E.-W.N.W. 

E.-W. 

N.B.-S.W. 



E.-W. 
E.-W. 
E.-W. 



0-5 0-6 
0-3 3-5 

very slight 

slight 

slight 

slight 
0-3 0-6 
very slight 
very slight 
0-6 1-7 

0-2 0-3 

1-3 0-6 
very slight 
very slight 

slight 

slight 

slight 

slight 



0-4 
0-3 



sli 



0-3 



sU 



0-2 
0-9 



ght 

0-2 
ght 



quick 
» 

quick 
)) 

quick 

slow 

quick 



On the Movements of Horizontal Pendulums. 

In a report to this Association in 1881 reference was made to tLe 
observation of earth- tremors which it was thought might be connected 
with the occurrence of earthquakes. The analysis of records obtained 
during succeeding years showed that the surmise was without foundation. 
In 1883 an account was given of experiments with various forms of 
tromometers and delicate levels. The Report for 1884 contained further 
notes on the observations of earth-pulsations and earth-tilting. In 1885 



216 BEPOBT — 1893. 

an instrument was described which gave a continuous record of tremors 
and deflections of the vertical, and reference was made to earth-waves 
which had a period of from fifteen to sixty minutes. The Reports for 
1887 and 1888 formulated certain laws respecting the occurrence of earth 
tremors or pulsations. Full accounts of all this work have been published 
in the ' Transactions of the Seismological Society.' Last year I described 
to this Association a method for the investigation of earth-pulsations and 
earth-tilting, which consisted in making a continuous photographic i-ecord 
of the spots of light reflected from mirrors carried by two horizontal 
pendulums. These pendulums, which swing in planes at right angles to 
each other, are each made from a piece of aluminium wire, 60 mm. in 
length, tipped with a needle point resting in an agate cup. This is held 
in a horizontal position by means of a quartz fibre. When adjusted so 
that the period of swing is from five to six seconds, I find that a deflection 
of the spot of hght upon the recording film of 1 mm. with one instrument 
corresponds to a tilting of 0"54<", and with the other instrument of 0'68". 
The distance of the lamp and film from the mirrors, which are arranged 
to swing one above the other, is 3 feet. 

When describing this instrument iu 1892 I referred to it as being 
new. In this I was mistaken, as similar arrangements have been used in 
Potsdam and other places by Dr. E. von Rebeur-Paschwitz (see ' Der, 
Ksl. Leop. -Carol. Deutschen Akademie der Naturforscher,' Band LX. 
No. 1). In Japan the primary object of the observations was to obtain 
continuous records of earth-waves (tremors), with the result that with 
these records the records of other phenomena like those of earth-tilting 
were found. In Potsdam the cycle of observations was reversed, the 
primary object being to record small changes in the vertical, with the 
unavoidable result that distant earthquakes, tremors, and other phenomena 
were also recorded. 

The pendulums I have used have been exceedingly light, and intended 
to follow the movements impressed upon them by a succession of earth- 
waves. 

The pendulums of Dr. von Rebeur-Paschwitz were comparatively heavy, 
and were adjusted to move with periods of from twelve to eighteen 
seconds. 

The results obtained in December and January last are described in 
detail in the ' Seismological Journal,' whilst that which has been done 
between February and April is briefly as follows : — 

Daily Tilting. 

Almost every day the records show that the spots of light have been 
displaced in a direction which would correspond with a displacement 
should the N.E. or N.N.E. side of the column on which the pendulums 
stand be gently raised, and then gently but rather more quickly lowered. 
Occasionally the tilting is from the north, the pendulum in the meridian 
which records the east and west motion remaining stationary. 

The movement commences about 7 p.m., and continues steadily up to 
about 7 or 8 a.m. From this to about 10 a.m. there is a quick return 
to the normal position, where it remains until evening. The amount of 
tilting which would produce these deflections is from 2" to 10". The 
average, as shown in the diagram, is about 4". 



ON THE EAETHQUAKE AND VOLCANIC PHENOMENA OF JAPAN. 217 

FiGf. 1. — Average daily N.E.-S.W. tilting of a stone column in Tokio, February 

and March 1893. 



x 
































/ 


/ 


/ 


\ 










?' 








i 




















/ 


/ 


/ 






\ 


L 








/• 






— V 
















^ 


y 


y 














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J 


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1 


^ 


^ 




















o 






4 AT--. 



Noon, I Z 3 4 5 6 7 S 9 W it m I. Z 3 4- 3 6 7 8 9 W UKocn. 



The following table is a comparison of the movements observed by 
Dr. von Rebeur-Pascbwitz and those observed in Tokio : — 



Movements of Pendulums 


Wilhelmshaven 


Potsdam 


Teneriffe 


Tokio 


Completion of Easterly move- 
ment (B. sunk) 


2 P.M. 


3.30 P.M. 


3 to 4 P.M. 


7 P.M. 


Completion of Westerly move- 
ment (E. risen) 


4 or 5 A..M. 


8 A.M. 


9 A.M. 


8 A.M. 


Amplitude of motion . 


l"-44 to 4"-32 


»"-14 to 1"-13 


0"-95 to 0"-04 


4" to 10" 



Effects of Chmujes in Temperature. 

The tests whicli have been applied to determine the effects produced 
by a change in temperature have been severe. After closing all doors a 
stove -which stands about 3 feet distant from the S.W. corner of the 
column has been lighted, and the temperature raised, for example, from 
49° F. to 85° F. This took three hours, and during this time the corner 
of the column became sensibly warm to the hand. All was then allowed 
to cool. The effect as shown upon the photographic trace and partly 
by other instruments upon the column was that about half-an-hour after 
lighting the fire the N.B. side of the column very quickly sank, indicating 
a tilting from S.W, to N.B. of 2". After this it sank until an amplitude 
of 6" was reached. Here it remained for several hours, and then gradually 
rose. This, it will be observed, is a result that can be obtained by a 
change of temperature of 36° F. 

Undoubtedly temperature effects exist in the records I have taken ; but 
as it has often happened that the change in temperature during twenty- 
four hours inside my observatory has not been more than 4° F., while 
the daily movements have exceeded that which I obtain by a change of 
36° F., I cannot attribute the movements I observe to fluctuations in 
atmospheric temperature in the vicinity of the column. 

To determine how far slow and regular changes in temperature may 
modify the diagrams will be a subject for future investigation. 



218 



REPORT — 1893. 
Barometrical Effects. 



On the soft, marshy ground near Wilhelmsliaven, Dr. von Rebenr- 
Paschwitz observes that a change in the vertical of ^" corresponds to a 
change of 1 mm. in barometrical pressure ; in fact, the district behaves as 
if it were the vacuum chamber of an aneroid. In Tokio the effects are 
not so pronounced, yet in many instances a N.N.B. tilting has corre- 
sponded with a rise in the barometer. On two or three days when the 
barometrical changes have been small the daily movements have been 
small, but there are other instances where the daily movement has 
continued and the barometer has been steady. In the smaller movements, 
and in the few cases where the direction of one component of the daily 
movement has been reversed, there does not appear to be any connection 
with the barometer. 

Mr. T. Wada, of the Meteorological Observatory, tells me that the daily 
maximum and minimum barometrical changes vary with the season, the 
yearly average being as follows : — 



— 


Minimum 


Maximum 


Minimum 


Maximum 


For North Japan 
For South Japan 


H. M. 

3 8 A.M. 
3 7 A.M. 


II. M. 

9 A.M. 
9 2 A.M. 


n. M. 

2 5 P.M. 

3 2 P.M. 


H. M. 

9 9 P.M. 

10 1 P.M. 



Those which are italicised are the most pronounced. In winter there 
are two other periods, viz. : — 



— 


Minimum 


Maximum 


For North Japan .... 
For South Japan .... 


H. M. 

5 A.M. 

.5 A.M. 


H. M. 

2 3 A.M. 

1 7 A.M. 



I have not observed any change accompanying these periods. 

Possible BelationsMp with Magnetic Movements. 

The relationship between the movements of the pendulums and the 
daily changes in magnetic declination suggests the idea that the pheno- 
mena which are being observed are not altogether unconnected with 
magnetic influences. 

In Tokio the declination is farthest west about 2 p.m., and farthest 
east at 8 a.m. ; that is to say, when the magnetic needle is farthest 
east the north end of a north south boom of my instrument is farthest 
west. That the movements of the horizontal pendulums and those of a 
magnetic needle take place at the same time but in opposite directions 
has also been observed by Dr. von Rebeur-Paschwitz in Potsdam and 
Wilhelmshaven. In my instrument the pivot, which is a steel needle point 
8 mm. in length, is pivoted at its southern end. 



Geological Structure and Direction of Movements. 

A very significant fact, possibly connecting the observed movements 
with geological structure, is that the N.E, or N.N.E. direction of tilting 



ON THE EARTHQUAKE AND VOLCANIC PHENOMENA OF JAPAN. 219^' 

is at right angles to a well-defined axis of rock cmmpling, whicli shows 
itself in the N.W. to S.E. strike of the mountains some thirty miles 
distant, and which line of folding probably continues beneath the plain of 
Tokio. 

Another point not to be overlooked is that the direction of earth- 
quake motion across the Tokio plain is in the majority of cases also at 
right angles to the direction of mountain strike. During the next 
summer I shall endeavour to instal horizontal pendulums on the rocks 
themselves, one of them parallel to the dip and the other at right angles 
to this direction. 

Irregular Movements. 

It often happens that superimposed upon the daily wave there are 
sinuosities with amplitudes of 1" or 2". These appear to be chiefly 
marked on the east and west components of the diagrams. They have 
periods of from three to six hours, and generally occur as a sinking 
during the early morning or between midnight and 8 or 9 a.m., at which 
time the east is usually rising. 

On February 17, March 24 and 26, small earthquakes occurred witb 
these sinkings, after which the normal rise was continued. Other earth- 
quakes, which, however, were too small to be measured by ordinary 
seismographs, were not accompanied by such changes. Before the 
earthquake of March 6, which probably was of local origin, the spots of 
light had moved off the scale as if by an abnormally large sinking on the 
N.E. side. This was at 8.45 p.m. on March 5. I therefore do not know 
what happened immediately before the shaking, which took place at 
8.52 A.M. next morning. 

Earth-waves or Earth-pulsatiotis. 
(Tremors or Microseismic Disturbances.) 

On February 17, 18, and 19 there was a large and well-marked storm 
of tremors. The barometer did not fall to any remarkable extent, the 
lowest I noted being 297 in. While the movements were continuing 
the east side of the column was depressed about 2", and the daily wave 
did not show itself. With other tremor-storms, which were, however, 
smaller, the daily wave has been unaffected. 

Earthquakes. 

From the list of earthquakes at the commencement of this report it 
will be seen that during the months of February and March nine earth- 
quakes were recorded at the Central Observatory in Tokio. Five of 
these were measurable by seismographs. Seven out of the nine were 
recorded at the University Laboratory, which is about 1^ mile distant 
from the central station. Owing to certain of these having occurred 
when there had been a temporary interruption in the taking of records — 
as, for example, when changing a film— it is only possible that three of 
the seven disturbances should have been photographically recorded. 

These records are remarkable for their smallness, apparently showing 
that, although there had been a sensible motion of the ground, the 
mirrors had either remained practically at rest, or else they had not been 
movmg for a sufficiently long period of time to produce an impression on 
the film. As the films, which were prepared for me by Professor W. K. 



220 EEPOET— 1893. 

Burton, are particularly sensitive, I am inclined to the opinion that there 
was less tilting accompanying these earthquakes than there is in the 
waves which constitute a tremor-storm ; in fact, the earthquakes which 
only produced deflections of 2 mm. were elastic tremors, while so-called 
tremors which may produce deflections of 25 mm. are earth- waves. 

These observations led me to note the effects produced upon a film 
when the mirrors had been caused to swing by placing my finger upon 
the iron bed-plate which acts as their support. The result was that 
either a band about 12 mm. in length was produced or else the trace 
was blurred, and at the blurr a permanent deflection of about 3 mm. was 
recorded. 

As a result of these experiments I conclude that in all cases where 
lines are invariably opposite to each other in both components, and 
are seen as transverse markings in the traces, such lines indicate that 
the mirrors have been swinging, and the question arises, whether these 
are due to undulations from distant earthquakes or whether they are 
due to undulations which, if they were continuous, would constitute a 
tremor- storm. 

If they are tiltings due to distant earthquakes, then on several occa- 
sions as many as fourteen of these disturbances have been noted in 
twenty-four hours. On other days the normal lines are unbroken. 

Comparing the photographic traces with the list of 101 earthquakes 
which were felt in Japan during the month of February, it is seen that 
only the large ones, like numbers 54 and 61, have been recorded on the 
film. The traces, however, show that there have been many large dis- 
turbances which do not coincide iu time with earthquakes noted on the 
list. It is possible that these may coincide with disturbances which had 
their origin in other countries, or, what is more likely, with disturbances 
originating beneath the bed of the Pacific, where, from what we know, 
seismic activity is at least as great as it is upon the land. An alternative 
suggestion is that they are the result of movements similar in character 
to those which constitute a tremor-storm ; but whether these are to be 
attributed to sudden but gentle bondings of rocky strata, or whether 
their origin is to be sought for amongst causes which are more complex, 
is for the present a subject about which we are hardly justified in 
attempting to formulate an hypothesis. 

Dr. von Rebeur-Paschwitz in Germany has observed fourteen earth- 
quakes — if all of these really are earthquakes — in eleven months. One 
of them corresponds in time to the great disturbance of October 28, 1891, 
when Central Japan was devastated. 

Possible Connecticut lehveen these Observations and oilier Phenomena. 

Assuming that with appliances similar to those used by Dr. von Rebeur- 
Paschwitz, or to those used in Japan, records of distant earthquakes may 
be noted, then it would be possible in England, or any other country, not 
only to note unfelt local disturbances, but also to record, at least, very 
many of the large disturbances which occur throughout the world. 

The importance of such records in determining the velocity with 
which earth-waves are propagated, or, as was suggested by Lord Kelvin, 
the determination of elastic constants for the earth's crust, and in solving 
other problems, is apparent. 

Already the observations on earth-tilting seem to have gone sufficiently 



ON THE EARTHQUAKE AND VOLCANIC PHENOMENA OF JAPAN, 221 

far to demand serious attention from practical astronomers. There are 
many reasons for believing that earth jjulsations or undnlations have a 
connection with the escape of fire-damp, and they do not appear to be 
wholly unconnected with the behaviour of certain physical instruments. 
For example, as the result of a long series of observations made with an 
Oertling and a Bunge balance, it seems that there are times when it 
would be impossible to carry out any delicate weighing operations. 

The more important results obtained from the observation of these 
balances were as follows : — 

1. The Oertling, which was a light assay balance, moved more than 
the Bunge. 

2. It was seldom that either of the balances was absolutely at rest. 

3. Daring a day the pointer of the Oertling usually crept through 
half a division of the ivory scale. 

4. Although when caused to swing the period of the Oertling was 
41 seconds, it would sometimes be found performing complete swings 
with periods varying between 17 and 60 seconds. Slower motions might 
take 50 minutes. 

5. It was often observed that both balances would start from rest 
simultaneously and in the same direction. 

6. Periods of disturbance usually occurred with tromometric disturb- 
ances, but both balances have often been found moving when tremors 
were not observable, when the weather was calm and the barometer high, 
while they have been absolutely at rest during a heavy gale and the 
barometer at 29*2 inches. 

7. The oscillations are not always about the same zero, and the zero 
for the pointer sometimes changes within a few minutes. 

A detailed account of the above observations is given in the ' Seismo- 
logical Journal,' vol. i. 

The Earth-waves of Earthquakes. 

From the observations of many who have experienced a large earth- 
quake we may be certain that at such times the surfaces of alluvial 
plains have been thrown into a series of undulations. During these dis- 
turbances, from observations on the behaviour of fluids in vessels the 
water in ponds, the irregular and erratic swinging of seismographs, and 
the character of the resulting records, it is also clear that undulatory, 
wave-like motions have taken place. 

On the occasion of the great earthquake of October 28, 1891, knowing 
that bracket and conical pendulum seismographs had been tilted, in the 
Twelfth Report to the Association calculations were given of the 
maximum slopes of the earth-waves which had caused these movements. 
Although these calculations may have been interesting on account of 
their novelty, because any arrangement like a heavy horizontal pendulum 
when quickly tilted is likely to overswing the point corresponding to that 
which it would take if the movement had been very slow, serious objec- 
tions may be raised to the accuracy of the results which were obtained. 
This consideration led me to devise an angle-measurer in which errors of 
this description are not likely to occur. It consists of a balance-beam, 
each arm of which carries a heavy weight so adjusted that the system 
has but feeble stability. When the stand carrying this is tilted in the 
plane of the arm, the arm remains horizontal, while a vertical pointer 



222 REPORT— 1893. 

projecting downwards, as in an ordinary balance, is relatively deflected 
through an angle corresponding to the tilt. This pointer moves a hori- 
zontal lever, at the outer extremity of which a sliding needle writes its 
record on a smoked-glass plate. Two such pieces of apparatus at right 
angles to each other, writing on the same surface, constitute a complete 
instrument. 

In one apparatus the balance-arm with its weights is replaced by 
a heavy metal disc, supported in a vertical plane by knife edges at its 
centre. 

Already one or two earthquakes have been recorded, and as these are 
the first written records of earth- waves, a portion of one of them is here 
reproduced :^ 

Fig. 2. 




It shows the E. and W. tilting during a small portion of an earth- 
•quake which occurred at 5.40 p.m. on January 8, 1893. The numbers 
indicate successive seconds, from which we see that the period of the 
waves varied from I- to ^ second. The average angular deflection was 
about 2' 40", and the smallest about 1' 30". 

The movement continued over at least 20 seconds, dying out with 
hardly perceptible waves having periods of about ^ second. The N. and 
■S. component of tilting was exceedingly small. The direction in which 
the waves were propagated was approximately E.N".E. to W.S.W. 

Inasmuch as tilting apparently occurs whenever we have vertical 
motion, an unpleasant conclusion — which, however, is not expressed for 
the first time — is that all the records hitherto published in Japan where 
vertical motion has been recorded are of but little value. Not only may 
the horizontal motion have been exaggerated, but the records of vertical 
motion have also suffered distortion, this being greatest when the arm of 
the lever seismograph has been parallel to the direction of the wave- 
slope. The disturbances in which the vertical component has been 
mai'ked form about 10 per cent, of what should be our most important 
records. 

What we require to know, for example, as an assistance in investi- 
gations relating to construction is the configuration, dimensions, and 
rapidity of recurrence of these earth- waves. 

The varying slope of the waves, their period, and their direction of 
advance, may be measured by the apparatus described. 

As an attempt to measure the vertical component of these waves, four 
lever seismographs have been arranged with their arms at 45° to each 
other, it being assumed that the record from the instrument with its arm 
most nearly at right angles to the direction of the advancing wave will 
be tbe one which will most closely measure the vertical motion. 

Another possible method of measuring this element of earthquake 
motion would be to avoid errors consequent on tilting by arranging a 
vertical lever seismograph on gimbals. 



ON THE EARTHyUAKB AND VOLCANIC PHENOMENA OF JAPAN. 223 

Gyroscopes as adjancts to the solation of these problems have not 
hitherto proved themselves successful. 

On the assumption that the earth-waves in alluvium were harmonic 
in character and symmetrical in form, in the Report for 1892 it was shown 
that they might be 20 feet in length ; and, knowing their length and 
period, the velocity of propagation was determined. Even should these 
waves have lengths several times this amount, some knowledge of their 
form might be obtained by simultaneously measuring the difference 
in movement between, say, the heads of a line of stakes at right angles to 
the direction of the advancing waves and different points of a wire or rod 
parallel to such a line, but only held in position at its two extremities. 

I am led to mention these latter experiments as indications of the 
important problems which seismologists have yet before them. 

List of Earthquakes recorded in Japan in February 1893. 

Tlie list of earthquakes appended to this section of the Report is given 
as an example of a catalogue which might be compiled from the material 
which since 1885 has been accumulating at the Central Meteorological 
Observatory in Tokio. 

The approximate centre of a disturbance is indicated by its latitude 
and longitude, while the energy of the disturbance may approximately be 
deduced from the figures which show in geographical miles the diameter 
of the area shaken. 

Hitherto investigations respecting seismic activity, the periodicity of 
earthquakes, &c., have been based upon catalogues where only the number 
of shocks have been recorded, and where the disturbances of one seismic 
area have been inextricably mixed with those from another. 

With a catalogue like the one suggested it would be possible to investi- 
gate the rate at which seismic activity is decreasing or increasing either 
in a given area or in Japan as a whole, giving values to the shocks pro- 
portional to the area they had shaken. It would assist us in determining 
whether there is any relationship between the frequency of earthquakes 
in neighbouring areas. Inasmuch as many earthquakes seem to be the 
result of sudden fractures or yieldings taking place during the process of 
rock-crumpling, it does not seem unlikely that the relief of strain along 
one axis should be altogether without effect upon neighbouring axes 
where folding may also be in operation. One interesting investigation of 
the records of a district which has very kindly been made by Mr. F. 
Omori has been to plot the shocks which succeeded the great disturb- 
ance of 1891 as a curve, the co-ordinates of which are equal intervals of 
time and the number of shocks occurring during these intervals. 

It will be remembered that the immediate cause of the disturbance 
was the formation of a large fault which can be traced some forty or fifty 
miles, together with several minor faults. During the seven months 
which followed the great shock no less than 3,000 shocks were recorded. 
How many have been recorded up to date has not been calciilated, but 
from the appended List for the month of February, that is sixteen months 
after the first shock, sixty-two disturbances were noted. 

The curve representing this decrease in activity closely approximates 
to a rectangular hyperbola, which now, with an average of two shocks 
per day, is becoming asymptotic. 

With the law of decrease deduced from these records Mr. Omori 



224 



REPOBT 1893. 



calculates that it will take about thirty years for the district to regain its 
original stability. The records for the Kumamoto earthquake, which took 
place in July 1889, show a like result, but with a rate of decrease 
directly proportional to the intensity of, or the area shaken by, the primary 
disturbance. 

One curious fact connected with the extinction of the Nagoya earth- 
quake is that the district of greatest visible faalting, where valleys were 
compressed and mountains were lowered, seems to have reached a fair 
state of quiescence, while the most active settlement, or the district where 
an extension of faulting is now taking place, is at the S.E. extremity of 
the main line of original disturbance— a few miles N.E. from Nagoya in 
Niwa-gun (N. lat. 35° 20', and E. long. 136° 50'). 

Not only would the publication of the catalogue here indicated furnish 
material very much better than that which has been hitherto attainable 
for the continuation of investigations like those made by Perrey, Mallet, 
and other seismologists, but we should have materials for investigations 
which would be entirely new. 

Earthquakes recorded m Japan in February 1893. 



No. 


Day 


1 


1 


2 


»» 


3 


iJ 


4 


)> 


5 


2 


6 


tt 


7 


3 


8 


J> 


9 


)t 


10 


») 


11 


») 


12 


»> 


13 


4 


14 


5 


15 


6 


16 


»» 


17 


)l 


18 


*» 


19 


7 


20 


»J 


21 


8 


22 


»» 


23 


J> 


24 


J» 


25 


J» 


26 


1) 


27 


9 


28 


»» 


29 


i9 


30 


») 


31 


10 


32 


J» 


33 


11 


34 


f> 



Time 



M. 

42 A.M. 

43 A.M. 

45 P.M. 

21 P.M. 
3 A.M. 

42 P.M. 

30 A.M. 

20 P.M. 

23 P.M. 
34 P.M. 
30 P.M. 

■7 

55 P.M. 
34 P.M. 

15 A.M. 

55 P.M. 

11 P.M. 

57 P.M. 

9 A.M. 

52 P.M. 

13 A.M. 
54 A.M. 
40 A.M. 
10 A.M. 

24 P.M. 

P.M. 
15 A.M. 
37 A.M. 
30 A.M. 

P.M. 
30 A.M. 

8 53 A.M. 
6 48 A.M. 
8 40 A.M. 



Position of centre 



Latitude 
N. 



35-20 

35-40 

35-5 

35-30 

35-30 

34-40 

34-50 

35-20 

34-50 

35-20 

35-20 

340 

35-20 

36-45 

350 

35-0 

36-25 

35-0 

3510 

35-20 

35-20 

43-20 

35-30 

35-10 

34-20 

35-30 

35-20 

35-20 

37-25 

35-10 

35-20 

35-20 

36-20 

36-10 



Diameter 

of area 

.^ , I shaken in 
Longitude namical 

miles 



1370 

137-0 

137-0 

137-10 

137-10 

132-30 

132-25 

136-50 

136-30 

137-0 

137-0 

132-10 

136-10 

1,380 

132-50 

13250 

1400 

132-50 

136-50 

136-50 

137-0 

145-30 

137-0 

136-50 

133-50 

137-20 

136-50 

136-50 

138-50 

136-50 

136-40 

136-40 

140-30 

137-20 



5 

3 

3 

3 

3 

70 

3 

20 

3 

S 

3 

3 

3 

3 

3 

3 

30 

3 

40 

20 

10 

3 

20 

10 

3 

3 

40 

3 

3 

3 

10 

10 

20 

3 



Remarlcs 



N. of Nagoya. 

s. „ „ 

N.E. of „ 

„ Nagoya. 
S.W. Nipon, Akiken. 

>» ,» II 

N. of Nagoya. 
N. of Ise. 
N. of Nagoya. 

i» 11 >» 
S.W. Nipon. 
W. of Gifu. 
Central Nipon. 
S.W. Nipon. 

» i> 

N. of Tokio. 
S.W. Nipon. 
Nagoya. 
N. of Nagoya. 

)i »j •» 
N.E. Yezo, Nemuro. 
N.W. Nagoya. 
S.W. 

N. Shikoku. 
N.W. Nagoya. 
N. of 

f* f* ), 

Central Nipon, Echigo. 
Nagoya. 
N. of Nagoya. 

n!w. of Tokio. 
Fukui Ken. 



ON THE EARTHQUAKE AND VOLCANIC PHENOMENA OF JAPAN. 225 
Eaethquakbs — cmitiniied. 









Position 


of centre 


Diameter 




No. 


Day 


Time 






of area 
shaken in 
nautical 


Remarks 


Latitude 


Longitude 








N. 


E. 


miles 






H. M. 










35 


11 


9 20 A.M. 


35-20 


137-0 


3 


N. of Nagoya. 


36 


tl 


6 20 P.M. 


37-5 


137-20 


3 


Fukui Ken. 


37 


)» 


8 42 P.M. 


35-30 


137-0 


3 


N. of Nagoya. 


38 


12 


20 P.M. 


37-5 


137-20 


3 


Fukui Ken. 


39 


It 


? 


36-5 


138-10 


3 


Suwo, Central Nipon. 


40 


)» 


5 55 P.M. 


35-30 


1370 


3 


N. of Nagoya. 


41 


13 


6 42 A.M. 


35-20 


136-50 


10 


») j> ij 


42 


1) 


7 32 A.M. 


35-30 


1370 


3 


>j »» 1) 


43 


It 


8 50 A.M. 


35-30 


137-0 


3 


»f »» »j 


44 


14 


6 5 A.M. 


39-40 


141-30 


3 


N. Nipon, Nambu. 


45 


)* 


11 10 A.M. 


35-30 


137-0 


3 


N. of Nagoya. 


46 


)) 


11 20 P.M. 


36-30 


136-50 


10 


»» )» )» 


47 


15 


2 10 A.M. 


35-30 


136-50 


10 


» n 11 


48 


J> 


8 30 a.m. 


35-30 


136-50 


3 


11 11 11 


49 


)l 


10 43 A.M. 


35-30 


137-20 


3 


N.W. of „ 


60 


16 


7 43 A.M. 


36-30 


136-50 


3 


N. „ „ 


51 


»1 


1 P.M. 


35-30 


136-50 


3 


)» »i ») 


52 


It 


9 10 P.M. 


35-30 


137-10 


15 


N W 


53 


17 


5 45 A.M. 


35-40 


136-50 


3 


-^^* tt It 


54 


J» 


7 15 A.M. 


35-30 


139-.S0 


50 


Central Nipon, near Tokio, 


55 


H 


7 35 A.M. 


35-20 


137-0 


5 


N. of Nagoya. 


56 


*» 


7 55 A.M. 


35-20 


1370 


3 


»? »» jj 


57 


It 


46 P.M. 


35-20 


137-0 


3 


if »» »t 


58 


18 


3 1 A.M. 


35-20 


136-50 


3 


N.W. of „ 


59 


»» 


7 56 P.M. 


35-50 


1370 


3 


N. „ „ 


60 


19 


2 1 A.M. 


36-20 


140-30 


3 


N.W. of Tokio. 


61 


»» 


1 57 P.M. 


36 


137-30 


20 


W. of Nagoya. 


62 


t» 


3 36 P.M. 


34-30 


133-50 


3 


Inland Sea. 


63 


J» 


8 26 P.M. 


34-50 


132-5 


3 


S.W. Nipon. 


64 


)l 


? 


35-0 


1350 


100 


Only felt at three places on a 
N.W.-S.E. line. 


65 


»» 


8 42 P.M. 


34-30 


133-0 


150 


S.W. Nipon, Shikoku, to centre 
of Kiushiu. 


66 


IJ 


10 1 P.M. 


35-50 


132-60 


3 


S.W. Shikoku. 


67 


»» 


11 P.M. 


34-10 


13210 


3 


S.W. Nipon. 


68 


»f 


11 55 P.M. 


35-20 


137-0 


3 


N. of Nagoya. 


69 


20 


1 A.M. 


34-0 


132-30 


40 


S.W. Nipon and W. Shiko- 
ku. 


70 


If 


2 8 A.M. 


35-20 


1370 


3 


N. of Nagoya. 


71 


5» 


5 2 A.M. 


34-20 


132-30 


3 


S. Nipon. 


72 


II 


10 55 A.M. 


34-50 


133-20 


10 


*» 11 


73 


»» 


8 12 P.M. 


33-20 


131-30 


3 


Kiushiu. 


74 


1* 


9 30 P.M. 


36-50 


135-30 


3 


Wahayama. 


75 


>f 


11 P.M. 


35-20 


137-0 


3 


N. of Nagoya. 


76 


*» 


11 P.M. 


37-20 


139-40 


3 


Central Nipon. 


77 


21 


2 48 A.M. 


36-0 


1380 


60 


Central Nipon, Kofu. 


78 


It 


2 48 A.M. 


35-20 


1370 


120 


Gifu. 


79 


Jl 


2 52 A.M. 


36-30 


14010 


3 


N. of Tokio. 


80 


U 


5 33 A.M. 


400 


141-0 


160 


N. Nipon. 


81 


l» 


6 40 P.M. 


31-55 


131-30 


3 


W. Kiushiu. 


82 


It 


8 62 P.M. 


35-20 


137-0 


3 


N. of Nagoya. 


83 


tt 


10 37 P.M. 


35-20 


137-0 


70 


» t9 *f 


84 


22 


3 7 A.M. 


35-20 


137-0 


3 


It Tt tt 


85 


*i 


6 55 A.M. 


35-20 


137-0 


3 


ft t* If 


86 


»> 


9 21 P.M. 


34-30 


132-0 


3 


6. Nipon. 



1893. 



226 



REPORT — 1893. 



Earthquakes — cotitinued. 









Position of centre 


Diameter 






No. 


Day 


Time 






of area 
shaken in 


Remarks 














Latitude 

N. 


Longitude 
E. 


nautical 
miles 










H. jr. 












87 


22 


9 47 P.M. 


35-20 


137-0 


3 


N. of Nagoya. 




88 


23 


? 


37-0 


140-40 


60 


N. and S. on coast, N. of | 














Tokio. 




89 


19 


8 40 A.M. 


35-10 


136-50 


3 


\V. of Nagoya. 




90 


fl 


5 P.M. 


35-20 


137-0 


40 


N. „ 




91 




8 30 P.M. 


37-40 


139-50 


3 


N. Nipon. 




92 


24 


4 50 A.M. 


35-20 


137-0 


3 


N. of Nagoya. 




93 


f» 


6 14 A.M. 


35-20 


137-0 


3 


5» J» 1) 




94 


»» 


5 P.M. 


35-20 


137-0 


3 




> » *) 




95 


25 


40 A.M. 


35-30 


137-20 


3 




) 1» )» 




96 


»1 


7 38 A.M. 


35-30 


136-50 


10 




) »» »» 




97 


»J 


8 20 A.M. 


35-30 


137-20 


3 




9 *f t9 




98 




5 14 P.M. 


35-20 


1.37-0 


3 




I )» »» 




99 


26 


11 20 P.M. 


35-20 


137-0 


3 




> '» 19 




100 


27 


4 50 A.M. 


35-20 


1370 


3 




9 )* It 




101 


28 


11 56 P.M. 


35-20 


1370 


3 




» »» >» 





Note. — The reason that the diameter of the area shaken by many shocks is given 
as three miles is because the shock was only recorded at one place, and from inves- 
tigations on areas disturbed by small shocks this number may be taken as approxi- 
mately correct (see ' On a Seismic Survey made in Tokio,' Trans. Seis. Soc, vol. x.). 

Overturning and Fracturing op Masonry and other Columns. 

Tn tlie Twelfth Report (1892) it was stated that the form of a wall or 
pier which, rather than snapping at its base, would, when subjected to 
horizontal reciprocating motion, be as likely to snap at any one horizontal 
section as at any other had been determined. 

A brick building with walls approximating to this form has been 
designed and built by Professor K. Tatsumo on the Univer.sity com- 
pound. Mr. 0. A. W. Pownall, M.I.C.E., has constructed brick piers 
for the bridges on the Usui Pass, some of which are 110 feet high with 
similar sections. 

An experiment relating to overturning which is in progress is to 
determine the relationship between the dimensions of a body and the 
amplitude of motion which will fail to overturn the same, no matter how 
short the period of motion may be. 



Publication of a Seismological Journal. 

In consequence of many persons who took an active interest in 
seismology having left Japan, because work which formerly found a place 
in the publication of the Seismological Society now finds a place else- 
where, and for other reasons, the Seismological Society, which between 
1880 and 1892 had published sixteen volumes, ceased its existence. As 
a certain amount of work still continues in order to bring this before 
those who are interested in seismology, a seismological journal has been 
published and the first volume already issued. 



ON THE BIBLIOGRAPHY OF SPECTROSCOPY. 227 



Bibliography of Spect7'oscopy.— Report of the Committee, consisting 
of Professor H. McLeod (Ghairman), Professor W. C. Roberts- 
Austen (>S'ecre/!a*^?/), Mr. H. G-. Mad AX, and Dr. D. H. Nagel. 

The collection and verification of titles of papers on spectroscopy have 
been continaed during the past year, and it is expected that another 
instalment will be ready for printing at the next meeting. 



Mathematical Functions. — Report of the Committee, consisting 
of Lord Rayleigh {Chairman), Lord Kelvin, Professor Cayley, 
Professor B. Price, Mr. J. W. L. GtLAISHER, Professor A. Gr. 
GrREENHiLL, Professor W. M. Hicks, and Professor A. Lodge 
(Secretary), appointed for the purpose of calculating Tables of 
certain Mathematical Functions, and, if necessary, of taking 
steps to carry out the Calculations, and to publish the results in 
an accessible for m . 

The first Report of the CoQimittee was in 1889 (at Newcastle-on-Tyne), 
when they published tables of I„(a;) for integral values of n from to 11, 
from a!=0 to 60, at intervals of 0-2 ; I,j(a;) being defined by 

^"^"^=^"'''^"^'^^=2^{^ + 2(2^ + 24(2. + 2)(2. + 4)+ ' ' -j' 

The present tables of Ii(ie) are from x=0 to S'lOO, at intervals of "001, 
and are given to nine decimal places, the last figure being approximate. 
They have been calculated by means of Taylor's Theorem, the successive 
derived functions being obtained by use of the formula 

and of the formnlte derivable from this by successive differentiations. 
The values of these derived functions were checked by double cal- 
culation of the values of Ii(a;) halfway between those given in the 1889 
table; thus, for exnmple, Ti(2-3) was calculated as Ii(2'2 + 0"1) and also 
as Ii(2'4 — O'l). This important check confirmed at the same time the 
values of Ii(,^;) which were given in the 1889 table, so that certainly the 
tables now given are free from any systematic error. When the present 
tables were finished, accidental errors were discovered and corrected by 
taking out first and second differences, and then, finally, the printed tables 
were checked by continuous addition of the first diiferences on Edmond- 
son's calculatiuif machine. It is confidently hoped, therefore, that the 
tables are free from serious error. 

Tables of lo(.f) have also been calculated, and are in a forward state, 
but are not quite ready for printing this year. 

It is proposed to have the tables republished in book form when com- 

a 2 



228 



REPORT 1893. 



plete, together with tables of J„(^)j to six decimal places. It will be 
noticed that the march of Ii(a;) in the present table is such that interpo- 
lation by first differences only will give accnrate results to six decimal 
places. It is proposed to preface the book of tables with a short account 
of the History, Theory, and Applications of the Bessel Functions, drawn 
up by Professor A. Gr. Greenhill. 

The Committee are adding to the present Report a short table of 
3o{x\/i). If desired, a table of J„(.«\/i) from x^O to 6'0 at intervals of 0-2, 
for integral values of n from to 11, could be published next year. 

The Committee have expended the grant of 15Z., and desire reappoint- 
ment, with a further grant of 15/. 

The Secretary has some copies of the 1889 Report, and will have some 
of the present Report, which he will be pleased to forward to anyone wish- 
ing to make use of the tables before their republication in book form. 
His address is, Englefield Green, Surrey. 

The Committee wish to point out an error in the 1889 Report. The 
differential equation of which I„ is one solution has a wrong sign before 
its third term ; it should be 

x^ --^■\-x-—{x^-\-n^)u=\j. 
ax^ ax 

The work of calculation has been much hindered by faults in the 
Edmondson's calculating machine which was bought by the Committee. 
It has been returned to the maker several times, and has never been 
entirely satisfactory. Latterly the greater part of the work has been 
done on Professor McLeod's machine, which he is always kindly ready to 
lend. 



X 


•JoC^VO 


X 


JoCa^^/O 


Real part 


Coefficient of { 


Real part 


Coefficient of i 


0-0 

0-2 
04 
0-6 
0-8 

1-0 


+ 1-000 000 000 


Nil 


30 

3-2 
3-4 

3-6 
3-8 


-0-221 380 250 


-1-937 586 785 


+ 0-999 975 000 
+ 0-999 600 004 
+ 0-997 975 114 
+ 0-993 601 138 


-0-009 999 972 
-0-039 998 222 
-0-089 979 750 
-0-159 886 230 


-0-564 376 430 
-0-968 038 995 
-1-435 305 322 
-1-967 423 273 


-2-101 573 388 
-2-233 445 750 
-2-319 863 655 
-2-345 433 061 


+ 0-984 381 781 


-0-249 566 040 


4-0 


-2-563 416 557 


-2-292 690 323 


1-2 
1-4 
1-6 
1-8 


+ 0-967 629 156 
+ 0-940 075 057 
+ 0-897 891 139 
+ 0-8.36 721 794 


-0-358 704 420 
-0-486 733 934 
-0-632 725 677 
-0-795 261 955 


4-2 
4-4 
4-6 

4-8 


-3-219 479 832 
-3-928 .306 623 
-4-678 356 937 
-5-453 076 175 


-2-142 167 987 
-1-872 563 796 
-1-461 036 836 
-0-883 656 854 


2-0 


+ 0-751 7.34 183 ! -0-972 291 627 


5-0 

5-2 
5-4 
5-6 

5-8 


-6-230 082 479 


-0-116 034 382 


2-2 
2-4 

2-6 
2-8 

4 


+ 0-637 690 457 1 -1-160 969 944 
+ 0-489 047 772 -1-357 485 476 
+ 0-300 092 090 | -1-556 877 774 
+ 0-065 112 108 : -1-752 850 564 


-6-980 346 403 +0865 8.39 727 
-7-667 394 .351 [ +2084 516 693 
-8-246 575 962 ^ +3559 746 593 
-8-664 445 263 ' +5-306 844 640 

i 


30 


-0-221 380 250 | -1-937 586 785 


6-0 


-8-858 315 966 [ +7-334 746 541 



ON MATHEMATICAL FUNCTIONS. 



229 



X 


I,.r 


Difference 


' X 


hx 


Difference 


•000 


Nil 


500,000 


-050 


0025 007 814 


500,477 


•001 
•002 
•003 

•004 
•005 
•006 
•007 
•008 
•009 


0^000 500 000 
0-001 000 001 

0001 500 002 

0002 000 004 

0002 500 008 

0003 000 014 
0003 500 021 
004 000 032 
0-004 500 046 


500,001 
1 
2 
4 
6 
7 

11 
14 

17 


•051 
•052 
•053 
•054 
•055 
•056 

•057 
•068 
-059 

-060 


0^025 508 291 

0026 008 789 
0-026 509 H06 

0-027 009 843 

0027 510 399 

0028 010 978 

0028 511 577 
0-029 012 196 
0-029 512 838 


500,498 
517 
637 
556 
579 
599 
619 
642 
664 


•010 


0^005 000 063 


20 


0-030 013 602 


686 


•oil 

•012 
•013 
•014 
•015 
•016 

■017 
•018 
■019 


0^005 600 083 
0006 000 108 
0-006 500 137 
0^007 000 172 
0^007 500 211 
0^008 000 256 
008 500 307 
0-009 000 365 
0-009 500 429 


25 
29 
35 
39 
45 
51 

58 
64 
71 


•061 
•062 
•063 
•064 
•065 
•066 

•067 
•068 
•069 


0-030 514 188 
0-031 014 898 
0031 515 630 
0-032 016 387 
0-032 517 167 
0-033 017 972 

0033 518 801 
0^034 019 656 

0034 520 536 


710 
732 
757 
780 
805 
829 
855 
880 
905 


•020 


0-010 000 500 


79 


•070 


0035 021 441 


932 


•021 
•022 
•023 
•024 
•025 
•026 
•027 
•028 
•029 


0010 500 579 
0-011 000 666 
0-011 500 760 
0-012 000 864 
0-012 500 977 
0-013 001 099 
0-013 501 230 
0-014 001 372 
0-014 501 524 


87 

94 

104 

113 
122 
131 
142 

152 
163 


•071 
•072 
•073 
•074 
•075 
•076 

•077 
•078 
•079 


0-035 522 373 
0-036 023 333 
0-036 524 319 

0-037 025 332 
0^037 526 374 
0-038 027 443 

0-038 528 540 
0-039 029 667 
0-039 530 823 


960 
986 
501,013 
042 
069 
097 

127 
156 

186 


•030 


0-015 001 687 


175 


•080 

•081 
•082 
•083 
•084 
•085 
•086 

•087 
•088 
•089 


0-040 032 009 


215 


•031 
•032 
■033 
•034 
•035 
•036 
•037 
•038 
•039 


0016 501 862 
0016 002 048 
0-016 502 246 
0-017 002 457 
0-017 502 680 
0-018 002 916 
0-018 503 166 
0-019 003 430 
0-019 503 707 


186 
198 
211 

223 
236 
250 
264 
277 
293 


0-040 533 224 
0-041 034 470 
0-041 535 747 

0-042 037 055 
0-042 538 395 
0043 039 766 
0-043 541 170 
0-044 042 606 
0-044 544 075 


246 
277 
308 

340 
371 
404 
436 
469 
502 


•040 


0-020 004 000 


308 


•090 


0-045 045 577 


638 


•041 
•042 
•043 

•044 
•045 
•046 
•047 
•048 
■049 


0-020 504 308 
0-021 004 631 
0-021 504 969 
0-022 006 324 
0-023 505 695 
0-023 006 085 
0023 506 490 
0-024 006 913 
0-024 507 354 


323 
338 
355 

371 
390 
405 
423 
441 
460 


•091 
-092 
•093 
•094 
•095 
•096 

•097 
•098 
•099 


0045 547 115 

0046 048 685 
0-046 550 290 
0-047 051 930 
0-047 553 607 
0-048 055 317 
0048 557 065 
0-049 058 847 
0-049 560 668 

0-060 062 526 


670 
605 
640 

677 
710 
748 

783 
821 
858 


•050 


0-025 007 814 


477 


•100 


896 



230 



EEPOET — 1893. 



X 


Iix 


Difference 


X 


I,X 


Difference 




100 


0-050 062 526 


501,896 


•150 


0075 211 135 


504,254 




101 
102 
•103 

•104 
•105 
•106 

•107 
•108 
109 


0-050 564 422 
0-051 066 354 

0051 568 325 

0052 070 334 
0-052 572 384 
0-053 074 473 

0-053 576 602 
0-054 078 770 
0-054 580 980 


932 
971 

502,009 

050 
089 
129 

168 
210 
250 


•151 
•152 
-153 

•154 
•155 
•156 

-157 

•158 
-159 


0-075 715 389 
0-076 219 699 
0-076 724 068 

0-077 228 492 
0-077 732 975 
0-178 237 517 

0-078 742 117 
0079 246 776 
0079 751 494 


310 
369 
424 

483 
542 
600 

659 

718 

778 




•110 

•111 
112 
113 

•114 
•115 
•116 

•117 
118 
119 


0-055 083 230 


290 


•160 


0^080 256 272 


838 


0055 585 520 
0-056 087 853 
0-056 590 228 

0-057 092 646 
0-057 595 107 
0-058 097 611 

0-058 600 158 
0059 102 748 
0-059 605 385 


333 
375 
418 

461 
504 
547 

590 
637 

680 


•161 
•162 
•163 

■164 
•165 
•166 

•167 
■168 
•169 


0-080 761 110 
0-081 266 010 
0-081 770 971 

0-082 275 993 
0082 781 077 
0-083 286 222 

0-083 791 430 
0-084 296 701 
0-084 802 034 


900 

961 

505,022 

084 
145 
208 

271 
333 
398 




120 


0-060 108 065 


725 


•170 1 0-085 307 432 


462 


121 
122 
123 

124 
125 
126 

127 
128 
129 


0-060 610 790 
0-06] 113 561 
0-061 616 378 

0062 119 240 
0062 622 149 
0-063 125 106 

0-063 628 110 
0-064 131 161 
0064 634 262 


771 

817 

862 

909 
957 

503,004 

051 
101 

148 


•171 
•172 
•173 

-174 
•175 
■176 

•177 

•178 
•179 


0-085 812 894 
0086 318 421 

0086 824 Oil 

0087 329 667 
0-087 835 388 

0088 341 176 

0-088 847 030 
0-089 352 950 
0-089 858 939 


527 
590 
656 

721 j 
788 
854 1 

920 

989 

506,054 




130 1 0-065 137 410 


196 


•180 


0-090 364 993 


122 




•131 
•132 
•133 

•134 
•135 
•136 

•137 
•138 
•139 


0065 640 606 
0-066 143 853 
0-066 647 147 

0-067 150 494 
0-067 653 890 
0-068 157 337 

0-068 660 835 
0-069 164 387 
0-069 667 987 


247 
294 
347 

396 
447 
498 

552 
600 

652 


■181 
•182 
•183 

•184 
•185 
•186 

•187 
•188 
•189 


0^090 871 115 
0091 377 306 
0-091 883 565 

0-092 389 893 
0-092 896 291 
0-093 402 759 

0-093 909 296 
0-094 415 904 
0-094 922 583 


191 
259 
328 

398 
468 
537 

608 
679 
749 




•140 


0-070 171 639 


707 


•190 


0-095 429 332 


821 




•141 
•142 
•143 

•144 
145 
146 

147 
148 
149 


0-070 675 346 
0-071 179 106 
0-071 682 919 

0-072 186 786 
0-072 690 707 
0-073 194 682 

0^073 698 712 
0074 202 796 
0-074 706 938 


760 
813 
867 

921 

975 
504,030 

084 
142 
197 


•191 
•192 
■193 

•194 
•195 
•196 

•197 
•198 
•199 


0-095 936 163 
0096 443 047 
0-096 950 014 

0-097 457 053 
0.097 964 165 
0-098 471 350 

0-098 978 608 
0-099 485 942 
0-099 993 351 


894 

967 

507,039 

112 
185 
258 

334 

409 
483 


■ 


150 0-075 211 135 j 254 


•200 


0-100 500 834 


559 



ON MATHEMATICAL FUNCTIONS. 



231 



X 


I,x 


Diflcrence 


X 


I,.r 


Difference 


•200 


0100 500 834 


507,559 


•250 


0-125 979 109 


511,817 


•201 
•202 
•203 

■204 
•205 
•206 

•207 
•208 
•209 


0^101 008 393 
0^101 516 028 
0-102 023 738 

0^102 531 524 
0-103 039 3S9 

0103 547 331 

0104 055 350 
0104 563 447 
0-105 071 622 


507,635 
710 

786 

865 

942 

508,019 

097 
175 
256 


•251 
•252 
•253 

-254 
-255 
-256 

•257 
•258 
•259 


0-126 490 926 
0-127 002 838 
0-127 514 846 

0-128 026 948 
0-128 539 147 
0-129 051 443 

0-129 563 836 
0-130 076 326 
0-130 588 914 


511.912 

512,008 

102 

199 
296 
393 

490 
588 
685 


•210 


0-106 579 878 


333 


•260 


0131 101 599 


782 


•211 
•212 
•213 

•214 
•215 
•216 

•217 
•218 
•219 


0-106 088 211 
0-106 596 624 
0-107 105 118 

0-107 613 691 
0108 122 345 
0-108 631 OSl 

0-109 139 899 
0-109 648 798 
0-110 157 779 


413 
494 
573 

654 

736 i 

818 ' 

899 

981 

509,064 


•261 
•262 
•263 

•264 
•265 
•266 

-267 
-268 
-269 


0-131 614 381 
0-132 127 264 
0-132 640 247 

0-133 153 329 
0-133 666 510 
0-134 179 792 

0-134 693 175 
0-135 206 657 
0-135 720 242 


883 

983 

513,082 

181 
282 
383 

482 
585 
688 


•220 


0-110 666 843 


148 


•270 


0-136 233 930 


790 


•221 
•222 
•223 

•224 
•225 
•226 

•227 
•228 
•229 


0-111 175 991 
0-111 685 222 
0-112 194 536 

0-112 703 934 
0-113 213 418 
0-113 722 985 

0^114 232 639 
0-114 742 379 
0-115 252 204 


231 
314 
398 
484 
567 
654 

740 
825 
912 


•271 
•272 
•273 

•274 
•275 
•276 

•277 
•278 
•279 


0-136 747 720 
0-137 261 611 
0-137 775 606 

0-138 289 706 
0-138 803 907 
0-139 318 212 

0-139 832 624 
0-140 347 141 
0-140 861 762 


891 

995 

514,100 

201 
305 
412 

517 
621 
727 


•230 


0-115 762 116 


998 


•280 


0-141 376 489 


834 


•231 
•232 
•233 

•234 
•235 
•236 

•237 
•238 
•239 


0-116 272 114 
0-116 782 200 
0-117 292 374 

0-117 802 636 
0-118 312 986 
0-118 823 425 

0-119 333 953 
0-119 844 570 
0-120 355 277 


510,086 
174 
262 

350 
439 
528 

617 
707 

798 


•281 
•282 
•283 

•284 
•285 
•286 

•287 
•288 
•289 


0-141 891 323 
0-142 406 262 
0-142 921 308 

0-143 436 463 
0-143 951 725 
0-144 467 096 

0-144 982 574 
0-145 498 161 
0-146 013 857 


939 

515,046 

155 

262 
371 

478 

587 
696 
806 


•240 1 0-120 866 075 


889 


•290 


0-146 529 663 


917 


•241 
•242 
•243 

•244 
•245 
•246 

•247 
•248 
•249 


0-121 376 964 
0-121 887 944 
0-122 399 015 

0-122 910 179 
0-123 421 435 
0-123 932 784 

0-124 444 224 
0-124 955 759 
0-125 467 387 


980 

511,071 

164 

256 
349 
440 

635 
628 
722 


•291 
•292 
•293 

•294 
•295 
•296 

•297 
•298 
•299 


0-147 045 580 
0-147 561 607 
0-148 077 744 

0-148 593 992 
0-149 110 352 
0-149 626 824 

0-150 143 409 
0-150 660 106 
0151 176 916 


516,027 
137 
248 

360 

472 
585 

697 
810 
924 


•250 


0125 979 109 


817 


•300 


0151 693 840 


517,038 



232 



REPORT 1893. 



X 


l,x 


Difference 


X liX 


Difference 


•300 


0-151 693 840 


517,038 


•350 


0^177 693 400 


523,232 


•301 
•302 
•303 

•304 
•305 
•306 

•307 
•308 
•309 


0-152 210 878 
0-152 728 031 
0-153 245 298 

0-153 762 680 
0-154 280 177 
0-164 797 789 

0155 315 518 

0156 833 364 
0-156 351 328 


153 

267 
382 

497 
612 
729 

846 

964 

518,081 


•351 
•352 
-353 

•354 
■355 
•356 

•367 
■358 
■359 


0-178 216 632 
0-178 739 997 
0-179 263 496 

0-179 787 131 
0-180 310 901 
0-180 834 807 

0-181 358 848 
0-181 883 025 
0-182 407 339 


523,366 
499 
635 

770 

906 

524,041 

177 
314 
460 


•310 


0156 869 409 


197 


•360 


0182 931 789 


589 


•311 
•312 
•313 

•314 
•316 - 
•316 

•317 
•318 
•319 


0-157 387 606 
0157 905 923 
0-158 424 357 

0-158 942 912 
0-159 461 585 

0159 980 378 

0160 499 292 

0161 018 326 
0-161 537 481 


317 
434 

555 

673 
793 
914 

519,034 
155 
275 


•361 
■362 
■363 

■364 
•365 
•366 

•367 
■368 
•369 


0-183 456 378 
0-183 981 103 
0-184 505 968 

0-185 030 971 

0185 556 114 
0-186 081 395 

0186 606 815 
0-187 132 378 
0-187 658 079 


725 

865 
525,003 

143 

281 
420 

563 
701 
843 


•320 


0-162 056 756 


399 


•370 


0188 183 922 


985 


•321 
•322 
•323 

•324 
•325 
-326 

-327 
-328 
-329 


0-162 576 155 
0163 095 675 
0-163 615 316 

0-164 135 082 
0-164 654 972 

0165 174 983 

0-165 695 120 
0-166 215 380 

0166 735 766 


520 
641 
766 

890 

520,011 

137 

260 
386 
512 


•371 
■372 
■373 

■374 
■375 
■376 

•377 
■378 
•379 


0-188 709 907 
0189 236 033 
0189 762 302 

0-190 288 712 
0-190 815 268 
0-191 341 965 

0191 868 806 
0-192 395 791 
0-192 922 921 


526,126 
269 
410 

566 
697 
841 

985 

527,130 

275 


•330 


0-167 256 278 


636 


•380 


0-193 450 196 


421 


-331 
-332 
•333 

•334 
•335 
•336 

•337 
•338 
•339 


0-167 776 914 
0-168 297 677 
0-168 818 564 

0169 339 582 
0169 860 724 
0-170 381 994 

0-170 903 393 
0171 424 920 
0-17] 946 576 


763 

887 
521,018 

142 
270 
399 

627 
656 

785 


•381 
•382 
•383 

•384 
•385 
•386 

•387 
•388 
•389 


0-193 977 617 
0-194 505 183 
0-195 032 895 

0-195 660 754 
0-196 088 760 
0-196 616 914 

0-197 145 213 
0197 673 663 
0-198 202 261 


666 
712 
859 

528,006 
164 
299 

450 
598 
747 


•340 


0-172 468 361 


914 


•390 


0-198 731 008 


896 


•341 
•342 
•343 

■344 
-345 
-346 

•347 
•348 
■349 


0-172 990 275 

0173 512 319 
0-174 034 494 

0174 556 799 
0-175 079 237 
0-175 601 805 

0-176 124 505 
0-176 647 337 
0177 170 302 


522,044 
175 
305 

438 
668 
700 

832 

965 

523,098 


•391 
•392 
•393 

•394 
•395 
•396 

•397 
•398 
■399 


0-199 259 904 
0^199 788 950 
0-200 318 146 

0-200 847 493 
0-201 376 991 
0-201 906 639 

0-202 436 439 
0-202 966 391 
0-203 496 497 


529,046 
196 
347 

498 
648 
800 

962 

630,106 

269 


•350 


0-177 693 400 


232 


•400 


0-204 026 756 


411 



ON MATHEMATICAL FUNCTIONS. 



233 



X 


I,x 


Difference 


X Ijr Difference 


■400 


0-204 026 756 


530,411 

530,566 
720 
874 

531,028 
1,S4 
340 

497 
654 
810 


•450 


0-230 743 570 


538,592 


■401 
■402 
•403 

•404 
•405 
•406 

•407 
■408 
•409 

•410 


0-204 557 167 
0-205 087 733 
0-205 618 453 

0-206 149 327 
0-206 680 355 
0-207 211 539 

207 742 879 
0-208 274 376 
0-208 806 030 


•451 
•452 
•453 

•454 
•455 
•456 

•457 

•458 
•459 


0-231 282 162 
0-231 820 929 
0-232 359 869 

0-232 898 986 
0-233 438 277 
0-233 977 743 

0-234 517 386 
0-235 057 205 
0-235 597 201 


767 

940 

539,116 

292 
466 
643 

819 

996 

540,172 


0-209 337 840 


967 


•460 


0-236 137 373 


350 


•411 
•412 
•413 

•414 
•415 
•416 

•417 
•418 
■419 


0-209 869 807 
0-210 401 931 
0-210 934 215 

0-211 466 656 
0-211 999 256 
0-212 532 016 

0-213 064 937 
0-213 598 017 
0-214 131 259 


532,124 
284 
441 

600 
760 
921 

533,080 
242 

401 


■461 
•462 
•463 

•464 
•465 
•466 

•467 

•468 
•469 


0-236 677 723 
0-237 218 252 
0-237 758 969 

0-238 299 845 
0-238 840 910 
0-239 382 155 

0-239 923 580 
0-240 465 185 
0-241 006 971 


529 

707 

886 

541,065 

- 245 

426 

605 

786 
967 


•420 


0-214 664 660 


663 


•470 


0-241 548 938 


642,149 


•421 
•422 
•423 

■424 
■425 
•426 

•427 
•428 
•429 


0-215 198 223 
0215 731 947 
0-216 265 834 

0-216 799 883 
0-217 334 096 
0-217 868 472 

0-218 403 012 
0-218 937 717 
0-219 472 585 


724 

887 
534,049 

213 
376 
540 

705 

868 

535,033 


•471 
•472 
•473 

•474 
•475 
•476 

•477 
•478 
•479 


0-242 091 087 
0-242 633 418 
0-243 175 932 

0-243 718 629 
0-244 261 510 
0-244 804 574 

0-245 347 822 
0-245 891 253 
0-24(! 434 871 


331 

514 
697 

881 
543,064 

248 

431 

618 
803 


•430 

•431 
•432 
•433 

•434 
•435 
•436 

•437 
•438 
•439 


0-220 007 618 


199 


•480 


0-246 97!S 674 


989 


0-220 542 817 
0-221 078 182 
0-221 613 713 

0-222 149 411 
0-222 685 276 
0-223 221 309 

0-223 757 508 
0-224 293 877 
0-224 830 414 


365 
531 
698 

865 

536,033 

199 

369 
537 
707 


•481 

•482 
•483 

•484 
•485 
•486 

•487 

•488 
•489 


0-247 522 663 
0-248 066 838 
0-248 611 200 

0-249 155 748 
0-249 700 485 
0-250 245 410 

0-250 790 521 
0-251 335 823 
0-251 881 312 


544,175 
362 
548 

737 

925 

545,111 

302 
489 
681 


•440 1 '>225 367 121 


876 


•490 


0-252 426 993 


869 


•441 
•442 
•443 

•444 
•445 
•446 

•447 
•448 
•449 


0-225 903 996 
0-226 441 041 
0-226 978 256 

0-227 515 643 
0-228 053 201 
0-228 590 931 

0-229 128 832 
0-229 666 905 
0-230 205 152 


537,045 
215 

387 

558 
730 
901 

538,073 
247 
418 


•491 
•492 
•493 

•494 
•495 
•496 

•497 
•498 
•499 


0-252 972 862 
0-253 518 922 
0-254 065 174 

0-254 611 615 
0-255 158 249 
0-255 705 074 

0-256 252 092 
0-256 799 303 
0-257 346 706 


546,060 
252 
441 

634 

825 

547,018 

211 
403 
598 


•450 


0-230 743 570 


592 


•500 


0-257 894 301 


793 



234 



EEPOET 1893. 





I,^- 


Difference 


X 


l,x 


Difference 


■500 


0^257 894 304 


547,793 


•550 


0-285 530 329 


558,029 


•501 
•502 
•503 


0'258 442 097 
0-258 990 084 
0-259 538 266 


987 

548,182 

375 


•551 
-552 
-553 


0-286 088 358 
0-286 646 603 
0-287 205 062 


558,245 
459 
676 


•504 
•505 
•50G 


0-260 086 641 
0-260 635 213 
0-261 183 983 


572 
770 
965 


-554 
■555 
•556 


0-287 763 738 
0-288 322 632 
0-288 881 741 


894 

559,109 

328 


•507 
•508 
•509 


0-261 732 948 
0-262 282 110 
0-262 831 469 


549,162 
359 
557 


•557 
-558 
-559 


0-289 441 069 
0-290 000 615 
0-290 560 378 


546 
763 
982 


•510 


0-263 381 026 


755 


-560 


0-291 120 360 


560,202 


•511 
•512 
•513 


0-263 930 781 
0-264 480 735 
0-265 030 888 


954 

550,153 

353 


-561 
•562 
-563 


0-291 680 562 
0-292 240 984 
0-292 801 626 


422 
642 
862 


•514 
•515 
•516 


0-265 581 241 
0-266 131 795 
0-266 682 548 


554 
753 
954 


-564 
•565 
■566 


0-293 362 488 
0-293 923 572 
0-294 484 876 


561,084 
304 
527 


•517 
•518 
•519 


0-267 233 502 
0-267 7«4 655 
0-268 336 012 


551,153 
357 
559 


■567 
•568 
-569 


0-295 046 403 
0-295 608 153 
0-296 170 124 


750 

971 

662,194 


•520 


0-268 887 571 


762 


-570 


0-296 732 318 


419 


•521 
•523 
•523 


0^269 439 333 
0^269 991 296 
0-270 543 463 


963 

552,167 

371 


-571 
•572 
-573 


0-297 294 737 
0-297 857 379 
0-298 420 245 


642 

866 

563,091 


•524 
•525 
•526 


0-271 095 834 
0-271 648 408 
0-272 201 187 


674 
779 

983 


-574 
•575 
•576 


0-298 983 336 
0-299 546 653 
0-300 110 195 


317 
542 

768 


•527 
•528 
•529 


0-272 754 170 
0-273 307 360 
0-273 860 756 


553,190 
396 
602 


•577 
•578 
-579 


0-300 673 963 
0-301 237 958 
0-301 802 180 


995 

564,222 

449 


•530 


0-274 414 358 


808 


-580 


0-302 3()6 629 


677 


•531 
•532 
•533 


0-274 968 166 
0-275 522 180 
0-276 076 403 


554,014 
223 
430 


-581 
•582 
•583 


0-302 931 306 
0-303 496 211 
0-304 061 346 


906 

565,134 

363 


•534 
•535 
•536 


0-276 630 833 
0-277 185 472 
0-277 740 319 


639 

847 
555,057 


•584 
•585 
•586 


0-304 626 708 
0-305 192 301 
0-305 758 124 


593 

823 

566,053 


•537 
•538 
•539 


0-278 295 376 
0-278 850 641 
0-279 406 117 


265 
476 
686 


•587 
•588 
•589 


0-306 324 177 
0-306 890 460 
0-307 456 976 


283 
515 
747 


•540 


0-279 961 803 


898 


•590 


0-308 023 722 


978 


•541 
•542 
■543 


0-280 517 701 
0-281 073 808 
0-281 630 129 


556,107 
321 
533 


•591 
•592 
•593 


0-308 590 700 
0-309 157 911 
0-309 725 356 


567,211 
445 
677 


•544 
•545 
•546 


0-282 186 662 
0-282 743 406 
0-283 300 363 


744 

957 

557,171 


•594 
•595 
•596 


0-310 293 033 
0-310 860 945 
0-311 429 091 


912 

568,146 

381 


■547 
•548 
•549 


0-283 857 534 
0-284 414 918 
0-284 972 516 


384 
598 
813 


•597 
•598 
•599 


0-3U 997 472 
0-312 566 088 
0-313 134 939 


616 

851 

569,087 


•550 


0-285 530 329 


558,029 j 


-600 


0-313 704 026 


323 



ON MATHEMATICAL FUNCTIONS. 



235 



X 


I,^- 


Difference 


X 


Ii.r 


Difference 


•600 


0-313 704 026 


569,323 




650 


0-342 468 895 


5.S 1,701 


-601 
•602 
•603 

•604 
•605 
•606 

•607 
•608 
•609 


0-314 273 349 
0-314 842 910 
0-315 412 708 

0-315 982 743 
0-316 553 017 
0-317 123 529 

0-317 694 280 
0-318 265 271 
0-318 836 502 


569,561 

798 

570,035 

274 
612 
751 

991 
571,231 

471 i 




651 
652 
653 

654 
655 
656 

657 
658 
659 


0-343 050 596 
0-343 632 556 
0-344 214 775 

0-344 797 253 
0-345 379 992 
0-345 962 992 

0-346 546 253 
0-347 129 775 
0-347 713 559 


581,960 
682,219 

478 

739 

583,000 

261 

522 

784 

584,046 


•610 


0-319 407 973 


712 1 




660 


0-348 297 605 


308 


•611 
•612 
•613 

•614 
-615 
•616 

•617 
•618 
•619 


0-319 979 685 
0-320 551 637 
0-321 123 831 

0-321 696 268 
0-322 268 947 
0-322 841 868 

0-323 415 034 
0-323 988 444 
0-324 562 098 


952 

572,194 

437 

679 

921 

573,166 

410 
654 
899 




661 
662 
663 

664 
665 
666 

667 
668 
669 


0-348 881 913 
0-349 466 485 
0-350 051 320 

0-350 636 419 
0-351 221 784 
0-351 807 413 

0-352 393 308 
0-352 979 468 
0-353 565 896 


572 

835 

585,099 

365 
629 
895 

586,160 
428 
694 


•620 


0^325 135 997 


574,143 




670 


0-354 152 590 


960 


•621 
•622 
•623 

•624 
•625 
-626 

•627 
•628 
•629 


0-325 710 140 
0-326 284 528 
0-326 859 163 

0^327 434 045 
0-328 009 173 
0-328 584 548 

0-329 160 172 
0-329 736 043 
0-330 312 163 


388 
635 
882 

575,128 
375 
624 

871 

576,120 

369 




671 
672 
673 

674 
675 
676 

677 
678 
679 


0-354 739 550 
0-355 326 778 
0-355 914 276 

0-356 502 041 
0-357 090 074 
0-357 678 378 

0-358 266 951 
0-358 855 796 
0-359 444 911 


587,228 
498 
765 

588,033 
304 
573 

845 

589,115 

386 


•630 


0-330 888 532 


619 




680 


0-360 034 297 


657 


•631 
•632 
•633 

•634 
•635 
•636 

•637 
•638 
•639 


0-331 465 151 
0-332 042 020 
0-332 619 139 

0-333 196 508 
0-333 774 128 
0-334 352 001 

0-334 930 126 
0-335 508 504 
0-336 087 134 


869 t 
577,119 ; 
369 

620 

873 

578,125 

378 
630 
884 




681 
682 
683 

684 
685 
686 

687 
688 
689 


0-360 623 954 
0-361 213 885 
0-361 804 088 

0-362 394 564 
0-362 985 313 
0-363 576 335 

0-364 167 632 
0-364 759 205 
0-365 351 053 


931 

590,203 

476 

749 

591,022 

297 

573 

848 

592,123 


•640 


0-336 666 018 


579,138 




690 


0-365 943 176 


399 


•641 
•642 
•643 

•644 
•645 
•646 

•647 
•648 
•649 


0-337 245 156 
0-337 824 549 
0-338 404 195 

0-338 984 097 
0-339 564 256 
0-340 144 670 

0-340 725 340 
0341 306 267 
0-341 887 452 


393 
646 
902 

580,159 
414 
670 

927 

581,185 

443 




691 
692 
693 

•694 
695 
696 

697 
698 
699 


0-366 535 575 
0-367 128 252 
0-367 721 206 

0-368 314 437 
0-368 907 945 
0-369 501 733 

0-370 095 800 
0-370 690 146 
0-371 284 771 


677 

954 

593,231 

508 

788 

594,067 

346 
625 
906 


•650 


0-342 468 895 


701 




700 


0-371 879 677 


595,187 



236 



KEPORT 1893. 



X 


l,,r 


Difference 


cc 


l^X 


Difference 


•700 


0371 879 677 


595,187 


•750 


0^401 992 463 


609,808 


■701 
•702 
•703 


0-372 474 864 
0373 070 333 
0-373 666 083 


595,469 

750 

596,031 


•751 
•752 
•753 


0^402 602 271 
0^403 212 384 
0^403 822 801 


610,113 
417 
723 


•704 
•705 
•706 


0^371 262 114 
0-374 858 428 
0375 455 025 


814 
597 

882 


•754 
•755 
•756 


©•404 433 524 
0-405 044 553 
0-405 655 888 


611,029 
335 
641 


•707 
•708 
•709 


0^376 051 907 
0-376 649 072 
0-377 246 521 


597,165 
449 
734 


•757 
•758 
•759 


0-406 267 529 
0-406 879 477 
0-407 491 732 


948 

612,255 

564 


•710 


0-377 844 255 


598,019 


•760 


0-408 104 296 


872 


•711 
•712 
•713 


0-378 442 274 
0-379 040 579 
0-379 639 171 


305 
692 
879 


•761 

•762 
•763 


0-408 717 168 
0-409 330 349 
0^409 943 840 


613,181 
491 

801 


•714 
•715 
•716 


0-380 238 050 
0-380 837 216 
0-381 436 668 


599,166 
452 
740 


•764 
•765 
•766 


0^410 557 641 
0^411 171 751 
0-411 786 172 


614,110 
421 
733 


•717 
•718 
•719 


0-382 036 408 
0-382 636 437 
0-383 236 756 


600,029 
319 
608 


•767 
•768 
•769 


0-412 400 905 
0-413 016 951 
0-413 631 307 


615,046 
356 
668 


•720 


0-383 837 364 


898 


•770 


0-414 246 975 


983 


•721 

•722 
•723 


0^384 438 262 
0-385 039 450 
0-385 640 928 


601,188 

478 
770 


•771 

•772 
•773 


0-414 862 958 
0-415 479 255 
0-416 095 865 


616,297 
610 
925 


•724 

•725 
•726 


0-386 242 698 
0-386 844 760 
0-387 447 114 


602,062 
354 
647 


•774 
•775 
•776 


0-416 712 790 
0-417 330 029 
0-417 947 586 


617,239 
557 
871 


■727 
•728 
•729 


0-388 049 761 
0-388 652 701 
0-389 255 934 


940 

603,233 

527 


■777 
•778 
■779 


0-418 565 457 
0-419 183 645 
0-419 802 149 


618,188 
504 
822 


•730 


0^389 859 461 


822 


■780 


0-420 420 971 


619,140 


•731 

•732 
•733 


©•390 463 283 
0391 067 399 
0-391 671 811 


604,116 
412 

708 


•781 
•782 
•783 


0-421 040 111 
0-421 659 669 
0-422 279 346 


458 

777 

620,097 


•734 
•735 
•736 


0-392 276 619 
0-392 881 524 
0-393 486 835 


605,005 
301 

598 


•784 
■785 
•786 


0-422 899 443 
0-423 519 860 
0-424 140 596 


417 

736 

621,057 


•737 
•738 
•739 


0-394 092 423 
0-394 698 320 
5-395 304 514 


897 

606,194 

493 


■787 
-788 
-789 


0^424 761 653 
0-425 383 032 
0-426 004 733 


379 

701 
622,022 


•740 


0-395 911 007 


792 


•790 


0-426 626 755 


345 


•741 

•742 
•743 


0-396 517 799 
0-397 124 890 
0-397 732 281 


607,091 
391 
692 


•791 

•792 
-793 


0-427 249 100 
0-427 871 768 
0-428 494 760 


668 

992 

623,315 


•744 
•745 
•746 


0-398 339 973 
0-398 947 967 
0-399 556 262 


994 

608,295 

597 


•794 
•795 
•796 


0-429 118 075 
0-429 741 715 
0-430 365 681 


640 

966 

624,291 


•747 
•748 
•749 


0-400 164 859 
0-400 773 758 
0-401 382 959 


899 

609,201 

504 


•797 
•798 
•799 


0-430 989 972 
0-431 614 588 
0^432 239 532 


616 

944 

625,270 


•750 


0-401 992 463 


808 


•800 


0-432 864 802 


598 



ON MATHEMATICAL FUNCTIONS. 



237 



X 


I,X 


Difference 


X 


l,x 


Difference 


-800 


0-432 864 802 


625,598 


-850 


0-464 555 845 


642,585 


•801 
-802 
-803 

-804 
•805 
•806 

-807 
-808 
-809 


0-433 490 400 
0-434 116 326 
0-434 742 580 

0-435 369 163 
0-435 996 075 
0-436 623 317 

0-437 250 888 
0-437 878 792 
0-438 507 026 


625,926 
626,254 

583 

912 

627,242 
571 

904 

628,234 

567 


-851 
-852 
-853 

•854 
-855 
-856 

■857 
-858 
-859 


0-465 198 430 
0-465 841 368 
0-466 484 659 

0-467 128 304 
0-467 772 303 
0-468 416 656 

0-469 061 363 
0-469 706 426 
0-470 351 844 


642,938 

643,291 

645 

999 
644,353 

707 

645,063 
418 

775 


•810 


0-439 135 593 


898 


-860 


0-470 997 619 


646,132 


-811 
-812 
-813 

-814 
-815 
-816 

-817 
-818 
-819 


0-439 764 491 
0-440 393 722 
0-441 023 287 

0-441 653 185 
0-442 283 418 
0-442 913 985 

0-443 544 886 
0-444 176 123 
0-444 807 696 


629,231 
565 

898 

630,233 
567 
901 

631,237 
573 
911 


-861 
-862 
-863 

-864 
-865 
-866 

-867 
-868 
-869 


0-471 643 751 
0-472 290 240 
0-472 937 087 

0-473 584 291 
0-474 231 854 
0-474 879 776 

0-475 528 058 
0-476 176 701 
0-476 825 705 


489 

847 

647,204 

563 

922 

648,282 

643 

649,004 

364 


-820 


0-445 439 607 


632,248 


■870 


0-477 475 069 


725 


•821 
•822 
-823 

-824 
-825 
-826 

-827 
-828 
-829 


0-446 071 855 
0-446 704 439 
0-447 337 362 

0-447 970 624 
0-448 604 223 
0-449 238 164 

0-449 872 445 
0-450 507 065 
0-45] 142 026 


584 

923 

633,262 

599 

941 

634,281 

620 

961 

635,303 


-871 
-872 
-873 

-874 
-875 

-876 

•877 
•878 
•879 


0-478 124 794 
0-478 774 883 
0-479 425 334 

0-480 076 148 
0-480 727 326 
0-481 378 868 

0-482 030 774 
0-482 683 046 
0-483 335 684 


650,089 
451 
814 

651,178 
542 
906 

652,272 

638 

653,004 


-830 


0-451 777 329 


646 


•880 


0-483 988 688 


371 


-831 
•832 
•833 

•834 
•835 
-836 

-837 
-838 
•839 


0-452 412 975 
0-453 048 961 
0-453 685 291 

0-454 321 964 
0-454 958 982 
0-455 596 344 

0-456 234 051 
0-456 872 103 
0-457 510 501 


986 

636,330 

673 

637,018 
362 
707 

638,052 
398 
744 


-881 
-882 
-883 

-884 
-885 
-886 

-887 
-888 
-889 


0-484 642 059 
0-485 295 797 
0-485 949 902 

0-486 604 375 
0-487 259 218 
0-487 914 430 

0-488 570 012 
0-489 225 964 
0-489 882 286 


738 

654,105 

473 

843 
655,212 

582 

952 

656,322 

693 


■840 


0-458 149 245 


639,091 


-890 


0-490 538 979 


657,066 


-841 
-842 
•843 

-844 
-845 
-846 

-847 
-848 
-849 


0-458 788 336 
0-459 427 775 
0-460 067 561 

0-460 707 696 
0-461 348 179 
0-461 989 012 

0-4G2 630 195 
0-463 271 728 
0-463 913 611 


439 

786 

640,135 

483 

833 

641,183 

533 

883 

642,234 


-891 
-892 
-893 

•894 
-895 
-896 

-897 
•898 
-899 


0-491 196 045 
0-491 853 483 
0-492 511 293 

0-493 169 477 
0-493 828 036 
0-494 486 968 

0-495 146 274 
0-495 805 955 
0-496 466 013 


438 

810 

658,184 

559 

932 

659,306 

681 

660,058 

435 


-850 


0-464 555 845 


585 


-900 


0-497 126 448 


811 



■238 



REPORT 1893. 



X 


\x 


Difference 


1 .r 


\x 


Difference 


•900 


\ 0497 126 448 


660,811 


■950 


0-530 639 310 


680,309 


•901 
•902 
•903 


: 0-497 787 259 

• 0-498 44S 447 

0-499 110 013 


661,188 
566 
945 


•951 
•952 
•953 


0-531 319 619 
0^532 000 331 
0^532 681 447 


680,712 

681,116 

520 


•904 
•905 
•906 


0^499 771 958 
0^500 434 281 
0^501 096 984 


662,323 

703 

663,082 


•954 
•955 
•956 


0^533 362 967 
0^534 044 892 
0-534 727 222 


925 

682,330 
737 


•907 
•908 
•909 


0^501 760 066 
0^502 423 530 
0^503 087 374 


464 

844 

664,225 


•957 
•958 
•959 


0-535 409 959 
0-536 093 102 
0-536 776 651 


683,143 
549 
957 


•910 


0-503 751 599 


608 


•960 

•961 
•962 
•963 


0-537 460 608 


684,365 


•911 
•912 
•913 


0-504 416 207 
0-505 081 197 
0^505 746 569 


990 

665,372 

756 


0^538 144 973 
0-538 829 747 
0-539 514 930 


774 

685,183 

592 


•914 
•915 
•916 


0^506 412 325 
0^507 078 466 
0507 744 991 


666,141 
525 
910 


•964 
•965 
•966 


0-540 200 522 
0-540 886 525 
0-541 572 938 


686,003 
413 

824 


•917 
•918 
■919 


0^508 411 901 
0-509 079 196 
0-509 746 878 


667,295 

682 

668,068 


•967 
•068 
•969 


0-542 259 762 
0-542 946 997 
0543 634 644 


687,235 

647 

688,061 


•920 


0-510 414 946 


455 


•970 


0^544 322 705 


475 


•921 
•922 
•923 


0-511 083 401 
0^51 1 752 243 
0-512 421 473 


842 

669,230 

619 


•971 

•972 
•973 


0^545 Oil 180 
0-545 700 0(55 
0-546 389 368 


885 

689,303 

717 


•924 
•925 
•926 


0^513 091 092 
0^513 761 102 
0514 431 502 


670,010 
400 

787 


•974 
•975 
•976 


0-547 079 085 
0-547 769 218 
0-548 459 766 


690,133 
548 
964 


•927 
•928 
■929 


0515 102 289 
0^515 773 468 
0^516 445 039 


671,179 
571 
962 


•977 
•978 
•979 


0-549 150 730 
0-549 842 113 
0-550 533 912 


691,383 

799 

692,217 


•930 

~93f^ 
•932 
•933 


0^517 117 001 


672,354 


•980 


0-551 226 129 


636 


0-517 789 355 
0518 462 101 
0-519 135 242 


746 

673,141 

535 


•981 
•982 
•983 


0-551 918 765 
0-552 611 821 
0-553 305 295 


693,056 
474 
896 


•934 
•935 
•936 


0-519 808 777 
0-520 482 706 
0521 157 030 


929 

674,324 

718 


•984 

•985 
•986 


0-553 999 191 
0-554 693 507 
0-555 388 244 


694,316 

737 

695,158 


•937 
•938 
•939 


0-521 831 748 
0-522 506 863 
0-523 182 373 


675,115 
510 
909 


-987 
•988 
•989 


0-556 083 402 
0-556 778 985 
0-557 474 989 


583 

696,004 

428 


•940 


0-523 858 282 


676,306 


•990 


0-558 171 417 


851 


•941 
•942 
•943 


0-524 534 588 
0-525 211 291 
0-525 888 393 


703 

677,102 

502 


-991 
-992 
•993 


0-558 868 268 
0-559 565 545 
0-560 263 247 


697,277 

702 

698,125 


•944 
•945 
■946 


0-526 565 895 
0-527 243 794 
0-527 922 096 


899 

678,302 

701 


•994 
•995 
•996 


0-560 961 372 
0-561 659 927 
0-562 358 906 


555 

979 

699,408 


•947 
•948 
•949 


0-528 600 797 
0-529 279 900 
0-529 959 404 


679,103 
504 
906 


•997 
•998 
-999 


0-563 058 314 
0-563 758 148 
0-564 458 412 


834 

700,264 

692 


•950 


0-530 639 310 


680,309 


1-000 


0-565 159 104 


701,122 



ON MATHEMATICAL FUNCTIONS. 



239 



X 

1-000 


l^x Difference 


X 


I,x 


Difference 


0-565 159 104 


701,122 ;l 1-050 

1 


0-600 752 614 


723,292 


1-001 
1002 
1-003 

1-004 
1-005 
1-006 

1-007 
1-008 
1-009 

1-010 

1-011 
1-012 
1-013 

1-014 
1-015 
1-016 

1-017 
1-018 
1-019 


0-565 860 226 
0-566 561 778 
0567 263 759 

567 966 172 
0-508 669 017 
0-569 372 294 

0-570 076 003 
0-570 780 145 
0-571 484 722 


701,552 

981 

702,413 

845 

703,277 

709 

704,142 

577 

705,011 


1-051 
1-052 
1-053 

1-054 
1-055 
1-056 

1-057 
1-058 
1-059 


0-601 475 906 
0-602 199 656 
0-602 923 864 

0-603 648 532 
0-604 373 058 
0-605 099 243 

0-605 825 289 
0-606 551 797 
0-607 278 766 


723,750 

724,208 
008 

725,126 

585 

726,046 

508 

969 

727,430 


0-572 189 733 


444 


1-060 

1-061 
1062 
1068 

1-064 
1-065 
1-006 

1067 
1-068 
1-009 


0-608 006 196 


895 


0-572 895 177 
0-573 601 059 
0-574 307 376 

0-575 014 130 
0-575 721 321 
0-576 428 949 

0-577 137 015 
0-577 845 521 
0-578 554 465 


882 

706,317 

754 

707,191 

628 

708,066 

506 

944 

709,382 


0-608 734 091 
0-609 462 447 
0-610 191 266 

0-610 920 552 
0-611 650 302 
0-612 380 517 

0-613 HI 198 
0-613 842 347 
0-614 578 961 


728.350 

819 

729,280 

750 

730,215 

681 

731,149 

614 

732,082 


1-020 


0-579 203 847 


825 


1-070 


0-615 306 043 


552 


1021 
1-022 
1-023 

1024 
1-025 
1-026 

1-027 
1-028 
1-029 

1-030 


0-579 973 672 
0-580 683 939 
0-581 394 644 

0-582 105 792 
0-582 817 384 
0-583 529 419 

0-584 241 896 
0-584 954 819 
0-585 668 186 


710,267 

705 

711,148 

592 

712,035 

477 

923 
713,367 

811 


1-071 
1-072 
1-073 

1-074 
1-075 
1-076 

1-077 
1-078 
1-079 


0-610 038 595 
0-616 771 614 
0-017 505 105 

0-618 239 064 

0018 973 496 

0019 708 396 

0-620 448 769 
0-621 179 615 
0-621 915 932 


733,019 
491 
959 

734,432 

900 

735,373 

846 
730,317 

792 


0-686 381 997 


714,259 


1-080 1 0-622 652 724 


737,266 


1-031 
1-032 
1033 

1034 
1-035 
1-036 

1-037 
1-038 
1-039 


0-5S7 096 256 
0-587 810 901 
0-588 526 112 

0-589 241 711 
0-589 957 759 
0-590 674 254 

0-591 391 198 
0-592 108 593 
0-592 826 438 


705 

715,151 

599 

716,048 
495 
944 

717,395 

845 

718,296 


1-081 
1-082 
1-083 

1-084 
1-085 

1-080 

1-087 
1-088 
1089 


0-628 889 990 
0-624 127 730 
0-624 865 947 

025 004 639 
0-626 343 806 
0-627 083 451 

0-627 823 573 
0-628 564 173 
0-029 305 252 


740 

788,217 

692 

739,167 

645 

740,122 

600 
741,079 

558 


1-040 


0-593 514 734 


747 


1-090 


0-630 046 810 | 742,038 


1041 
1042 
1-043 

1-044 
1-045 
1046 

1-047 
1-048 
1049 


0-694 263 481 
0-594 982 682 
0-595 702 333 

0-596 422 438 
0-597 142 998 
0-597 864 009 

0-598 585 477 
0-599 307 400 
0000 029 778 


719,201 

651 

720,105 

560 

721,011 

468 

923 

722,378 
836 


1-091 
1-092 
1-093 

1-094 
1-095 
1-096 

1-097 
1-098 
1-099 


0-630 788 848 
0-031 531 366 
0-632 274 305 

0-633 017 846 
0-633 761 809 
0-634 500 254 

0-635 251 184 
0-635 996 597 
0-686 742 493 


518 

999 

743,481 

963 

744,445 

930 

745,413 

896 

746,383 


1-050 


0-600 752 614 


723,292 1 


1-100 


0-637 488 876 


869 



240 



EEPORT — 1893. 



X 


ll.r 


Difference 


X 


I,x 


Difference 


1-100 


0-637 488 876 


746,869 


1-150 


0-675 439 326 


771,897 


l-lOl 
1-102 
1-103 

1-104 
1-105 
1-106 

1-107 
1-108 
1-109 


0-638 235 745 
0-638 983 099 
0-639 730 938 

0-640 479 267 
0-641 228 084 
0-641 977 387 

0-642 727 181 
0-643 477 463 
0-644 228 238 


747,354 

839 ' 
748,329 i 

817 

749,303 

794 

750,282 

775 

751,265 


1-151 
1-152 
1-153 

1-154 
1-155 
1-156 

1-157 
1-158 
1-159 


0-676 211 223 
0676 983 636 
0-677 756 565 

0678 530 012 
0-(;79 303 976 
0-680 078 458 

0-680 .S53 458 
0-681 628 980 
0-682 405 019 


772,413 

929 

773,447 

964 

774,482 
775,000 

522 

776,039 

563 


1-110 


0-644 979 503 755 j 


1-160 0-683 181 582 


777,081 


1-111 
1-112 
1-113 

1114 
1-115 
1116 

1-117 
1-118 
1-119 


0-645 731 258 
0-646 483 506 
0-647 236 246 

0-647 989 479 
0-648 743 207 
0-649 497 428 

0-650 252 145 
0-651 007 357 
0-651 763 066 


752,248 1 

740 
753,233 

728 
754,221 

717 
755,212 

709 
756,204 


1-161 
1-162 
1163 

1164 
1-165 
1166 

1167 
1-168 
1-169 


0-683 958 663 
0-684 736 268 
0-685 514 395 

0-686 293 044 
0-687 072 218 
0-687 851 916 

0-688 632 138 
0-689 412 885 
0-690 194 159 


605 

778,127 
649 

779,174 

698 

780,222 

747 

781,274 

801 


1-120 


0-652 519 270 


702 i 


1170 


0-690 975 960 782,329 


1-121 
1122 
1123 

1-124 
1-125 
1126 

1-127 
1128 
1-129 


0-653 275 972 
0-654 033 172 
0-654 790 871 

0-655 549 069 
0-656 307 766 
0-657 066 963 

0-657 826 661 
0-658 586 861 
0-659 347 564 


757,200 ; 
699 

758,198 

697 

759,197 

698 

760,200 

703 

761,205 


1171 
1-172 
1-173 

1-174 
1-175 
1-176 

1177 
1-178 
1-179 


0-691 758 289 
0-692 541 144 
0-693 324 528 

0-694 108 442 
0-694 892 885 
0-695 677 859 

0-696 463 363 
0-697 249 399 
0-698 035 968 


855 

783,384 

914 

784,443 

974 

785,504 

786,036 

569 

787,100 


1-130 


0-660 108 769 


706 


1-180 


0-698 823 068 


635 


1-131 
1-132 
1-133 

1134 
1-135 
1136 

1-137 
1-138 
1139 


0-660 870 475 
0-661 632 687 
0-662 395 402 

0-663 158 624 
0-663 922 351 
0-664 686 584 

0-665 451 322 
0-66(; 2U; 569 
0-666 982 324 


762,212 

715 

763,222 

727 

764,233 

738 

765,247 

755 

766,264 


1181 
1-182 
1183 

1-184 
1185 
1-186 

1-187 
1-188 
1-189 


0-699 610 703 
0-700 398 873 
0-701 187 576 

0-701 976 815 
0-702 766 590 
0-703 556 901 

0-704 347 750 
0-705 139 135 
0-705 931 059 


788,170 

703 

789,239 

775 

790,311 

849 

791,385 

924 

792,465 


1140 


0-667 748 588 


773 


1190 


0-706 723 524 


793,003 


1-141 
1-142 
1-143 

1-144 
1-145 
1146 

1-147 
1-148 
1-149 


0-668 515 361 
0-669 282 642 
0-670 050 436 

0-670 818 738 
0-671 587 555 
0-672 356 882 

0-673 126 722 
0-673 897 076 
0-674 667 944 


767,281 

794 

768,302 

817 

769,327 

840 

770,354 

868 
771,382 


1191 
1-192 
1-193 

1-194 
1195 
1196 

1197 
1-198 
1199 


0-707 516 527 
0-708 310 071 
0-709 104 155 

0-709 898 781 
0-710 693 949 
0-711 489 658 

0-712 285 912 
0-713 082 711 
0-713 880 054 


544 

794,084 

626 

795,168 

709 

796,254 

799 
797,343 

888 


1-150 


0-675 439 326 


897 


1-200 


0-714 677 942 


798,433 



ON MATHEMATICAL FUNCTIONS. 



241 



X 


\,x 


Difference 


X 


l,x 


Difference 


1-200 


0-714 677 942 


798,433 


1-250 


0-755 281 420 


826,532 


1-201 

1-202 
1-203 

1-204 
1-205 
1-206 

1-207 
1-208 
1-209 


0-715 476 375 
0-716 275 355 
0-717 074 883 

0-717 874 958 
0-718 675 681 
0-719 476 753 

0-720 278 475 
0-721 080 747 
0-721 883 570 


798,980 
799,528 
800,075 

623 

801,172 

722 

802,272 

823 

803,374 


1-251 
1-252 
1-253 

1-254 
1-255 
1-256 

1-257 

1-258 
1-259 


0-756 107 952 
0-756 935 062 
0-757 762 752 

0-758 591 022 
0-759 419 871 
0-760 249 302 

0-761 079 314 
0-761 909 908 
0-762 741 085 


827,110 

690 

828,270 

849 
829,431 
830,012 

594 

831,177 

761 


1-210 


0-722 686 944 


927 


1-260 


0-763 572 846 


832,346 


1-211 
1-212 
1-213 

1-214 
1-215 
1-216 

1-217 
1-218 
1-219 


0-723 490 871 
0-724 295 351 
0-725 100 384 

0-725 905 970 
0-726 712 110 

0-727 518 807 

0-728 326 061 
0-729 133 869 
0-729 942 235 


804,480 

805,033 

586 

806,140 
697 

807,254 

808 

808,366 

925 


1-261 
1-262 
1-263 

1-264 
1-265 
1-266 

1-267 
1-268 
1-269 


0-764 405 ]92 
0-765 238 123 
0-766 071 637 

0-766 905 737 
0-767 740 425 
0-768 575 702 

0-769 411 566 
0-770 248 019 
0-771 085 059 


931 

833,514 
834,] 00 

688 

835,277 

864 

836,453 

837,040 

632 


1-220 


0-730 751 160 


809,483 


1-270 

1-271 
1-272 
1-273 

1-274 
1-275 
1-276 

1-277 

1-278 
1-279 


0-771 922 691 


838,223 


1-221 
1-222 
1-223 

1-224 
1-225 
1-226 

1-227 
1-228 
1-229 


0-731 560 643 
0-732 370 685 
0-733 181 285 

0-733 992 447 
0-734 804 170 
0-735 616 454 

0-736 429 300 
0-737 242 710 
0-738 056 683 


810,042 

600 

811,162 

723 

812,284 

846 

813,410 

973 

814,536 


0-772 760 914 
0-773 599 729 
0-774 439 135 

0-775 279 133 
0-776 119 725 
0-776 960 911 

0777 802 693 
0-778 615 070 
0-779 488 042 


815 

839,406 

998 

840,592 
841,186 

782 

842,377 

972 

843,568 


1-230 


0-738 871 219 


815,104 


1-280 


0-780 331 610 


844,166 


1-231 
1-232 
1-233 

1-234 
1-235 
1-236 

1-237 
1-238 
1-239 


0-739 686 323 
0-740 501 989 
0-741 318 222 

0-742 135 022 
0-742 952 390 
0-743 770 325 

0-744 588 829 
0-745 407 902 
0-746 227 545 


666 

816,233 

800 

817,368 

935 

818,504 

819,073 

643 

820,213 


1-281 

1-282 
1-283 

1-284 
1-285 
1-286 

1-287 
1-288 
1-289 


0-781 175 776 
0-782 020 541 
0-782 865 905 

0-783 711 866 
0-784 558 427 
0-785 405 591 

0-786 253 356 
0-787 101 722 
0-787 950 691 


765 

845,364 

961 

846,561 

847,164 

765 

848,366 

969 

849,572 


1-240 


0-747 047 758 


785 


1-290 


0-788 800 263 


850,176 


1-241 
1-242 
1-243 

1-244 
1-245 
1-246 

1-247 
1-248 
1-249 


0-747 868 543 
0-748 689 900 
0-749 511 830 

0-750 334 333 
0-751 157 409 
0-751 981 060 

0-752 805 285 
0-753 630 087 
0-754 455 465 


821,357 

930 

822,503 

823,076 

651 

824,225 

802 

825,378 

955 


1-291 
1-292 
1-293 

1-294 
1-295 
1-296 

1-297 
1-298 
1-299 


0-789 650 439 
0-790 501 220 
0-791 352 607 

0-792 204 599 
0-793 057 198 
0-793 910 404 

0-794 764 218 
0-795 618 641 
0-796 473 673 


781 

851,387 

992 

852,599 

853,206 

814 

. 854,423 

855,032 

641 


1-250 


0-755 281 420 


826,532 


1-300 


0-797 329 314 


856,253 



1893. 



242 



REPORT — 1893. 



X 


\,x 


Difference 


X 


l,x 


Difference 


1-300 


0-797 329 314 


856,253 


1-350 


0-840 904 230 


887,659 


1-301 
1-302 
1-.303 

1-304 
1-305 
1-306 

1-307 
1-308 
1-309 


0-798 185 567 
0-799 042 432 
0-799 899 908 

0-800 757 997 
0-801 616 700 
0-802 476 017 

0-803 335 948 
0-804 196 495 
0-805 057 659 


856,865 
857,476 
858,089 

703 

859,317 

931 

860,547 

861,164 

779 


1-351 
1-352 
1-353 

1-354 

1-355 
1-356 

1-357 
1-358 
1-359 


0-841 791 889 
0-842 680 193 
0-843 569 142 

0-844 458 739 
0-845 348 983 
0-846 239 878 

0-847 131 419 
0-848 023 611 
0-848 916 454 


888,304 
949 

889,597 

890,244 
895 

891,541 

892,192 

843 

893,495 


1-310 


0-805 919 438 


862,397 


1-360 


0-849 809 949 


894,147 


1-311 
1-312 
1-313 

1-314 
1-315 

1-316 

1-317 
1-318 
1-319 


0-806 781 835 
0-807 644 850 
0-808 508 483 

0-809 372 737 
0810 237 612 
0-811 103 105 

0-811 969 222 
0-812 835 960 
0-813 703 322 


863,015 

633 

864,254 

875 
865,493 
866,117 

738 

867,.362 

985 


1-361 
1-362 
1-363 

1-364 
1-365 
1-366 

1-367 
1-368 
1-369 


0-850 704 096 
0-851 598 895 
0-852 494 348 

0-853 390 456 
0-854 287 217 
0-855 184 634 

0-856 082 707 
0-856 981 4.39 
0-857 880 827 


799 
895,453 
896,108 

761 
897,417 
898,073 

732 
899,388 
900.045 

707 


1-320 


0-814 571 307 


868,610 


1-370 


0-858 780 872 


1-321 
1-322 
1-323 

1-324 
1-325 
1-326 

1-327 
1-328 
1-329 


0-815 439 917 
0-816 309 151 
0-817 179 010 

0-818 049 496 
0-818 920 609 
0-819 792 351 

0-820 664 719 
0-821 537 718 
0-822 411 345 


869,234 

859 
870,486 

871.113 

742 
872,368 

999 
873,627 
874,258 


1-371 
1-372 
1-373 

1-374 
1-375 
1-376 

1-377 
1-378 
1-379 


0-85:^ 681 579 
0-860 582 946 
0-861 484 971 

0-862 387 658 
0-863 291 007 
0-864 195 019 

0-865 099 695 
866 005 036 
0-866 911 041 


901,367 

902,025 

687 

903,349 

904,012 

676 

90.5,341 

906,005 

669 


1-330 

1-331 
1-332 
1-333 

1-334 
1335 
1-336 

1-337 
1-338 
1-339 


0-823 285 603 


890 


1-380 


0-867 817 710 


907,336 


0-824 160 493 
0-825 036 015 
0-825 912 169 

0-826 788 955 
0-827 666 377 
0-828 544 434 

0-829 423 123 
0-830 302 451 
0-831 182 413 


875,522 

876,154 

786 

877,422 

878,057 

689 

879,328 

962 

880,602 


1-381 
1-382 
1-383 

1-384 
1-385 
1-386 

1-387 
1-388 
1-389 


0-868 725 046 
0-869 633 050 
0-870 541 720 

0-871 451 060 
0-872 361 068 
0-873 271 746 

0-874 183 095 
0-875 095 115 
0-876 007 808 


908,004 

670 

909,340 

910,008 

678 

911,349 

912,020 

693 

913,364 

914,040 


1-340 


0-832 063 015 


881,238 


1-390 


0-876 921 172 


1.341 
1-342 
1-343 

1-344 
1-345 
1-346 

1-347 
1-.S48 
1-349 


0-832 944 253 
0-833 826 132 
0-834 708 648 

0-835 591 805 
0-836 475 604 
0-837 360 043 

0-838 245 125 
0-839 130 849 
0-840 017 218 


879 
882,516 
88.3,157 

799 
884,439 
885,082 

724 
886,369 

887,012 


1-391 
1392 
1-393 

1-394 
1-395 
1-396 

1-397 
1-398 
1-399 

"^1-400^ 


0-877 835 212 
0-878 749 924 
0-879 665 311 

0-880 581 374 
0-881 498 114 
0-882 415 530 

0-883 333 625 
0-884 252 397 
0-885 171 8.50 


712 

915,387 
916,063 

740 
917,416 
918,095 

772 
919,453 
920,131 


1-350 


840 904 230 


659 


0-886 091 981 813 



ON MATHEMATICAL FUNCTIONS. 



243 



X 


I,x 


Difference 


X 


I,x 


Difference 


1-400 


0-880 091 981 


920,813 


1-450 


0-932 981 780 


955,788 


1-401 
1-402 
1-403 

1-404 
1-405 
1-406 

1-407 
1-408 
1-409 


0-887 012 794 
0-887 934 289 
0-888 856 465 

0-889 779 324 
0-890 702 866 
0-891 627 094 

0-892 552 007 
0-893 477 604 
0-894 403 888 


921,495 

922,176 

859 

923,542 

924,228 
913 

925,597 

926,284 

972 


1-451 
1-452 
1-453 

1-454 
1-455 
1-456 

1-457 

1-458 
1-459 


0-933 937 568 
0-934 894 075 
0-935 851 301 

0-936 809 247 
0-937 767 913 
0-938 727 301 

0-939 687 412 
0-940 648 246 
0-941 609 805 


956,507 

957,226 

946 

958,666 
959,388 
960,111 

834 
961,559 
962,282 


1-410 


0-895 330 860 


927,660 


1-460 


0-942 572 087 


963,008 


1-411 
1-412 
1-413 

1-414 
1-415 
1-416 

1-417 
1-418 
1-419 


0-896 258 520 
0-897 186 869 
0-898 115 908 

0-899 045 G36 
0-899 976 054 
0-900 907 166 

0-901 838 968 
0-902 771 466 
0-903 704 656 


928,349 
929,039 

728 

930,418 

931,112 

802 

932,498 
933,190 

884 


1-461 
1-462 
1-463 

1-464 
1-465 
1-466 

1-467 
1-468 
1-469 


0-943 535 095 
0-944 498 827 
0-945 463 289 

0-946 428 478 
947 394 395 
0-948 361 043 

0-949 328 417 
0-950 296 525 
0-951 265 363 


732 
964,462 
965,189 

917 
966,648 
967,374 

968,108 

838 

969,572 


1-420 


0-904 638 540 


934,581 


1-470 


0-952 234 935 

0-953 205 239 
0-954 176 278 
0-955 148 051 

0-956 120 557 
0-957 093 801 
0-958 067 782 

0-959 042 502 
0-960 017 959 
0-960 994 155 


970,304 


1-421 
1-422 
1 423 

1-424 
1-425 
1-426 

1-427 
1-428 
1-429 


0-905 573 121 
906 508 398 
907 444 371 

0-908 381 041 
0-909 318 411 
0-910 256 480 

0-911 195 247 
0-912 134 716 
0-913 074 887 


935,277 

973 

936,670 

937.370 
938,069 

767 
939,469 
940,171 

871 


1-471 
1-472 
1-473 

1-474 
1-475 
1-476 

1-477 
1-478 
1-479 


971,039 

773 

972,506 

973,244 
981 

974,720 

975,457 

976,196 

937 


1-430 


0-914 015 758 


941,575 


1-480 


0-961 971 092 


977,678 


1-431 
1-432 
1-433 
1-434 
1-435 
1-436 

1-437 
1-438 
1-439 


0-914 957 333 
0-915 899 611 
0-916 842 593 

0-917 786 282 
0-918 730 675 
0-919 675 774 

0-920 621 582 
0-921 568 097 
0-922 515 320 


942,278 

982 

943,689 

944,393 

945,099 

808 

946,515 

947,223 

935 


1-481 
1-482 
1-483 

1-484 
1-485 
1-486 

1-487 
1-488 
1-489 


0-962 948 770 
0-963 927 190 
0-964 906 350 

0-965 886 255 
0-966 866 902 
0-967 848 295 

968 830 435 
0-969 813 318 
0-970 796 951 


978,420 

979,160 

905 

980,647 
981,393 
982,140 

883 
983,633 
984,379 


1-440 


0-923 463 255 


948,645 


1-490 


0-971 781 330 


985,129 


1 441 
1-442 
1-443 

1-444 
1-445 
1-446 

1-447 
1-448 
1-449 


924 411 900 
0-925 361 253 
0-926 311 321 

0-927 262 100 
0-928 213 593 
0-929 165 799 

0-930 118 720 
0-931 072 356 
0-932 026 709 


949,353 

950,068 

779 

951,493 

952,206 

921 

953,636 
954,353 
955,071 


1-491 
1-492 
1-493 

1-494 
1-495 
1-496 

1-497 
1-498 
1-499 


0-972 766 459 
0-973 752 335 
0-974 738 964 

0-975 726 343 
0-976 714 474 
0-977 703 355 

0-978 692 992 
0-979 683 382 
980 674 527 


876 
986,629 
987,379 

988,131 

881 

989,637 

990,390 

991,145 

901 


1-450 


0-932 981 7 80 1 788 


1-500 


0-981 666 428 


992,657 



244 



KEPORT — 1893. 



X 


Iia- 


Difference 


X 


1,X 


Difference 


1-500 


0-981 666 428 


992,657 


1-550 


1-032 242 518 


1,031,498 


1-501 
1-502 
1-503 

1-504 
1-505 
1-506 

1-507 
1-508 
1-509 


0-982 659 085 
0-983 652 501 
0-984 646 674 

0-985 641 605 
0-986 637 296 
0-987 633 747 

0-988 630 959 
0-989 628 934 
0-990 627 671 


993,416 

994,173 

931 

995,691 
996,451 
997,212 

975 
998,737 
999,499 


1-551 
1-552 
1-553 

1-554 
1-555 
1-556 

1-557 
1-558 
1-559 

1-560 


1-033 274 016 

1034 306 312 

1035 339 407 

1-036 373 300 
1-037 407 993 
1-038 443 488 

1-039 479 783 
1-040 516 881 
1041 554 782 


1,032,296 

1,033,095 

893 

1,034,693 
1,035,495 
1,036,295 

1,037,098 

901 

1,038,706 


1-510 


0-991 627 170 


1,000,266 


1-042 593 488 


1,039,511 


1-511 

1-512 
1-513 

1-514 
1-515 
1-516 

1-517 
1-518 
1-519 


0-992 627 436 
0-993 628 467 
0-994 630 263 

0-995 632 826 
0-996 636 156 
0-997 640 255 

0-998 645 123 
0-999 650 762 
1-000 657 171 


1,001,031 

796 

1,002,563 

1,003,330 

1,004,099 

868 

1,005,639 
1,006,409 
1,007,180 


1-561 
1-562 
1-563 

1-564 
1-565 
1-566 

1-567 
1-568 
1-569 


1-043 632 999 
1-044 673 316 
1-045 714 438 

1-046 756 368 
1-047 799 106 
1-048 842 653 

1-049 887 010 
1-050 932 179 
1051 978 159 


1,040.317 

1,041,122 

930 

1,042,738 
1,043,547 
1,044,357 

1,045,169 

980 

1,046,792 


1-520 


1-001 664 351 


953 


1-570 


1-053 024 951 


1,047,604 


1-521 
1-522 
1-523 

1-524 
1-525 
1-526 

1-527 
1-528 
1-629 


1-002 672 304 
1-003 681 030 
1-004 690 528 

1-005 700 803 
1-006 711 852 
1-007 723 678 

1-008 736 283 
1-009 749 665 
1-010 763 824 


1,008,726 
1,009,498 
1,010,275 

1,011,049 

826 

1,012,605 

1,013,382 

1,014,159 

941 


1-571 
1-572 
1-573 

1-574 
1-575 
1-576 

1-577 
1-578 
1-579 

1-580 


1-054 072 555 
1-055 120 974 
1-056 170 209 

1-057 220 260 

1058 271 126 

1059 322 809 

1-060 375 311 
1061 428 633 
1-062 482 773 


1,048,419 
1,049,235 
1,050,051 

866 
1,051,683 
1,052,502 

1,053,322 

1,054,140 

962 


]-530 


1-011 778 765 


1,015,720 


1-063 537 735 


1,055,784 


1-531 
1-532 
1-533 

1-534 
1-535 
1-536 

1-537 
1-538 
1-539 


1-012 794 485 
1-013 810 985 
1-014 828 270 

1-015 846 336 
1016 865 186 
1-017 884 818 

1-018 905 239 
1-019 926 444 
1-020 948 436 


1,016,500 
1,017,285 
1,018,066 

850 
1,019,632 
1,020,421 

1,021,205 

992 

1,022,780 


1-581 
1-582 
1-583 

1-584 
1-585 
1-586 

1-587 
1-588 
1-589 


1-064 593 519 
1065 650 124 
1-066 707 553 

1-067 765 807 
1-068 824 885 
1-069 884 790 

1-070 945 521 
1-072 007 079 
1073 069 465 


1,056,605 
1,057,429 
1,058,254 

1,059,078 

905 

1,060,731 

1,061,558 
1,062,386 
1,063,216 


1-540 


1-021 971 216 


1,023,570 


1-590 


1-074 132 681 


1,064,047 


1-541 
1-542 
1-543 

1-544 
1-545 
1-546 

1-547 
1-548 
1-549 


1-022 994 786 
1-024 019 143 
1-025 044 291 

1026 070 230 
1-027 096 960 

1028 124 483 

1029 152 802 
1-030 181 911 
1031 211 817 


1,024,357 

1,025,148 

939 

1,026,730 
1,027,523 
1,028,319 

1,029,109 

906 

1,030,701 

1,031,498 


1-591 
1-592 
1-593 

1-594 
1-595 
1-596 

1-597 
1-598 
1-599 


1-075 196 728 
1-076 261 605 
1077 327 313 

1-078 393 855 
1-079 461 229 
1-080 529 439 

1-081 598 483 
1-082 668 363 
1-083 739 080 


877 
1,065,708 
1,066,542 

1,067,374 
1,068,210 
1,069,044 

880 
1,070,717 
1,071,555 


1-550 


1-032 242 518 


1-600 


1-084 810 635 


1,072,393 



ON MATHEMATICAL FUNCTIONS. 



245 



X 


I,x 


Difference 


.r 


l,x 


Difference 


1-600 

1-601 
1-602 
1-603 

1-604 
1-605 
1-606 

1-607 
1-608 
1-609 


1-084 810 635 


1,072,393 


1-650 

1-651 
1-652 
1-653 

1-654 
1-655 
1-656 

1-657 
1-658 
1-659 


1-139 475 574 


1,115,429 


1-085 883 028 
1-086 956 261 
1-088 030 335 

1-089 105 249 
1-090 181 005 
1-091 257 605 

1-092 335 047 
1-093 413 335 
1-094 492 468 


1,073,233 

1,074,074 

914 

1,075,756 
1,076,600 
1,077,442 

1,078,288 

1,079,133 

979 


1-140 591 003 
1141 707 315 
1-142 824 510 

1-143 942 591 
1-145 061 558 
1146 181 412 

1-147 302 153 
1-148 423 783 
1-149 546 302 


1,116,312 
1,117,195 
1,118,081 

967 
1,119,854 
1,120,741 

1,121,630 
1,122,519 
1,123,410 


1-610 

1-611 
1-612 
1-613 

1-614 
1-615 
1-616 

1-617 
1-618 
1-619 


1-095 572 447 


1,080,826 


1-660 


1-150 669 712 


1,124,300 


1-096 653 273 
1-097 734 948 
1-098 817 471 

1-099 900 844 
1-100 985 067 
1102 070 143 

1-103 156 071 
1-104 242 852 
1-105 330 487 


1,081,675 
1,082,523 
1,083,373 

1,084,223 

1,085,076 

928 

1,086,781 
1,087,635 
1,088,490 


1-661 
1-662 
1-663 

1-664 
1-665 
1-666 

1-667 
1-668 
1-669 


1-151 794 012 
1-152 919 204 
1-154 045 291 

1-155 172 272 
1-156 300 146 
1-157 428 916 

1-158 558 584 
1-159 689 149 
1-160 820 609 


1,125,192 

1,126,087 

981 

1,127,874 
1,128,770 
1,129,608 

1,130,565 
1,131,460 
1,132,364 


1-620 


1-106 418 977 


1,089,346 


1-670 


1-161 952 973 


1,133,263 


1-621 
1-622 
1-623 

1-624 
1-625 
1-626 

1-627 
1-628 
1-629 


1-107 508 323 
1-108 598 525 
1-109 689 585 

1-110 781 503 
1-111 874 282 
1-112 967 920 

1-114 062 419 
1-115 167 780 
1-116 254 003 


1,090,202 

1,091,060 

918 

1 ,092,779 
1,093,638 
1,094,499 

1,095,361 
1,096,223 
1,097,088 


1-671 
1-672 
1-673 

1-674 
1-675 
1-676 

1-677 
1-678 
1-679 


1-163 086 236 
1-164 220 399 
1-165 355 465 

1-166 491 434 
1-167 628 306 
1-168 766 085 

1-169 904 768 
1171 044 358 
1-172 184 856 


1,134,163 

1,135,066 

969 

1,136,872 
1,137,779 
1,138,683 

1,139,590 
1,140,498 
1,141,405 


1-630 


1-117 351 091 


952 


1-680 


1-173 326 261 


1,142,314 


1-631 
1-632 
1-633 

1-634 
1-635 
1-636 

1-637 
1-638 
1-639 


1-118 449 043 
1-119 547 861 
1-120 647 544 

1-121 748 095 
1-122 849 514 
1-123 951 804 

1-125 054 961 
1-126 158 990 
1-127 263 890 


1,098,818 
1,099,683 
1,100,551 

1,101,419 
1,102,290 
1,103,157 

1,104,029 

900 

1,105,774 


1-681 
1-682 
1-683 

1-684 
1-685 
1-686 

1-687 
1-688 
1-689 


1-174 468 575 
1-175 611. 801 
1-176 755 937 

1-177 900 986 
1-179 046 948 
1-180 193 825 

1-181 341 615 
1-182 490 321 
1-183 639 944 


1,143,226 
1,144,136 
1,145,049 

962 
1,146,877 
1,147,790 

1,148,706 
1,149,623 
1,150,542 


1-640 


1-128 369 664 


1,106,646 


1-690 


1-184 790 486 


1,151,459 


1-641 
1-642 
1-643 

1-644 
1-645 
1-646 

1-647 
1-648 
1-649 

1-650 


1-129 476 310 
1-130 583 831 

1131 692 226 

1132 801 497 
1-133 911 645 
1-135 022 672 

1-136 134 577 
1-137 247 362 
1-138 361 028 


1,107,521 
1,108,395 
1,109,271 

1,110,148 

1,111,027 

905 

1,112,785 
1,113,666 
1,114,546 


1-691 
1-692 
1-693 

1-694 
1-695 
1-696 

1-697 
1-698 
1-699 


1-185 941 945 
1-187 094 324 

1-188 247 623 

1-189 401 843 
1-190 556 986 
1-191 713 052 

1-192 870 042 
1194 027 957 
1-195 186 797 


1,152,379 
1,153,299 
1,154,220 

1,155,143 

1,156,066 

990 

1,157,915 
1,158,840 
1,159,768 


1-139 475 574 


1,115,429 


1-700 


1-196 346 565 


1,160,695 



246 



IlEPOET — 1893. 



X 


Iix 


Difference 


X 


l,x 


Difference 


1-700 


1-196 346 


565 


1,160,695 


1-750 


1-255 537 


513 


1,208,290 


1-701 
1-702 
1-703 


1-197 507 
1-198 668 
1-199 831 


260 
885 
439 


1,161,625 
1,162,554 
1,163,485 


1-751 
1-752 
1-753 


1-256 745 
1-257 955 
1-259 165 


803 
068 
311 


1,209,265 
1,210,243 
1,211,223 


1-704 
1-705 
1-706 


1-200 994 
1-202 159 
1-208 324 


924 
341 
690 


1,164,417 
1,165,349 
1,166,282 


1-754 
1-755 
1-756 


1-260 376 
1-261 588 
1-262 801 


534 
736 

918 


1,212,202 
1,213,182 
1,214,160 


1-707 
1-708 
1-709 


1-204 490 
1-205 658 
1-206 826 


972 
189 
341 


1,167,217 
1,168,152 
1,169,088 


1-757 
1-758 
1-759 


1-264 016 
1-2G5 231 
1-266 447 


078 
223 
351 


1,215,145 
1,216,128 
1,217,112 


1-710 


1-207 995 


429 


1,170,026 


1-760 


1-267 664 


463 


1,218,097 


1-711 

1-712 
1713 


1-209 165 
1-210 336 
1-211 508 


455 
418 
320 


963 
1,171,902 
1,172,843 


1-761 
1-762 
1-763 


1-268 882 
1-270 101 
1-271 321 


560 
643 

712 


1,219,083 
1,220,069 
1,221,059 


1-714 
1-715 
1-716 


1-212 681 
1-213 854 
1-215 029 


163 
945 
672 


1,173,782 
1,174,727 
1,175,667 


1-764 
1-765 
1-766 


1-272 542 
1-273 764 
1-274 987 


771 
818 
854 


1,222,047 
1,223,036 
1,224,029 


1-717 
1-718 
1-719 


1-216 205 
1-217 381 
1-218 559 


339 

950 

507 


1,176,611 
1,177,557 
1,178,502 


1-767 
1-768 
1-769 


1-276 211 
1-277 436 
1-278 662 


883 
903 
916 


1,225,020 
1,226,013 
1,227,007 


1-720 


1-219 738 


009 


1,179,449 


1-770 


1-279 889 


923 

924 
921 
916 


1,228,001 

997 
1,229,995 
1,230,993 


1-721 

1-722 
1-723 


1-220 917 
1-222 097 
1-223 279 


458 
855 
199 


1,180,397 
1,181,344 
1,182,294 


1-771 
1-772 
1-773 


1-281 117 
1-282 346 
1-283 576 


1-724 
1-725 
1-726 


1-224 461 
1-225 644 
1-226 828 


493 
738 
933 


1,183,245 
1,184,195 
1,185,148 


1-774 
1-775 
1-776 


1-284 807 
1-286 039 
1-287 272 


909 
900 

891 


1,231,991 
1,232,991 
1,233,992 


1-727 
1-728 
1-729 


1-228 014 081 
1-229 200 182 
1-230 387 238 


1,186,101 
1,187,056 
1,188,011 

966 


1-777 
1-778 
1-779 


1-288 506 
1-289 741 
1-290 977 


883 
877 
874 


1,234,994 
1,235,997 
1,237,000 


1-730 


1-231 575 


249 


1-780 


1-292 214 


874 


1,238,006 


1-731 
1-732 
1-733 


1-232 764 
1-233 954 
1-235 145 


215 
138 
020 


1,189,923 
1,190,882 
1,191,841 


1-781 
1-782 
1-783 


1-293 452 
1-294 691 
1-295 931 


880 
891 
909 


1,239,011 
1,240,018 
1,241,026 


- 1-734 
1-735 
1-736 


1-236 336 
1-237 529 
1-238 723 


861 
662 
423 


1,192,801 
1,193,761 
1,194,723 


1-784 
1-785 
1-786 


1-297 172 
1-298 414 
1-299 658 


935 
969 
014 


1,242,034 
1,243,045 
1,244,055 


1-737 
1-738 
1-739 


1-239 918 
1-241 113 
1-242 310 


146 

832 
482 


1,195,686 
1,196,650 
1.197,614 


1-787 
1-788 
1-789 


1-300 902 
1-302 147 
1-303 393 


069 
137 
216 


1.245,068 
1,246,079 
1,247,094 


1-740 


1-243 508 


096 


1,198,581 


1-790 


1-304 640 


310 


1,248,109 


1-741 
1-742 
1-743 


1-244 706 
1-245 906 
1-247 106 


677 
223 

738 


1,199,546 
1,200,515 
1,201,483 


1-791 

1-792 

i 1-793 


1-305 888 
1-307 137 
1-308 387 


419 
544 
685 


1,249,125 
1.250,141 
1,251,159 


1-744 
1-745 
1-746 


1-248 308 
1-249 510 
1-250 714 


221 

673 
096 


1,202,452 
1.203,423 
1,204,395 


1-794 
1-795 
1-796 


1-309 638 
1-310 891 
1-312 144 


844 
022 
220 


1,252,178 
1,253,198 
1,254,219 


1-747 
1-748 
1-749 


1-251 918 
1-253 123 
1 254 330 


491 
857 
197 


1,205,366 
1,206,340 
1,207,316 


1-797 

\ 1-798 

1-799 


1-313 398 
1-314 653 
1-315 909 


439 
679 
943 


1,255,240 
1,256,264 
1,257,287 


1-750 


1-255 537 


513 


1,208,290 


1-800 


1-317 167 


230 


1,258,313 



ON MATHEMATICAL FUNCTIONS. 



247 



1 ' 


Iix 


Difterence 


X 


I.x 


Difference 


1 1-800 


1-317 167 230 


1,258,313 

1,259,338 
1,260,366 
1,261,393 

1,262,422 
1,263,452 
1,264,483 

1,265,615 
1,266,549 
1,267,583 


1-850 


1-381 359 709 1,310,868 


1 1-801 
1-802 
1-808 

1-804 
1-805 
1-806 

1-807 
1-808 
1-809 


1-318 425 543 
1-319 684 881 
1-320 945 247 

1-322 206 640 
1-323 469 062 
1-324 732 514 

1-325 996 997 
1-327 262 512 
1-328 529 061 


1-851 
1-852 
1-853 

1-854 
1-855 
1-856 

1-857 
1-858 
1-859 


1-382 670 577 
1-383 982 525 
1-385 295 551 

1-386 609 656 
1-387 924 843 
1-389 241 HI 

1-390 558 462 
1-391 876 899 
1-393 196 419 


1,311,948 
1,313,026 
1,314,105 

1,315,187 
1,316,268 
1,317,351 

1,318,437 
1,319,520 
1,320,607 


1-810 


1-329 796 644 


X268.618 


1-860 

1-861 
1-862 
1-863 

1-864 
1-865 
1-866 

1-867 
1-868 
1-869 


1-394 517 026 | 1,321,694 


1-811 
1-812 
1-813 

1-814 
1-815 
1-816 

1-817 

1-818 
1-819 


1-331 065 262 
1-332 334 915 
1-333 605 605 

1-334 877 334 
1-336 150 103 
1-337 423 911 

1-338 698 761 
1-339 974 653 
1-341 251 588 


1,269,653 
1,270,690 
1,271,729 

1,272,769 

1,273,808 
1,274,850 

1,275,892 
1,276,935 
1,277,980 


1-395 838 720 
1-397 161 502 
1-398 485 374 

1-399 810 338 
1-401 136 392 
1-402 463 539 

1-403 791 780 
1-405 121 116 
1-406 451 547 


1,322,782 
1,323,872 
1,324,964 

1,326,054 
1,327,147 
1,328,241 

1,329,336 
1,330,431 
1,331,529 


1-820 


1-342 529 568 


"T.279,024 


1-870 


1-407 783 076 


1,332,626 


1-821 

1-822 
1-823 

1-824 
1-825 
1-826 

1-827 
1-828 
1-829 


1-343 808 592 
1-345 088 6G3 
1-346 369 78] 

1-347 651 949 
1-348 935 166 
1-350 219 433 

1-351 504 752 
1-352 791 123 
1-354 078 548 


1,280,071 
1,281,118 
1,282,168 

1,283.217 
1,284,267 
1,285,319 

1,286,371 
1,287,425 
1,288,479 


1-871 

1-872 
1-873 

1-874 
1-875 
1-876 

1-877 
1-878 
1-879 


1-409 115 702 
1-410 449 427 
1-411 784 253 

1-413 120 180 
1-414 457 210 
1-415 795 341 

1-417 134 577 
1-418 474 921 
1-419 816 370 


1,333,725 
1,334,826 
1,335,927 

1,337,030 
1,338,131 
1,339,236 

1,340,344 
1,341,449 
1,342,557 


1-830 


1-355 367 027 | 1,289,535 ' 


1-880 


1-121 158 927 


1,343,666 


1-831 
1-832 
1-833 

1-834 
1-835 
1-836 

1-837 
1-838 
1-839 


1-356 656 562 
1-357 947 155 
1-359 238 805 

1-360 531 514 
1-361 825 282 
1-363 120 111 

1-364 416 004 
1-365 712 959 
1-367 010 977 


1,290,593 
1,291,650 
1,292,709 

1,293,768 
1,294,829 
1,295,893 

1,296.955 
1,298,018 
1,299,084 


1-881 
1-882 
1-883 

1-884 
1-885 
1-886 

1-887 
1-888 
1-889 


1-422 502 593 
1-423 847 368 
1-425 193 255 

1-426 540 254 
1-427 888 367 
1-429 237 593 

1-430 587 934 
1-431 939 394 
1-433 291 969 


1,344,775 
1,345,887 
1,346,999 

1,348,113 
1,349,226 
1,350,341 

1,351,460 
1.352,575 
1,353,694 


1-840 


1-368 310 061 


1,300,149 


1-890 


1 434 645 663 


1,354,814 


1-841 
1-842 
1-843 

1-844 
1-845 
1-846 

1-847 
1-848 
1-849 


1-369 610 210 
1-370 911 427 
1-372 213 712 

1-373 517 066 
1-374 821 492 
1-376 126 988 

1-377 433 557 
1-378 741 198 
1-380 049 915 


1,301,217 
1,302,285 
1,303,354 

1,.304,426 
1,305,496 
1,306,569 

1,307,641 
1,308,717 
1,309,794 


1-891 
1-892 
1-893 

1-894 
1-895 
1-896 

1-897 
1-898 
1-899 


1-436 000 477 
1-437 356 412 
1-438 713 468 

1-440 071 648 
1-441 430 953 
1-442 791 382 

1-444 152 937 
1-445 515 620 
1-446 879 432 


1,355,935 
1,357,056 
1,358,180 

1,359,305 
1,360.429 
1,361,555 

1,362,683 
1,363,812 
1,364,941 


1-850 


1-381 359 709 


1,310,868 


1-900 


1-448 244 373 


1,366,071 

.- 



248 



REPORT — 1893. 



X 


I,x 


Difference 


X 


l^x 


Difference 


1-900 

1-901 
1-902 
1-903 

1-904 
1-905 
1-906 

1-907 
1-908 
1-909 


1-448 244 373 


1,366,071 


1-950 


1-517 956 370 


1,424,038 


1-449 610 444 
1-450 977 648 
1-452 345 985 

1-453 715 455 
1-455 086 061 
1-456 457 803 

1-457 830 682 
1-459 204 700 
1-460 579 859 


1,367,204 
1,368,337 
1,369,470 

1,370,606 
1,371,742 
1,372,879 

1,374,018 
1,375,159 
1,376,298 


1-951 
1-952 
1-953 

1-954 
1-955 
1-956 

1-957 
1-958 
1-959 


1-519 380 408 
1-620 805 634 
1-522 232 049 

1-523 659 666 
1-525 088 453 
1-626 618 444 

1-527 949 630 
1-529 382 010 
1-530 815 587 


1,425,226 
1,426,415 
1,427,606 

1,428,798 
1,429,991 
1,431,186 

1,432,380 
1.433,577 
1,434,775 


1-910 


1-461 956 157 


1,377,440 


1-960 


1-532 250 362 


1,435,973 


1-911 
1-912 
1-913 

1-914 
1-915 
1-916 

1-917 
1-918 
1-919 


1-463 333 597 
1-464 712 179 
1-466 091 907 

1-467 472 780 
1-468 854 799 
1-470 237 964 

1-471 622 279 
1-473 007 743 
1-474 394 358 

1-475 782 125 


1,378,582 
1,379,728 
1,380,873 

1,282,019 
1,383,165 
1,384,315 

1,385,464 
1,386,615 
1,387,767 


1-961 
1-962 
1-963 

1-964 
1-965 
1-966 

1-967 
1-968 
1-969 


1-533 686 335 
1-535 123 508 
1-636 561 882 

1-538 001 458 
1-539 442 239 
1-540 884 224 

1-542 327 414 
1-643 771 811 
1-545 217 418 


1,437,173 

1,438,374 
1,439,576 

1,440,781 
1,441,985 
1,443,190 

1,444,397 
1,445,607 
1,446,816 


1-920 


1,388,919 


1-970 

1-971 

1-972 
1-973 

1-974 
1-975 
1-976 

1-977 
1-978 
1-979 


1-546 664 233 


1,448,023 


1-921 
1-922 
1-923 

1-924 
1-925 
1-926 

1-927 
1-928 
1-929 


1-477 171 044 
1-478 561 118 
1-479 952 347 

1-481 344 733 
1-482 738 276 
1-484 132 979 

1-485 528 841 
1-486 9-25 864 
1-488 324 048 


1,390,074 
1,391,229 
1,392,386 

1,393,543 
1,394,703 
1,395,862 

1,397,023 
1,398,184 
1,399,347 


1-548 112 256 
1-549 561 493 
1-561 Oil 944 

1-552 463 607 
1-553 916 485 
1-655 370 581 

1-556 825 894 
1-568 282 425 
1-569 740 176 


1,449,237 
1,450,451 
1,451,663 

1,452,878 
1,454,096 
1,455,313 

1,456,531 
1,457,751 
1,458,972 


1-930 


1-489 723 395 


1,400,513 


1-980 


1-561 199 148 


1,460,195 


1-931 
1-932 
1-933 

1-934 
1-935 
1-936 

1-937 
1-938 
1-939 


1-491 123 908 
1-492 525 585 
1-493 928 429 

1-495 332 441 
1-496 737 622 
1-498 143 972 

1-499 551 494 
1-500 960 188 
1-502 370 055 


1,401,677 
1,402,844 
1,404,012 

1,405,181 
1,406,350 
1,407,522 

1,408,694 
1,409,867 
1,411,041 


1-981 
1-982 
1-983 

1-984 
1-985 
1-986 

1-987 
1-988 
1-989 


1-562 659 343 
1-564 120 762 
1-665 583 406 

1-567 047 273 
1-568 512 369 
1-569 978 694 

1-571 446 246 
1-572 915 029 
1-574 385 044 


1,461,419 
1,462,643 
1,463,868 

1,465,096 
1,466,326 
1,467,552 

1,468,783 
1,470,015 
1,471,249 


1-940 


1-503 781 096 


1,412,218 


1-990 


1-575 856 293 


1,472,483 


1-941 
1-942 
1-943 

1-944 
1-945 
1-946 

1-947 
1-948 
1-949 


1-505 193 314 
1-506 606 710 
1-508 021 283 

1-509 437 034 
1-510 853 965 
1-512 272 078 

1-513 691 374 
1-515 111 854 
1-516 533 519 


1,413,396 
1,414,573 
1,415,751 

1,416,931 
1,418,113 
1,419,296 

1,420,480 
1.421,665 
1,422,851 


1-991 
1-992 
1-993 

1-994 
1-996 
1-996 

1-997 
1-998 
1-999 


1-577 328 776 
1-578 802 494 
1-580 277 449 

1-581 753 642 
1-583 231 073 
1-584 709 743 

1-586 189 655 
1-587 670 811 
1-589 153 211 


1,473,718 
1,474,955 
1,476,193 

1,477,431 
1,478,670 
1,479,912 

1,481,156 
1,482,400 
1,483,644 


1-950 


1-517 956 370 


1,424,038 


2 000 


1-590 636 855 


1,484,890 



ON MATHEMATICAL FUNCTIONS. 



249 



X 


I,x 


Difterence 


t 

1 X 


I,:r 


Difference 


2-000 1 1-590 636 855 


1,484,890 


2-050 


1-666 433 299 


1,548,758 

1,550,067 
1,551,380 
1,552,688 

1,554,004 
1,555,316 
1,556,631 

1,557,949 
1,559,266 
1,560,586 


2001 
2-002 
2-003 

2004 
2-005 
2-006 

2007 
2-008 
2009 

2010 


1-592 121 745 
1-593 607 882 
1-595 095 268 

1-596 583 904 
1-598 073 791 
1-599 564 930 

1-601 057 323 
1-602 550 970 
1-604 045 872 


1,486,137 
1,487,386 

1,488,636 

1.489,887 
1,491,139 
1,492,393 

1,493,647 
1,494,902 
1,496,161 


2-051 
2052 
2053 

2054 
2-055 
2-056 

2-057 
2-058 
2-059 


1-667 982 057 
1-669 532 124 
1-671 083 504 

1-672 636 192 
1-674 190 196 
1-675 745 512 

1-677 302 143 
1-678 860 092 
1-680 419 358 


1-605 542 033 


1,497,418 

1,498,678 
1,499,938 
1,501,201 

1,502,463 
1,503,728 
1,504,994 

1,506,261 

1,507,528 
1,508,797 


2060 


1-681 979 944 


1,561,906 


2-011 
2-012 
2-013 

2-014 
2-015 
2-016 

2-017 
2-018 
2-019 


1-607 039 451 

1-608 538 129 
1-610 038 067 

1-611 539 268 
1-613 041 731 
1-614 545 459 

16 16 050 453 
1-(;17 556 714 
1-619 064 242 


2061 
2-062 
2063 

2-064 
2-065 
2-066 

2-067 
2-068 
2-069 


1-683 541 850 
1-685 105 077 
1-686 669 628 

1-688 235 503 
1-689 802 704 
1-691 371 231 

1-692 941 087 
1-694 512 271 
1-696 084 786 


1,563,227 
1,564,551 
1,565,875 

1,567,201 
1,568,527 
1,669,856 

1,671,184 
1,672,515 
1.573,849 


2-020 


1-620 573 039 


1,510,068 


2-070 


1-697 {)58 635 


1,575,179 


2-021 
2022 
2-023 

2-024 
2-025 
2-026 

2-027 
2-028 
2-020 

2-030 


1-622 083 107 
1-623 594 447 
1-625 107 060 

l-(;26 620 947 
1-628 136 109 
1-629 652 549 

1-631 170 266 
1-632 689 261 
1-634 209 637 


1,511,340 
1,512,613 
1,613,887 

1,615,162 
1,516,440 
1,517,717 

1,518,995 
1,520,276 
1,521,558 


2-071 
2-072 
2-073 

2-074 
2-075 
2-076 

2-077 
2-078 
2-079 


1-699 233 814 
1-700 810 330 
1-702 388 181 

1-703 9()7 369 
1-705 547 896 
1-707 129 762 

1-708 712 969 
1-710 297 518 
1-711 883 410 


1,576,516 
1,577,851 
1,579,188 

1,580,527 
1,581,866 
1,583,207 

1,584.549 
1,585,892 
1,587,238 


1-635 731 095 


1,522,841 


2-080 


1-713 470 648 


1,688,584 


2031 
2-032 
2-033 

2034 
2-035 
2-036 

2037 
2038 
2-039 


1-637 253 936 
1-638 778 061 
1-640 303 470 

l-6tl 830 166 
1-643 358 151 
1-644 887 426 

1-646 417 990 
1-647 949 844 
1-649 482 992 


1,524,125 
1,525,409 
1,526,696 

1,527,985 
1,529,275 
1,530,564 

1,531,854 
1,533,148 
1,534,442 


2-081 
2-082 
2-083 

2-084 
2-085 
2-086 

2-087 
2-088 
2-089 


1-715 059 232 
1-716 649 163 
1-718 240 442 

1-719 833 072 
1-721 427 053 
1-723 022 386 

1-724 619 075 
1-726 217 117 
1-727 816 516 


1.589,931 
1.591,279 
1.592,630 

1,593,981 
1,595,333 
1,596,689 

1,598,042 
1,599,399 
1,600,767 


2-040 


1-651 017 434 


1,535,787 


2-090 


1-729 417 273 


1,602,116 

1,603,477 
1,604.838 
1,606,201 

1,607,566 
1,608,930 
1,610,298 

1,611,667 
1,613,036 
1,614,408 


2-041 
2-042 
2-043 

2-044 
2-045 
2-046 

2-047 
2-048 
2-049 

2-050 


1-652 653 171 
1-654 090 205 
1-665 628 536 

1-657 168 167 
1-658 709 098 
1-660 251 330 

1-661 794 865 
1-663 339 704 
1-664 885 848 


1,537,034 
1,538,331 
1,539,631 

1,540,931 
1,542,232 i 
1,543,535 

1,544,839 
1,546,144 
1,547,451 


2091 
2 092 
2093 

2-094 
2-095 
2-096 

2-097 
2-098 
2-099 


1-731 019 389 
1-732 622 866 
1-734 227 704 

1-735 833 905 
1-737 441 471 
1-739 050 401 

1-740 660 699 
1-742 272 366 
1-743 885 402 


1-666 433 299 


1,548,758 


2-100 


1-745 499 810 


1,615,779 



250 



EEPOBT 1893. 



X 


Iix 


Difference 


X 


\x 


Difference 


2-100 


1-745 499 810 


1,615,779 


2-150 


1-827 997 461 


1,686,095 


2-101 
2-102 
2-103 

2-104 
2-105 
2-106 

2-107 
2-108 
2-109 


1-747 115 589 
1-748 732 741 
1-750 351 269 

1-751 971 172 
1-753 592 454 
1-765 215 114 

1-756 839 154 
1-758 464 575 
1-760 091 380 


1,617,152 
1,618,628 
1,619,903 

1,621,282 
1,622,660 
1,624,040 

1,625,421 
1,626,805 
1,628,187 


2151 
2-152 
2-153 

2-154 
2-155 
2-156 

2-157 
2-158 
2-169 


1-829 683 556 
1-831 371 091 
1-833 060 069 

1-834 750 490 
1-836 442 357 
1-838 135 670 

1-839 830 431 
1-841 526 641 
1-843 224 303 


1,687,535 
1,688,978 
1,690,421 

1,691,867 
1,693,313 
1,694,761 

1,696,210 
1,697,662 
1,699,112 


2-110 


1-761 719 567 


1,629,574 


2-160 


1-844 923 415 


1,700,565 


2-111 
2-112 
2113 

2-114 
2115 

2-116 

2-117 
2-118 
2-U9 


1-763 349 141 
1-764 980 102 
1-766 612 451 

1-768 246 189 
1-769 881 319 
1-771 517 839 

1-773 155 754 
1-774 795 063 
1-776 435 769 


1,630,961 
1,632,349 
1,633,738 

1,635,130 
1,636,520 
1,637,915 

1.639,309 
1,640,706 
1,642,102 


2-161 
2-162 
2163 

2-164 
2-165 
2-166 

2-167 
2-168 
2-169 


1-846 623 980 
1-848 326 002 
1-850 029 478 

1-861 734 413 
1-853 44U 807 
1-855 148 661 

1-856 857 977 
1-858 568 755 
1-860 281 000 


1,702,022 
1,703,476 
1,704,935 

1,706,394 

1,707,854 
1,709,316 

1,710,778 
1,712,245 
1,713,709 


2-120 


1-778 077 871 


1,643,501 


2-170 


1-861 994 709 


1,715,176 


2121 
2-122 
2-123 

2-124 
2-125 
2126 

2127 
2-128 
2129 


1-779 721 372 
1-781 366 276 
1-783 012 577 

1-784 660 283 
1-786 309 394 
1-787 959 909 

1-789 611 832 
1-791 265 164 
1-792 919 904 


1,644,903 
1,646,302 
1,647,706 

1.649,111 
1,650,515 
1,651,923 

1,653,332 
1,654,740 
1,656,151 


2171 
2-172 
2-173 

2-174 
2-175 
2-176 

2-177 

2-178 
2-179 


1-863 709 886 
1-865 426 630 
1-867 144 646 

1-868 864 233 
1-870 685 294 
1-872 307 828 

1-874 031 839 
1-875 767 326 
1-877 484 291 


1,716,645 
1,718,116 

1,719,587 

1,721,061 
1,722,.';34 
1,724,011 

1,725,487 
1,726,965 
1,728,447 


21 30 


1-794 576 055 


1,657,564 


2-180 


1-879 212 738 


1,729,928 


2-131 
2-132 
2-133 

2-134 
2135 
2136 

2-137 
2-138 
2-139 


1-796 233 619 
1-797 892 596 
1-799 552 987 

1-801 214 796 
1-S02 878 022 
1-804 542 667 

1-806 208 732 
1-807 876 219 
1-809 545 131 


1,658,977 
1.660.391 
1,661,809 

1,663,226 
1,664,645 
1,666,065 

1,667,487 
1,668,912 
1,670,334 


2-181 

2-182 
2-183 

2-184 
2-185 
2-186 

2-187 
2-188 
2-189 


1-880 942 666 
1-882 674 075 
1-884 406 970 

1-886 141 352 
1-887 877 218 
1-889 614 573 

1-891 353 421 
1-893 093 767 
1-894 835 588 


1,731,409 
1,732,896 
1,734,382 

1,735,866 
1,737,355 

1,738,848 

1,740,336 
1,741,831 
1,743,324 


2-140 


1-811 215 465 


1,671,761 


2-190 


1-896 678 912 \ 1,744,819 


2141 
2-142 
2-143 

2-144 
2-145 
2-146 

2-147 
2-148 
2-149 


1-812 887 226 
1-814 560 414 
1-816 235 030 

1-817 911 077 
1-819 588 554 
1-821 267 466 

1-822 947 810 
1-824 629 590 
1-826 312 806 


1,673,188 
1,674,616 
1,676,047 

1,677,477 
1,678,911 
1,680,345 

1,681,780 
1,683,216 
1,684,655 


2-191 
2-192 
2-193 

2-194 
2-195 
2-196 

2-197 
2-198 
2-199 


1-898 323 731 
1-900 070 048 
1-901 817 864 

1-903 567 179 
1905 317 996 
1-907 070 316 

1-908 824 139 
1-910 679 468 
1-912 336 305 


1,746,317 
1,747,816 
1,749,316 

1,750,817 
1,752,320 
1,753,823 

1,755,329 
1,756,837 
1,758,346 


2-150 


1-827 997 461 


1,686,095 


2-200 


1-914 094 651 


1,759,854 



ON MATHEMATICAL FUNCTIONS. 



251 



X 

2-200 


l,x 


Difference | 


.r 


Ii-r 


Difference 


1-914 094 651 


1,759,854 


2-250 


2-003 967 457 


1,837,218 


2-201 
2-202 
2-203 


1-915 854 505 
1-917 615 872 
1-919 378 751 


1,761,367 ! 
1,762,879 ! 
1,764,393 


2-251 
2-252 
2-253 


2-005 804 675 
2-007 643 478 
2-009 483 868 


1,838,803 
1,840,390 
1,841,978 


2-204 
2-205 
2-206 


1-921 143 144 
1-922 909' 054 
1-924 676 481 


1,765,910 ! 
1,767,427 1 
1,768,945 


2-254 
2-255 
2-256 


2-011 325 846 
2-013 169 414 
2-015 014 573 


1,843,568 
1,845,159 
1,846,751 


2-207 
2-208 
2-209 


1-926 445 426 
1-928 215 892 
1-929 987 879 


1,770,466 
1.771,987 
1,773,509 : 


2-257 
2 258 
2-259 


2-016 861 324 
2-018 709 670 
2-020 559 612 


1,848,346 
1,849,942 
1,851,539 


2-210 


1-931 761 388 


1,775,034 


2-260 


2-022 411 151 


1,853,137 


2-211 
2-212 
2-213 


1-933 536 422 
1-935 312 983 
1-937 091 071 


1,776,561 
1,778,088 
1,779,616 


2-261 
2-262 
2-263 


2 024 264 288 
2-026 119 026 
2-027 975 366 


1,854,738 
1,856,340 

1,857,943 


2-214 

2-215 
2-216 


1-938 870 687 
1-940 651 834 
1-942 434 512 


1,781,147 

1,782,678 
1,784,210 


2264 
2-265 
2-266 


2-029 833 309 
2031 692 856 
2033 554 010 


1,859,547 
1,861,154 
1,862,762 


2-217 
2-218 
2-219 


1-944 218 722 
1-946 004 469 
1-947 791 752 


1,785,747 
1,787,283 

1,788,820 


2-267 
2-268 
2-269 


2-035 416 772 
2-037 281 144 
2-039 147 127 


1,864,372 
1,865,983 
1,867,595 


2-220 


1-949 580 572 


1,790,359 


2-270 


2-041 014 722 


1,869,208 


2-221 
2-222 
2-223 


1-951 370 931 
1-953 162 830 
1-954 956 271 


1,791,899 
1.793,441 

1,794,985 


2-271 

2-272 
2-273 


2-042 883 930 
2-044 754 754 
2-046 627 196 


1,870,824 
1,872,442 
1,874,061 


2-224 
2-225 
2-226 


1-956 751 256 
1-958 547 786 
1-960 345 863 


1,796,530 
1,798.077 
1,799.623 


, 2-274 

2-275 

' 2-276 


2-048 501 257 
2-050 376 938 
2-052 254 240 


1,875,681 
1,877,302 
1,878,925 


2-227 
2-228 
2-229 


1-962 145 486 
1-963 946 659 
1-965 749 383 


1,801,173 
1.802.724 
1,804,277 


2-277 

2-278 

' 2-279 


2-054 133 165 
2-056 013 714 
2-057 895 890 


1,880,549 
1,882,176 
1,883,805 


2-230 


1-967 553 660 


1,805,830 


2-280 


2-059 779 695 


1,885,434 


2-231 
2-232 
2-233 


1-969 359 490 
1-971 166 875 
1-972 975 818 


1.807.385 
1,808,943 
1.810,501 


2-281 
2-282 
2-283 


2-061 665 129 
2-063 552 193 
2-065 440 890 


1,887,064 
1,888,697 
1,890,332 


2-234 
2-235 
2-236 


1-974 786 319 
1-976 598 379 
1-978 412 000 


1,812,060 
1,813,621 
1,815,184 


2-284 
2-285 
2-286 


2-067 331 222 
2-069 223 189 
2-071 116 793 


1.891,967 
1,893,604 
1,895,242 


2-237 
2-238 
2-239 


1-980 227 184 
1-982 043 932 
1-983 862 246 


1,816,748 
1,818,314 
1,819,881 


2-287 
2-288 
2-289 


2-073 012 035 
2-074 908 918 
2-076 807 443 


1,896,883 
1,898,525 
1,900,168 


2-240 


1-985 682 127 


1,821,448 


2-290 


2-078 707 611 


1,901,813 


2-241 
2-242 
2-243 


1-987 503 575 
1-989 326 595 
1-991 151 187 


1,823,020 
1,824,592 
1,826,165 


2-291 
2-292 
2-293 


2-080 609 424 
2-082 512 885 
2-084 417 994 


1,903,461 
1.905,109 
1,906,757 


2-244 
2-245 
2-246 


1-992 '977 352 
1-994 805 091 
1-996 634 406 


1,827.739 
1,829,315 
1,830,891 


2-294 
2-295 
2-296 


2-086 324 751 
2-088 233 160 
2-090 143 222 


1,908,409 
1,910.062 
1,911,715 


2-247 
2-248 
2-249 


1-998 465 297 
2-000 297 769 
2002 131 822 


1,832,472 
1,834,053 
1,835,635 


2-297 
2-298 
2299 

2-300 


2-092 054 937 
2-093 968 309 
2-095 883 339 


1,913,372 
1,915,030 
1,916,689 


2-250 


2-003 967 457 


1,837,218 


2-097 800 028 


1,918,349 



252 



EEPOKI 1893. 



X 


l,x 


Difference 


X 


\,x 


Difference 


2-300 

2-301 
2-302 
2-303 

2-304 
2-305 
2-306 

2-307 
2-308 
2-309 


2-097 800 028 


1,918,349 


2-350 


2-195 784 977 


2,003,423 


2-099 718 377 
2-101 638 388 
2103 560 063 

2-105 4S3 404 
2-107 408 411 
2-109 335 088 

2-111 263 435 
2-113 193 453 
2115 125 143 


1,920,011 
1,921,675 
1,923,341 

1,925,007 
1,926,677 
1,928,347 

1,930,018 
1,931,690 
1,933,367 


2-351 
2-352 
2-353 

2-354 
2-355 
2-356 

2-357 
2-358 
2-359 


2-197 788 400 
2- 199 793 564 
2201 800 473 

2-203 809 129 
2-205 819 533 
2-207 831 685 

2-209 846 588 
2-211 861 245 
2 213 878 657 


2,005,164 
2,006,909 
2,008,656 

2,010,404 
2,012,152 
2,013,903 

2,015,657 
2,017,412 
2,019,168 


2-310 


2-117 058 510 


1,935,043 


2-360 


2-215 897 826 


2,020,925 


2-311 
2-312 
2-313 

2-314 
2-315 
2-316 

2-317 
2-318 
2-319 


2-118 993 553 
2-120 930 273 
2-122 868 673 

2-124 808 756 
2-126 750 621 
2-128 693 970 

2-130 639 105 
2-132 585 928 
2-134 534 440 


1,936,720 
1,938,400 
1,940,083 

1,941,765 
1,943,449 
1,945,135 

1,946,823 
1,948,512 
1,950,202 


2-361 
2-362 
2-363 

2-364 
2-365 
2-366 

2-367 
2-368 
2-369 


2-217 918 750 
2-219 941 435 
2-221 965 880 

2-223 992 089 
2-226 020 062 
2-228 049 801 

2-230 081 308 
2-232 114 585 
2-234 149 633 


2,022,685 
2,024,445 
2,026,209 

2,027,973 
2,029,739 
2,031,507 

2,033,277 
2,035,048 
2,036,820 


2-320 


2-136 484 642 


1,951,895 


2-370 


2-236 186 453 


2,038,595 


2-321 
2-322 
2-323 

2-324 
2-325 
2-326 

2-327 
2-328 
2-329 


2-138 436 537 
2-140 390 126 
2-142 345 411 

2-144 302 393 
2-146 261 074 
2148 221 456 

2-150 1S3 540 
2-152 147 328 
2-154 112 821 


1,953,589 
1,955,285 
1,956,982 

1,958,681 
1,960,382 
1,962,084 

1,963,788 
1,965,493 
1,967,200 


2-371 

2-372 
2-373 

2374 
2-375 
2376 

2-377 
2-378 
2-379 


2-238 225 048 
2-240 265 419 
2-242 307 569 

2-244 351 497 
2-246 397 206 
2-248 444 700 

2-250 493 976 
2-252 545 040 
2-254 597 893 


2,040,371 
2,042,150 
2,043,928 

2,045,709 
2,047,494 
2,049,276 

2,051,064 
2,052,853 
2,054,641 


2-330 


2-156 080 021 


1,968,908 


2-380 


2-256 652 534 


2,056,433 


2-331 
2-332 
2-333 

2-334 
2-335 
2-336 

2-337 
2-338 
2-339 


2-158 048 929 
2-160 019 547 
2-161 991 877 

2-163 965 921 
2-165 941 680 
2-167 919 155 

2-169 898 349 
2-171 879 263 
2-173 861 899 


1,970,618 
1,972,330 
1,974,044 

1,975,759 
1,977,475 
1,979.194 

1,980,914 
1,982.636 
1,984,358 


2-381 
2-382 
2-383 

2-384 
2-385 
2-386 

2-387 
2-3«8 
2-389 


2-258 708 967 
2-260 767 192 
2-262 827 213 

2-264 889 029 
2-266 952 645 
2-269 018 060 

2-271 085 276 
2-273 154 296 
2-275 225 121 


2,058,225 
2,060,021 
2,061,816 

2,063,616 
2,065,415 
2,067,216 

2,069,020 
2,070,825 
2,072,632 


2-340 


2-175 846 257 


1,986,083 


2-390 


2-277 297 763 


2,074,439 


2-341 
2-342 
2-343 

2-344 
2-345 
2-346 

2-347 
2-348 
2-349 


2-177 832 340 
2-179 820 150 
2-181 809 688 

2-183 800 957 
2-185 793 955 
2-187 788 686 

2-189 785 153 
2-191 783 357 
2-193 783 296 


1,987,810 
1,989,538 
1,991,269 

1,992,998 
1,994,731 
1,996,467 

1,998,204 
1,999,939 
2,001,681 


2-391 
2-392 
2-393 

2-394 
2-395 
2-396 

2-397 
2-398 
2-399 


2-279 372 192 
2-281 448 442 
2-283 526 505 

2-285 60(; 381 
2-287 688 071 
2-289 771 579 

2-291 856 906 
2-293 944 051 
2-296 033 020 


2,076,250 
2,078,063 
2,079,876 

2,081,690 
2,083,508 
2,085,326 

2,087,146 
2,088,969 
2,090,793 


2-350 


2-195 784 977 


2,003,423 


2-400 


2-298 123 813 


2,092,618 



ON MATHEMATICAL FUNCTIONS. 



2o3 



X 


Ii-^ 


Difference 


X 


l,x 


Difterence 


2-400 


2-298 123 813 


2,092,618 


2-450 

2-451 
2-452 
2-453 


2-405 027 363 


2,186,129 


2-401 
2-402 
2-403 


2-300 216 431 
2-302 810 877 
2-304 407 151 


2,094,446 
2,096,274 
2,098,104 


2-407 213 492 
2-409 401 537 
2-411 591 499 


2,188,045 
2,189,962 
2,191,881 


2-404 
2-405 
2-406 


2-306 505 255 
2-308 605 193 
2-310 706 965 


2,099,938 
2,101,772 
2,103,608 


2-454 
2-455 
2-456 


2-413 783 380 
2-415 977 183 
2-418 172 909 


2,193,803 
2,195,726 
2,197,649 


2-407 
2-408 
2-409 


2-312 810 573 
2314 916 018 
2-317 023 303 


2,105,445 
2,107,285 
2,109,126 


2-457 
2-458 
2-459 


2-420 370 558 
2-422 570 134 
2-424 771 639 


2,199,576 
2,201,505 
2,203,436 


2-410 


2-319 132 429 


2,110,969 


2-460 


2-426 975 075 


2,205,367 


2-411 
2-412 
2-413 


2-321 243 398 
2-323 356 212 
2-325 470 872 


2,112,814 
2,114,660 
2,116,508 


2-461 
2-462 
2-463 


2-429 180 442 
2-431 387 743 
2-433 596 979 


2,207,301 
2,209,236 
2,211,173 


2-414 
2-415 
2-416 


2-327 587 380 
2-329 705 737 
2-331 825 946 


2,118,357 
2,120,209 
2,122,063 


2-464 

2-465 

. 2-466 


2-435 808 152 
2-438 021 264 
2-440 236 319 


2,213,112 
2,215,055 
2,216,997 


2-417 
2-418 
2-419 


2-333 948 009 
2-336 071 928 
2-338 197 703 


2,123,919 
2,125,775 
2,127,633 


2-467 
2-468 
2-469 


2-442 453 316 
2-444 672 257 
2-446 893 144 

2-449 115 981 


2,218,941 

2,220,887 
2,222,837 


2-420 


2-340 325 336 


2,129,493 


2-470 

2-471 
2-472 
2-473 


2,224,786 


2-421 

2-422 
2-423 


2-342 454 829 
2-344 586 186 
2-346 719 406 


2,131,357 
2,133,220 
2,135,086 


2-451 340 767 
2-453 567 505 
2-455 796 200 


2,226,738 
2,228,695 
2,230,648 


2-424 
2-425 
2-426 


2-348 854 492 
2-350 991 445 
2-353 130 267 


2,136,953 

2,138,822 
2,140,692 


2-474 
2-475 
2-476 


2-458 026 848 
2-460 259 455 
2-462 494 019 


2,232,607 
2,234,564 
2,236,526 


2-427 
2-428 
2-429 


2-355 270 959 
2-357 413 524 
2-359 557 964 


2,142,565 
2,144,440 
2,146,317 


2-477 
2-478 
2-479 


2-464 730 545 
2-4G6 969 036 
2-469 209 489 


2,238,491 
2,240,453 
2,242,423 


2-430 


2-361 704 281 


2,148,194 

2,150,074 
2,151,956 
2,153,840 


2-480 


2-471 451 912 


2,244,390 


2-431 
2-432 
2-433 


2-363 852 475 
2-366 002 549 
2-368 154 505 


2-481 
2-482 
2-483 


2-473 696 302 
2-475 942 662 
2-478 190 995 


2,246,360 
2,248,333 
2,250,309 


2-434 
2-435 
2-436 


2-370 308 345 
2-372 464 070 
2-374 621 681 


2,155,725 
2,157,611 
2,159,500 


2-484 
2-485 
2-486 


2-480 441 304 
2-482 693 588 
2-484 947 848 


2,262,284 
2,254,260 
2,256,241 


2-437 
2-438 
2-439 


2-376 781 181 
2-378 942 571 
2-381 105 853 


2,161,390 
2,163,282 
2,165,176 


2-487 
2-488 
2-489 


2-487 204 089 
2-489 462 313 
2-491 722 521 


2,258,224 
2,260,208 
2,262,191 


2-440 


2-383 271 029 


2,167,073 


2-490 


2-493 984 712 


2,264,179 


2-441 
2-442 
2-443 


2-385 438 102 
2-387 607 073 
2-389 777 942 


2,168,971 
2,170,869 
2,172,769 


2-491 
2-492 
2-493 


2-496 248 891 
2-498 515 059 
2-500 783 219 


2,266,168 
2,268,160 
2,270,153 


2-444 
2-445 
2-446 


2-391 950 711 
2-394 125 385 
2-396 301 965 


2,174,674 
2,176,580 

2,178,484 


2-494 
2-495 
2-496 


2-503 053 372 
2-505 325 521 
2-507 599 665 


2,272,149 
2.274,144 
2,276,142 


2-447 
2-448 
2-449 


2 398 480 449 
2-400 660 842 
2-402 843 146 


2,180,393 
2,182,304 
2,184,217 


9-497 
2-498 
2-499 


2-509 875 807 
2-512 153 950 
2-514 434 096 


2,278,143 
2,280,146 
2,282,150 


2-450 


2-405 027 363 


2,186,129 


2-500 


2-516 716 246 


2,284,156 



254 



REPORT — 1893. 



X 

2-500 


l,x 


Difference 


X 


I,x 


DifFerence 


2-516 716 246 


2,284,156 


2-550 


2-633 421 351 


2,386,908 


2-501 
2-502 
2-503 


2-519 000 402 
2-521 286 566 
2-523 574 740 


2,286,164 
2,288,174 
2,290,185 


2-561 

2-552 
2-553 


2-635 808 269 
2-638 197 271 
2-640 588 394 


2,389,012 
2,391,123 
2,393,228 


2-504 
2-505 
2-506 


2-525 864 925 
2-528 157 124 
2-530 451 339 


2,292,199 
2,294,215 
2,296,233 


2-564 
2-556 
2-556 


2-642 981 622 
2-645 376 961 
2-647 774 413 


2,395,339 

2,397,452 
2,399,568 


2-507 
2-508 
2 509 


2-532 747 572 
2-535 045 824 
2-537 346 098 


2,29S.252 
2,300,274 
2,302,296 


2-557 
2'558 
2-559 


2-650 173 981 
2-652 675 664 
2-654 979 465 


2,401,683 
2,403,801 
2,405,924 


2-510 


2-539 648 394 


2,304,321 


2-560 


2-657 385 389 


2,408,047 


2-511 
2-512 
2-513 


2-541 952 715 
2-544 259 064 
2-546 567 442 


2,306,349 

2,308,378 
2,310,408 


2-561 
2-562 
2-563 


2-659 793 436 
2-662 203 605 
2-664 615 902 


2,410,169 
2,412,297 
2,414,426 


2-514 
2-515 
2-516 


2-548 877 850 
2-551 190 291 
2-553 504 767 


2,312,441 
2,314,476 
2,316,512 


1 2-564 

: 2-565 

2-666 


2-667 030 328 
2-669 446 883 
2-671 865 572 


2,416,655 

2,418,689 
2,420,824 


2-517 
2-518 
2-519 


2-555 821 279 
2-658 139 830 
2-560 460 421 


2,318,551 
2,320,691 
2,322,634 


2-567 
2-568 
2-569 


2-674 286 396 
2-676 709 365 
2-679 134 454 


2,422,959 
2,425,099 
2,427,240 


2-520 


2-562 783 056 


2,324,678 


2-570 


2-681 561 694 


2,429,382 


2-521 
2-522 
2-523 


2-565 107 733 
2-567 434 457 
2-569 763 229 


2,326,724 
2,328,772 
2,330,822 


! 2-571 
2-572 
2-673 


2-683 991 076 
2-686 422 602 
2-688 856 275 


2.431,526 
2,433,673 
2,435,823 


2-524 
2-525 
2-526 


2-572 094 051 
2-574 426 926 
2-576 761 853 


2,332,875 
2.334,927 
2,336,985 


2-574 
2-675 
2-676 


2-691 292 098 
2-693 730 070 
2-696 170 197 


2,437,972 
2,440,127 

2,442,280 


2-527 
2-528 
2-529 


2-579 098 838 
2-581 437 879 
2-683 778 980 


2.339,041 
2,341,101 
2,343,163 


2-577 
2-578 
2-579 


2-698 612 477 
2-701 056 915 
2-703 503 610 


2,444,438 
2,446,595 
2,448,759 


2-530 


2-586 122 143 


2,345,227 


2-580 


2-705 962 269 


2,450,920 


2-531 
2-532 
2-533 


2-688 467 370 
2-590 814 662 
2-593 164 022 


2,347,292 
2,349,360 
2,351,429 


2-581 
2-582 
2-683 


2-708 403 189 
2-710 866 273 
2-713 311 526 


2,453,084 
2,455,253 
2,457,420 


2-534 
2-685 
2-536 


2-595 515 451 
2-597 868 950 
2-600 224 525 


2,353,499 
2,355,575 
2,357,648 


2-584 
2-585 
2-586 


2-715 768 946 
2-718 228 638 
2-720 690 303 


2,459,592 
2,461,765 
2,463,941 


2-537 
2-538 
2-539 


2-602 582 173 
2-604 941 900 
2-607 303 705 


2,359,727 
2,361,805 
2,363,887 


2-587 
2-588 
2-589 


2-723 154 244 
2-725 620 362 
2-728 088 659 


2,466,118 
2,468,297 
2,470,478 


2-540 


2-609 667 592 


2,365,969 


2-590 


2-730 559 137 


2,472,661 


2-541 

2-542 
2 543 


2-612 033 661 
2-614 401 616 
2-616 771 758 


2,368,055 
2,370,142 
2,372,231 


2-591 
2-592 
2-593 


2-733 031 798 
2.735 606 644 
2-737 983 679 


2,474,846 
2,477,035 
2,479,224 


2-544 
2545 
2-546 


2-619 143 989 
2-621 518 310 
2-623 894 724 


2,374,321 
2,376,414 

2,378,508 


2-594 
2-695 
2-696 


2-740 462 903 
2-742 944 318 
2-745 427 927 


2,481,416 
2,483,609 

2,486,805 


2-547 
2-548 
2-549 


2-626 273 232 
2-628 653 841 
2-631 036 546 


2,380,609 
2,382,705 
2,384,805 


2-597 
2-598 
2-599 


2-747 913 732 
2-750 401 734 
2-752 891 936 


2,488,002 
2,490,202 
2,492,405 


2-550 


2-633 421 351 


2,386,908 


2-600 


2-755 384 341 


2,494,607 



ON MATHEMATICAL FUNCTIONS. 



255 



J.- 


I,:;: 


Difference 


X 


I,.: 


Difference 


2-600 


2-755 384 341 


2,494,607 


2-650 


2-882 858 180 


2,607,486 


2-601 
2-602 
2-603 

2-604 
2-605 
2-606 

2-607 
2-608 
2-609 


2-757 878 948 
2-760 375 762 
2-762 874 784 

2-765 376 017 
2-767 879 462 
2-770 385 121 

2-772 892 995 
2-775 403 090 
2-777 915 404 


2,496,814 
2,499,022 
2,501,233 

2,503,445 
2,505,659 

2,507,874 

2,510,095 
2,512,314 
2,514,537 


2-651 
2-652 
2-653 

2-654 
2-655 
2-656 

2-657 
2-658 
2-659 


2-885 465 666 
2-888 075 464 
2-890 687 576 

2-S93 :502 004 
2-895 918 750 
2-898 537 819 

2-901 159 209 
2-903 7S2 925 
2-906 408 967 


2,609,798 
2,612,112 

2,614,428 

2,616,746 
2,619,069 
2,621,390 

2,623,716 
2,626,042 
2,628,373 


2-610 


2-780 429 941 


2,516,761 


2-660 


2-900 037 340 


2,630,703 


2-611 
2-612 
2-613 

2-614 
2-615 
2-616 

2-617 
2-618 
2-619 


2-7.S2 946 702 
2-785 465 691 
2-787 986 908 

2-790 510 357 
2-793 036 038 
2-795 563 954 

2-798 094 110 
2-800 626 503 
2-803 161 137 


2,518,989 
2,521,217 
2,523,449 

2,525,681 
2,527,916 
2,530,156 

2,532,393 
2,534,634 
2,536,880 


2-661 
2-662 
2-663 

2-664 
2-665 
2-666 

2-667 
2-668 
2-669 


2-911 668 043 
2-914 301 082 
2-916 936 455 

2-919 574 167 
2922 214 220 
2-924 856 615 

2-927 501 354 
2-930 148 440 
2-932 797 878 


2.633,039 
2,635,373 
2,637,712 

2.640.053 
2.642.395 
2,644,739 

2,647,086 
2,649,438 
2,651,787 


2-620 


2-805 698 017 


2,539,124 


2-670 


2-935 449 665 


2,654,139 


2-621 
2-622 
2-623 

2-624 
2-625 
2-626 

2-627 
2-628 
2-629 


2-808 237 141 
2-SlO 778 513 
2-813 322 135 

2-815 868 009 
2-818 416 138 
2-820 966 522 

2-823 519 165 
2-826 074 068 
2-828 631 234 


2,541,372 
2,543,622 
2,545,874 

2,548,129 
2,550,384 
2,552,643 

2,554,903 
2,557,166 
2,559,432 


2-671 
2-672 
2-673 

2-674 
2-675 
2-676 

2-677 

2-678 
2-679 

2-680 


2-938 103 804 
2-940 760 301 
2-943 419 156 

2-946 OHO 371 
2-948 743 948 
2-951 409 889 

2-954 078 199 
2-956 748 877 
2-959 421 927 


2,656,497 

2.658,855 
2,661,215 

2,663,577 
2,665,941 
2,668,310 

2,670,678 
2.673,050 
2,675,422 


2-630 

2-631 
2-632 
2-633 

2-634 
2-635 
2-636 

2-637 
2-638 
2-639 


2-831 190 666 


2,561,698 


2-962 097 349 


2,677,798 


2-833 752 364 
2 836 316 331 

2-838 882 570 

2-841 451 082 
2-844 021 869 
2-846 594 932 

2-849 170 276 
2-851 747 903 
2-854 327 813 


2,563,967 
2,566,239 
2,568,512 

2,570,787 
2,573,063 
2,575,344 

2,577,627 
2,579,910 
2,582,196 


2-681 
2-682 
2-683 

2-684 
2-685 
2-686 

2-687 
2-688 
2-689 


2-964 775 147 
2-967 455 324 
2-970 137 881 

2-972 822 821 
2-975 510 145 
2-978 199 856 

2-980 891 956 
2-9S3 586 446 
2-986 283 331 


2,680,177 
2,682,557 
2,684,940 

2,687,324 
2,689,711 
2,692,100 

2.694,490 

2.(596,885 
2,699,283 


2-640 


2-856 .910 009 


2,584,484 


2-690 


2-988 982 613 


2,701,679 


2-641 
2-642 
2-643 

2-644 
2-645 
2-646 

2-647 
2-648 
2-649 


2-859 494 493 
2-862 081 268 
2-864 670 335 

2-867 261 697 
2-869 855 356 
2-872 451 314 

2-875 049 574 
2-877 650 136 
2-880 253 004 


2,586,775 
2,589,067 
2,591,362 

2,593,659 
2 595,958 
2,598,260 

2,600,562 

2,602,868 
2,605,176 


2-691 
2-692 
2-693 

2-694 
2-695 
2-696 

2-697 
2-698 
2-699 


2-991 684 292 
2-994 388 372 
2-997 094 854 

2-999 803 741 
3002 515 035 
3-005 228 739 

3-007 944 854 
3-010 663 383 
3-013 384 330 


2.704,080 
2.706,482 
2,708,887 
2.711,294 
2,713,704 
2,716,115 

2,718,529 
2,720,947 
2,723,364 


2-650 


2-882 858 180 


2,607,486 


2-700 


3-016 107 694 


2,725,784 



256 



BEPORT — 1893. 



X 


I,.r 


Difference 


.r 


Ii-r 


Difference 


2-700 


3-016 107 


694 


2.725,784 


2-750 


3-155 410 


139 


2,849,759 


2-701 
2-702 
2-703 


3-018 833 
3-021 561 
3-024 292 


478 
685 
319 


2,728,207 
2,730,634 
2,733,061 


2-751 
2-752 
2-753 


3-15« 259 
3-161 112 
3-163 967 


898 
197 
038 


2,852,299 
2,854,841 

2,857,385 


2-704 
2-705 
2-706 


3-027 025 
3-029 760 
3-032 498 


380 
870 
793 


2,735,490 
2,737,923 
2,740,356 


2-754 
2-755 
2-756 


3-166 824 
3-169 684 
3-172 546 


423 
355 
834 


2,859.932 
2,862,479 
2,865,031 


2-707 
2-708 
2-709 


3-035 239 
3-037 981 
3-040 727 


149 
943 
175 


2,742,794 
2,745,232 

2,747,675 


2-757 
2-758 
2-759 


3-175 411 
3-178 279 
3-181 149 


865 
450 
.591 


2,867,585 
2,870,141 
2,872,699 


2-710 


3-043 474 


850 


2,750,118 


2-760 


3-184 022 


290 


2,875,259 


2-711 
2-712 
2-713 


3-046 224 
3-048 977 
3-051 732 


968 
530 
541 


2,752,562 
2,755,011 
2,757,462 


2-761 
2-762 
2-763 


3-186 897 
3-189 775 
3-192 655 


549 
372 
760 


2,877.823 
2,880,388 
2,882,956 


2-714 
2-715 
2-716 


3-054 490 003 
3-057 249 917 
3-060 012 287 


2.759,914 
2,762,370 
2,764,827 


2-764 
2-765 
2-766 


3-195 .538 
3-198 424 
3-201 312 


716 
242 
341 


2,885,526 
2,888,099 
2,890,674 


2-717 
2-718 
2-719 


3-062 777 
3-065 544 
3-06S 314 


114 
400 

148 


2,767.286 
2.769,748 
2,772,214 


2-767 
2-768 
2-769 


3-204 203 
3-207 096 
3-209 992 


015 
267 
099 


2,893,252 
2,89.5,832 
2,898,414 


2-720 


3-071 086 


362 


2,774,679 


2-770 


3-212 890 513 


2,900,999 


2-721 
2-722 
2-723 


3-073 861 
3-076 638 
3-079 417 


041 

188 
807 


2,777,147 
2,779,619 
2,782,093 


2-771 
2-772 
2-773 


3-215 791 
3-218 695 
3-221 601 


512 
098 
275 


2.903.586 
2,906,177 
2,908,768 


2-724 
2-725 
2-726 


3-082 199 
3-084 984 
3-087 771 


900 
469 
514 


2,784,569 
2,787,045 
2,789,527 


2-774 
2-775 
2-776 


3-224 510 
3-227 421 
3-2.30 335 


043 
405 
364 


2,911,362 
2.913,959 
2,916,559 


2-727 
2-728 
2-729 


3-090 561 
3-093 353 
3-096 147 


041 
051 
546 


2,792,010 
2,794,495 
2,796,982 


2-777 
2-778 
2-779 


3-233 251 
3-236 171 
3-239 092 


923 

084 
849 


2.919,161 
2.921,765 
2,924,370 


2-730 


3-098 944 


528 


2,799,472 


2-780 

2-781 

2-782 
2-783 


3-242 017 


219 


2,926,980 


2-731 
2-732 
2-733 


3-101 744 
3-104 545 
3-107 350 


000 
964 
423 


2,801,964 
2,804,459 
2,806,956 


3-244 944 
3-247 873 
3-250 805 


199 

792 
998 


2.929.593 
2.932,206 
2.934,822 


2-734 
2-735 
2-736 


3-110 157 
3-112 966 
3-115 778 


379 
833 

789 


2,809,454 
2,811,956 
2,814,459 


2-784 
2-785 
2-786 


3-253 740 
3-256 678 
3-259 618 


820 
261 
324 


2,937,441 
2.940.063 

2,942,687 


2-737 
2-738 
2-739 


3-118 593 
3-121 410 
3-124 229 


248 
214 
688 


2,816,966 
2,819,474 
2,821,985 


2-787 
2-788 
2-789 


3-262 561 
3-265 506 
3-268 454 


Oil 
323 
264 


2,945,312 
2,947,941 
2,950,573 


2-740 


3-127 051 


673 


2,824,498 


2-790 


3-271 404 


837 


2,953,207 


2-741 
2-742 
2-743 


3-129 876 
3-132 703 
3-135 532 


171 
185 
717 


2,827,014 
2,829,532 
2,832,052 


2-791 
2-792 
2-793 


3-274 358 
3-277 313 
3-280 272 


044 

887 
368 


2,955,843 
2,958,481 
2,961,121 


2-744 
2-745 
2-746 


3138 364 
3-141 199 
3-144 036 


769 
343 
443 


2,834,574 
2,837.100 
2,839,628 


2-794 
2-795 
2-796 


3 283 233 
3-286 197 
3-289 163 


489 
255 
666 


2,963,766 
2,966,411 
2,969,060 


2-747 
2-748 
2-749 


3-146 876 071 
3-149 718 227 
3-152 562 915 


2,842,156 

2,844,688 
2,847,224 


2-797 

2-798 
2-799 

2-800 


3292 1.32 
3-295 104 

3-298 078 


726 
438 
803 


2,971,712 
2,974,365 
2,977,020 


2-750 


3-155 410 


139 


2,849,759 


3-301 055 


823 


2,979,678 



ON MATHEMATICAL FUNCTIONS. 



257 



X 

2-800 


1,X 


Difference 


X 


I,.v 


Difference 


3-301 


055 823 


2,979,678 


2-850 


3-453 


348 


735 


3,115,822 


2-801 
2-802 
2-803 


3-304 
3-307 
3-310 


035 501 
017 840 
002 844 


2,982,339 
2,985,004 
2,987,670 


2-851 
2-852 
2-853 


3-456 
3-459 
3-462 


464 
583 
704 


557 
167 
567 


3,118,610 
3,121,400 
3,124,194 


2-804 
2-805 
2806 


3-312 
3-315 
3-318 


990 514 
980 851 
973 859 


2,990,337 
2,993,008 
2,995,681 


2-854 
2-855 
2-856 


3-465 
3-468 
3-472 


828 
955 
085 


761 
751 
541 


3,126,990 
3,129,790 
3,132,590 


2-807 
2-808 
2-809 


3-321 
3-324 
3-327 


969 540 

967 898 

968 934 


2,998,358 
3,001.036 
3,003,717 


2-857 
2-858 
2-859 


3-475 

3-478 
3-481 


218 
353 
491 


131 
625 
726 


3,135,394 
3,138,201 
3,141,011 


2-810 

2-811 
2-812 
2-813 


3-330 


972 651 


3,006,400 


2-860 


3-484 


632 


737 


3,143,823 


3-333 
3-336 
3-339 


979 051 
988 137 
999 913 


3,009,086 
3,011,776 
3,014,465 


! 2-861 
2-862 
2-863 


3-487 776 
3-490 923 
3-494 072 


560 
198 
652 


3,146,638 
3,149,464 
3,152,273 


2-814 
2-815 
2-816 


3-343 
3-346 
3-349 


014 378 
031 536 
051 390 


3,017,158 
3,019,854 
3,022,554 


2-864 

2-865 
2-866 


3-497 
3-500 
3-503 


224 
380 
537 


925 
021 
943 


3,155,096 
3,157,922 
3,160,749 


2-817 
2-818 
2-819 


3-352 073 944 
3-355 099 200 
3-358 127 157 


3,025,256 
3,027,957 
3,030,664 


2-867 
2-868 
2-869 


3-506 
3-509 
3-513 


698 
862 
028 


692 

272 
685 


3,163,580 
3,166,413 
3,169,248 


2-820 


3-361 


157 821 


3,033,374 


2-870 


3-516 


197 933 


3,172,086 


2-821 

2-822 
2-823 


3-364 

3-367 
3-370 


191 195 

227 278 
266 077 


3,036,083 
3,038,799 
3,041,514 


2-871 

2-872 
2-873 


3-519 
3-522 
3-525 


370 
544 

722 


019 
947 

719 


3.174,928 
3,177,772 
3,180,618 


2-824 
2-825 
2-826 


3-373 
3-376 
3-379 


307 591 
351 823 

398 777 


3,044,232 
3,046,954 
3,049,678 


2-874 
2-875 
2-876 


3-528 
3-532 
3-535 


903 
086 
273 


337 

803 
120 


3,183,466 
3,186,317 
3,189,172 


2-827 
2-828 
2-829 


3-382 
3-385 
3-38S 


448 455 
600 860 
555 993 


3,052,405 
3,055,133 
3,057,864 


2-877 
2-878 
2-879 


3-538 
3-541 
3-544 


462 
654 
849 


292 
322 
211 


3,192,030 
3,194,889 
3,197,751 


2-830 


3-391 


613 857 


3,060,600 


2-880 


3-548 


046 


962 


3,200,617 


2-831 
2-832 
2-833 


3-394 
3-397 
3-400 


674 457 
737 793 
803 868 


3,063,336 
3,066,075 
3,068,817 


2-881 
2-882 
2-883 


3-551 
3-554 
3-557 


247 
451 
657 


579 
063 
418 


3,203,484 
3,206,355 
3,209,226 


2-834 
2-835 
2-836 


3-403 872 685 
3-406 944 246 
3-410 018 553 


3,071,561 
3,074,307 
3,077,057 


2-884 
2-885 
2-886 


3-560 
3-564 
3-567 


866 
078 
293 


644 
747 
729 


3,212,103 
3,214,982 

3,217,862 


2-837 
2-838 
2-839 


3-413 
3-416 
3-419 


095 610 
175 420 

257 985 


3,079,810 
3,082,565 
3,085,321 


2-887 
2-888 
2-889 


3-570 
3-573 
3-576 


511 
732 
955 


591 
338 
970 


3,220,747 
3,223,632 
3,226,522 


2-840 


3-422 


343 306 


3,088,081 


2-890 


3-580 


182 


492 


3,229,413 


2-841 
2-842 
2-843 


3-425 
3-428 
3-431 


431 387 
522 230 
615 839 


3,090,843 
3,093,609 
3,096,376 


2-891 
2-892 
2-893 


3-5S3 
3-586 
3-589 


411 
644 

879 


905 
213 
419 


3,232,308 
.3,235.206 
3,238,106 


2-844 
2-845 
2-846 


3-434 
3-437 
3-440 


712 215 
811 361 
913 279 


3,099,146 
3,101,918 
3,104,695 


2-894 
2-895 
2-896 


3-593 
3-596 
3-599 


117 

358 
602 


525 
534 

448 


3,241,009 
3.243,914 
3,246,822 


2-847 
2-848 
2-849 


3-444 
3-447 
3-450 


017 974 
125 447 
235 699 


3,107,473 
3,110,252 
3,113,036 


2-897 
2-898 
2-899 


3-602 
3-606 
3-609 


849 
099 
351 


270 
003 
649 


3,249,733 
3,2.52,646 
3,255,563 


2-850 


3-453 


348 735 


3,115,822 


2-900 


3-612 


607 


212 


3,258,482 



1893. 



258 



REPORT — 1893. 



X 


l,x 


Difference 


X 


l,x 


Difference 


2-900 


3-612 607 212 


3,258,482 


2-950 


3-779 164 648 


3,407,969 


2-901 
2-902 
2-903 


3-615 865 694 
3-619 127 098 
3-622 391 426 


3,261,404 
3,264,328 
3,267,255 


2-951 
2-952 
2-953 


3-782 572 617 
3-785 983 648 
3-789 397 743 


3,411,031 
3,414,095 
3,417,161 


2-904 
2-905 
2-906 


3-625 658 681 
3-628 928 867 
3-632 201 986 


3,270,186 
3,273,119 
3,276,054 


2-954 
2-955 
2-956 


3-792 814 904 
3-796 235 136 
3-799 658 442 


3,420,232 
3,423,306 
3,426,382 


2-907 
2-908 
2-909 


3-635 478 040 
3-638 757 032 
3-642 038 964 


3,278,992 
3,281,932 

3,284,876 


2-957 
2-958 
2-959 

~2-960 

2-961 
2-962 
2-963 


3-803 084 824 
3-806 514 284 
3-809 946 825 


3,429,460 
3,432,541 
3,435,627 


2-910 


3-645 323 840 


3,287,823 


3-813 382 452 


3,438,714 


2-911 
2-912 
2-913 


3-648 611 663 
3-651 902 436 
3-655 196 161 


3,290,773 
3,293,725 
3,296,679 


3-816 821 166 
3-820 262 969 
3-823 707 866 


3,441,803 
3.444,897 
3,447,994 


2-914 
2-915 
2-916 


3-658 492 840 
3-661 792 477 
3-665 095 074 


3,299,637 
3,302,597 
3,305,560 


2-964 
2-965 
2-966 


3-827 155 860 
3-830 606 952 
3-834 061 146 


3.451,092 
3,454,194 
3,457,298 


2-917 
2-918 
2-919 


3-668 400 634 
3-671 709 160 
3-675 020 654 


3,308,526 
3,311,494 
3,314,466 


2-967 
2-968 
2-969 


3-837 518 444 
3-840 978 851 
3-844 442 368 


3,460,407 
3,463,517 
3,466,631 


2-920 


3-678 335 120 


3,317,440 


2-970 


3-847 908 999 


3,469,747 


2-921 
2-922 
2-923 


3-681 652 560 
3-684 972 977 
3-688 296 373 


3,320,417 
3,323,396 
3,326,379 


2-971 
2-972 
2-973 


3-851 378 746 
3-854 851 612 
3-858 327 600 


3,472.866 
3,475,988 
3,479,114 


2024 
2-925 
2-926 


3-691 622 752 
3-694 952 117 
3-698 284 470 


3,329,365 
3,332.353 
3,335,343 


2-974 
2-975 
2-976 


3-861 806 714 
3-865 288 956 
3-868 774 328 


3,482,242 
3,485,372 

3,488,506 


2-927 
2-928 
2-929 


3-701 619 813 
3-704 958 149 
3-708 299 482 


3,338,336 
3,341,333 
3,344,332 


2-977 
2-978 
2-979 


3-872 262 834 
3-875 754 477 
3-879 249 261 


3,491,643 
3,494,784 
3,497,927 


2-930 


3-711 643 814 


3,347,335 


2-980 


3-882 747 188 


3,501,071 


2-931 
2-932 
2-933 


3-714 991 149 

3-718 341 488 
3-721 694 835 


3,350,339 
3,353,347 
3,356,359 


2-981 

2-982 
2-983 


3-886 248 259 
3-889 752 479 
3-893 2.59 851 


3,504,220 
3,507,372 
3,510,526 


2-934 
2-935 
2-936 


3-725 051 194 
3-728 410 565 
3-731 772 952 


3,359,371 
3,362,387 
3,365,405 


2-984 
2-985 
2-986 


3-896 770 377 
3-900 284 060 
3-903 800 904 


3,513,683 
3,516,844 
3,520,007 


2-937 
2-938 
2-939 


3-735 138 357 
3-738 506 785 
2-741 878 237 


3,368.428 
3,371,452 
3,374,481 


2-987 
2-988 
2-989 


3-907 320 911 
3-910 844 085 
3-914 370 428 


3,523,174 
3,526,343 
3,529,516 


2-940 


3-745 252 718 


3,377,510 


2-990 


3-917 899 943 


3,532,690 


2-941 
2-942 
2-943 


3-748 630 228 
3-752 010 771 
3-755 394 351 


3,380.543 
3,383,580 
3,386,618 


2-991 
2-992 
2-993 


3-921 432 633 
3-924 968 501 
3-928 507 550 


3,.5,35,868 
3,539,049 
3,542,234 


2-944 
2-945 
2-946 


3-758 780 969 
3-762 170 628 
3-765 563 331 


3,389,659 
.3.392,703 
3,395,752 


2-994 
2-995 
2-996 


3-932 049 784 
3-935 595 204 
3-939 143 815 


3,545,420 
3,548,611 
3,551,804 


2-947 
2-948 
2-949 


3-768 959 083 
3-772 357 884 
3-775 759 738 


3,398,801 
3,401,854 
3,404,910 


2-997 
2-998 
2-999 


3-942 695 619 
3-946 2.50 til8 
3-949 808 817 


3,554,999 
3,558,199 
3,561,400 


2-950 


8-779 164 648 


3,407,969 


3-000 


3-953 370 217 


3,564,606 



ON MATHEMATICAL FDNCTIONS. 



259 



X 


I,x 


Difference 


X 


1,X 


Difference 


3-000 


3'953 


370 217 


3,564,606 1 

3,567,813 
3,571,025 
3,574,238 


3-0.50 


4-135 


589 


648 


3,728,731 


3001 
3 002 
3003 


3-956 
3-960 
3-964 


934 

502 
073 


823 
636 
661 


3-051 
3-052 
3-053 


4-139 
4-143 
4-146 


318 
050 

785 


379 
470 
927 


3,732,091 
3,735,457 

3.738,824 


3004 
3005 
3006 


3-967 
3-971 
3-974 


647 
225 
806 


899 
354 
030 


3,577,455 

3,580,676 
3,583,898 


3-054 
3-055 
3-056 


4-1.50 
4-154 
4-158 


524 

266 
012 


751 
946 
515 


3,742,195 
3,745,569 
3,748,946 


3007 
3-008 
3009 


3-978 
3-981 
3-985 


389 
977 
567 


928 
051 
405 


3,587,123 
3,590.354 
3,593,586 


3-057 
3-058 
3-059 


4-161 
4-165 
4-169 


761 
513 
269 


461 

789 
498 


3,752,328 
3,755,709 
3,759,096 


3010 

3011 
3012 
3013 


3-989 


160 


991 


3,596,820 


3-060 


4-173 


028 


594 


3,762,486 


3-992 
3-996 
3-999 


757 
357 
961 


811 
869 
169 


3,600.058 
3,603,300 
3,606,544 


3-061 
3-062 
3-063 


4-176 791 
4-180 556 
4-184 326 


080 
959 
234 


3,765,879 
3,769,275 
3,772,674 


3014 
3015 
3016 


4-003 
4-007 
4-010 


567 
177 
790 


713 
504 
545 


3,609,791 
3,613,041 
3,616,294 


3-064 
3-065 
3-066 


4-188 
4-191 
4-195 


098 
874 
654 


908 
983 
464 


3,776,075 
3,779,481 
3,782,891 


3017 
3018 
3019 


4-014 
4-018 
4-021 


406 
026 
649 


839 
389 
199 


3,619,550 
3,622,810 
3,626,072 


3-067 
3-068 
3-069 


4-199 
4-203 
4-207 


437 
223 
013 


355 
658 
375 


3.786,303 
3,789,717 
3,793,135 


3020 


4-025 


275 


271 


3,629,337 i 


3-070 


4-210 


806 


510 


3,796,567 


3021 
3022 
3023 


4-028 
4-0^2 
4-036 


904 
537 
173 


608 
214 
091 


3,632,606 
3.635,877 
3,639,152 


3-071 
3-072 
3-073 


4-214 

4-218 
4222 


603 
403 

206 


067 
049 
459 


3,799,982 
3,803,410 

3,806,841 


3024 
3025 
3026 


4-039 
4-043 
4-047 


812 
454 
100 


243 
673 
383 


3,642.430 
3,645,710 
3,648,994 


3-074 
3-075 
3-076 


4-226 
4-229 
4-233 


013 
823 
637 


300 
575 

288 


3,810,275 
3,813,713 
3,817,153 


3027 
3028 
3029 


4-050 
4-054 
4-058 


749 
401 
057 


377 
658 
230 


3,652,281 
3,655,572 
3,658,864 


3-077 
3-078 
3-079 


4-237 
4-241 
4-245 


454 

275 
099 


441 

038 
082 


3,820,597 
3,824,044 
3,827,495 


3030 


4-061 


716 


094 


3,662,159 


3-080 


4-248 


926 


577 


3,830,949 


3031 
3032 
3033 


4-065 
4-069 
4-072 


378 
043 
712 


253 
711 
472 


3,665,458 
3,668,761 
3.672,067 


3-081 
3-082 
3083 


4-252 
4-256 
4-260 


757 
591 
429 


526 
930 
795 


3,834,404 
3,837,866 
3,841,329 


3034 
3035 
3036 


4-076 
4-080 
4-083 


384 
059 

738 


539 
914 
599 


3,675,375 
3,678,685 
3,682,001 


3-084 
3-085 
3-086 


4-264 
4-268 
4-271 


271 
115 
964 


124 
919 
183 


3,844,795 
3,848,264 
3,851,737 


3037 
3038 
3039 


4-087 
4-091 
4-094 


420 
105 
794 


600 
919 
568 


3,685,319 
3,688,639 
3,691,962 


3-087 
3-088 
3-089 


4-275 
4-279 
4-283 


815 
671 
529 


920 
134 

827 


3,855,214 
3,858,693 
3,862,176 


3040 


4-098 


486 


520 


3,695,290 


3-090 


4-287 


392 003 


3,865,662 


3041 
3042 
3043 


4-102 
4-105 
4-109 


181 

880 
582 


810 
430 
384 


3,698,620 
3,701,954 
3,705,289 


3-091 
3-092 
3-093 


4-291 
4-295 

4-298 


257 
126 
999 


665 
816 
459 


3,869,161 
3,872,643 
3,876,139 


3044 
3045 
3046 


4-113 
4-116 
4-120 


287 
996 
708 


673 
302 
274 


3,708,629 
3,711,972 
3,715,317 


3-094 
3095 
3-096 


4-302 
4-306 
4-310 


875 
755 
638 


598 
237 
377 


3,879,639 
3,883,140 
3,886,646 


3047 
3048 
3049 


4-124 
4-128 
4-131 


423 
142 

864 


591 

256 
274 


3,718,665 
3,722,018 
3,725,374 


3-097 
3-098 
3-099 


4-314 
4-318 
4-322 


525 
415 

308 


023 

178 
844 


3,890,155 
3,893,666 
3,897,183 


3-050 


4-135 


589 


648 


3,728,731 


3-100 


4-326 


206 


027 


3,900,702 



s 2 



260 



KEPORT — 1893. 





X 


l,x 


Difference 


X 


Ii.r 


Difference 




3-100 


4-326 206 027 


3,900,702 


3-160 


4-525 620 649 


4,080,888 




3-101 
3-102 
3-103 


4-330 106 729 
4-334 010 952 
4-337 918 700 


3,904,223 
3,907,748 
3,911,277 


3-151 
3-152 
3-153 


4-529 701 537 
4-533 786 116 
4-537 874 388 


4,084,579 
4,088,272 
4,091,970 




3-104 
3-105 
3-106 


4-341 829 977 
4-345 744 786 
4-349 663 130 


3,914,809 
3,918,344 
3,921,882 


3-154 
3155 
3-156 


4-541 966 358 
4-546 062 029 
4-550 161 403 


4,095,671 
4,099,374 
4,103,082 




3-107 
3-108 
3-109 


4-353 585 012 
4-357 510 435 
4-361 439 403 


3,925,423 
3,928.968 
3,932,518 


3-157 
3-158 
3-159 


4-554 264 485 
4-558 371 278 
4-562 481 784 


4,106,793 
4,110,506 
4,114,225 




3-110 


4-365 371 921 


3,936,070 


3-160 


4-566 596 009 


4,117,947 




3-111 
3-112 
3113 


4-369 307 991 
4-373 247 615 
4-377 190 797 


3,939,624 
3,943,182 
3,946,743 


3-161 
3-162 
3-163 


4-570 713 956 
4-574 835 627 
4-578 961 026 


4,121,671 
4,125,399 
4,129,131 




3-114 
3-115 
3-116 


4-381 137 540 
4-385 087 848 
4-389 041 725 


3,950,308 
3,953,877 
3,957,449 


3-164 
3-165 
3-166 


4-583 090 157 
4-587 223 024 
4-591 359 630 


4,132,867 
4,136,606 
4,140,348 




3-117 
3-118 
3-119 


4-392 999 174 
4-396 960 199 
4-400 924 801 


3,961,025 
3,964,602 
3,968,183 


3-167 
3-168 
3-169 


4-595 499 978 
4-599 644 071 
4-603 791 913 


4,144,093 
4,147,842 
4,151,595 




3-120 


4-404 892 984 


3,971,768 


3-170 


4-607 943 508 


4,155,352 




3121 
3-122 
3-123 


4-408 864 752 
4-412 840 108 
4-416 819 056 


3,975,356 
3.978,948 
3,982,544 


3-171 
3172 
3-173 


4-612 098 860 
4-616 257 972 
4-620 420 846 


4,159,112 
4,162,874 
4,166,641 




3124 
3-125 
3-126 


4-420 801 600 
4-424 787 74:! 
4-428 777 487 


3,986,143 
3,989,744 
3,993,348 


3-174 
3-175 
3-176 


4-624 587 487 
4-628 757 899 
4-632 932 085 


4,170,412 
4,174,186 
4,177,963 




3-127 
3-128 
3-129 


4-432 770 835 
4-436 767 792 
4-440 768 361 


3.996,957 
4,000,569 
4,004,184 


3177 
3178 
3-179 


4 637 110 048 
4-641 291 791 
4-645 477 319 


4,181,743 
4,185,528 
4,189,316 




3-130 


4-444 772 545 


4,007,804 


3-180 

3-181 
3-182 
3183 


4-649 666 635 


4,193,108 




3131 
3-132 
3133 


4-448 780 349 
4-452 791 773 
4-456 806 823 


4,011,424 
4,015,050 
4,018,680 


4-653 859 743 
4-658 056 646 
4-662 257 347 


4,196,903 
4,200,701 
4,204,502 




3-134 
3135 
3-136 


4-460 825 503 
4-464 847 814 
4-468 873 760 


4,022,311 
4,025.946 
4,029,585 


3-184 
3-185 
3-186 


4-666 461 849 
4-670 670 158 
4-674 882 276 


4,208,309 
4,212,118 
4,215,932 




3-137 
3-138 
3-139 


4-472 903 345 
4-476 936 572 
4-480 973 446 


4,033,227 
4,036,874 
4,040,524 

4,044,175 


3-187 
3-188 
3-189 

3-190 


4-679 098 208 
4-683 317 955 
4-687 541 522 


4,219,747 
4,223,567 
4,227,390 




3-140 


4-485 013 970 


4-691 768 912 


4,231,218 




3-141 
3-142 
3-143 


4-489 058 145 
4-493 105 976 
4-497 157 467 


4,047,831 
4,051,491 
4,055,153 


3-191 
3-192 
3-193 


4-696 000 130 
4-700 235 178 
4-704 474 060 


4,235,048 
4,238,882 
4,242,720 




3-144 
3- 145 
3-146 


4-501 212 620 
4-505 271 439 
4-509 333 928 


4.058,819 
4,062,489 
4.066,162 


3-194 
3-195 
3196 


4-708 716 780 
4-712 963 342 
4-717 213 749 


4,246,562 
4,250.407 
4,254,254 




3-147 
3148 
3-149 

3-150 


4-513 400 090 
4-517 469 929 
4-521 543 448 


4.069,839 
4,073.519 
4,077,201 


3-197 
3-198 
3-199 


4-721 468 003 
4 725 726 110 
4-729 988 073 


4,258,107 
4,261,963 
4,265,822 




4-525 620 649 


4,080,888 


3-200 


4-734 253 895 


4,269,685 



ON MATHEMATICAL FDNCTIONS. 



261 



X 


lia- 


Difference 


X 


IjX 


Difference 


3-200 


4-734 


253 895 


4,269.685 


3-250 


4-952 


546 165 


4,467,501 


3-201 
3-202 
3-203 


4-738 
4-742 

4-747 


523 580 
797 132 
074 553 


4,273,552 
4,277,421 
4,281,294 


3-261 
3-252 
3-253 


4-957 013 666 
4-961 485 217 
4-965 960 823 


4,471,551 
4,475,606 
4,479,665 


3-204 
3-205 
3-206 


4-751 
4-755 
4-759 


355 847 
641 020 
930 074 


4,285,173 
4,289,054 
4,292,939 


3-254 
3-255 
3-256 


4-970 
4-974 
4-979 


440 488 
924 216 
412 010 


4,483,728 
4,487,794 
4,491,865 


3-207 
3-208 
3-209 


4-764 
4-768 
4-772 


223 013 
519 840 
820 558 


4.296,827 
4,300,718 
4,304,613 


3-257 
3-258 
3-259 


4-983 
4-988 
4-992 


903 875 
399 812 
899 827 


4,495,937 
4,500,015 
4,504,098 


3-210 


4-777 


125 171 


4,308,513 


3-260 


4-997 


403 925 


4,508,183 


3-211 
3-212 
3-213 


4-781 433 684 
4-785 746 100 
4-790 062 422 


4,312,416 
4,816,322 
4,320,232 


3-261 
3-262 
3-263 


5-001 
5-006 
5010 


912 108 
424 380 
940 745 


4,512,272 
4,516,365 
4,520,462 


3-214 
3-215 
3-216 


4-794 

4-798 
4-803 


382 654 
706 800 
034 863 


4,324,146 
4,328,063 
4,331,984 


3-264 
3-265 
3-266 


5-015 
6-019 
5-024 


461 207 
985 770 
514 437 


4,524,563 
4,528,667 
4,532,774 


3-217 
3-218 
3-219 


4-807 
4-811 
4 816 


366 847 
702 756 
043 593 


4,335,909 
4,339,837 
4,343,770 


3-267 
3-268 
3-269 


5 029 
5-033 
5-038 


047 211 

584 099 
125 103 


4.536,888 
4,541,004 
4,545,124 


3-220 


4-820 


386 363 


4,347,705 


3-270 


5-042 


670 227 


4,549,246 


3-221 
3222 
3-223 


4-824 
4-829 
4-833 


734 068 
085 713 
441 300 


4,351,645 
4,355,587 
4,359,534 


3-271 
3-272 
3-273 


5047 
5-051 
5 056 


219 473 
772 847 
330 353 


4,553,374 
4,557.506 
4,561,640 


3-224 
3-225 
3-226 


4-837 
4-842 
4-846 


800 834 
164 319 
531 757 


4,363,485 
4,367,438 
4,371,397 


3-274 
3-275 
3-276 


5060 891 993 
5065 457 774 
5-070 027 698 


4,565,781 
4,569,924 
4,574,070 


3-227 
3-228 
3-229 


4-850 
4-855 
4-859 


903 154 
278 512 
657 835 


4,375,358 
4,379.323 
4,383,291 


3-277 
3-278 
3-279 

3-280 


5-074 
5-079 
5-083 


601 768 
179 989 
762 364 


4,578,221 
4,582,-375 
4,586,533 


3-230 


4-864 


041 126 


4,387,265 ■ 


5-088 


348 897 


4,590,696 


3-231 
3-232 
3-233 


4-868 

4-872 
4-877 


428 391 
819 633 
214 854 


4,391,242 
4,395,221 
4,399,204 


3-281 
3-282 
3-283 


5-092 
5-097 
5102 


939 593 
534 456 
133 489 


4,594,863 
4,599,033 
4,603,206 


3-234 
3-235 
3-236 


4-881 614 058 
4-886 017 250 
4-890 424 434 


4,403,192 
4,407,184 
4,411,178 


3-284 
3-285 
3-286 


5-106 
5111 
5-115 


736 695 
344 080 
955 646 


4,607,385 
4,611,566 
4,615,751 


3-237 
3-238 
3-239 


4-894 
4-899 
4-903 


835 612 
250 789 
669 968 


4.415,177 
4,419,179 
4,423,185 


3-287 
3-288 
3-289 


5-120 
5-1 25 
5 129 


571 397 
191 339 
815 474 


4,619,942 
4,624,135 
4,628,333 


3-240 


4-908 


093 153 


4,427,195 


3-290 


5-134 


443 807 


4,632,534 


3-241 
3-242 
3-243 


4-912 
4-916 
4-921 


520 348 
951 556 

386 782 


4,431,208 
4,435,226 
4,439,247 


3-291 
3-292 
3-293 


5-139 076 341 
5-143 713 080 
5-148 354 028 


4,636,739 
4,640,948 
4,645,161 


3-244 
3-245 
3-246 


4-925 
4-930 
4-934 


826 029 
269 301 
716 602 


4,443,272 
4,447,301 
4,451,334 


3-294 
3-295 
3-296 


5-152 
5-157 
5-162 


999 189 
648 568 
302 169 


4,649,379 
4,653,601 
4,657,825 


3-247 
3-248 
3249 


4-939 
4-943 
4-948 


167 936 
623 306 
082 713 


4,455,370 
4,459.407 
4,463,452 


3-297 
3-298 
3-299 


5-166 
5-171 
5-176 


959 994 
622 047 
288 333 


4,662,053 
4.666.286 
4,670,523 


3-250 


4-952 


546 165 


4,467,501 


3-300 


5-180 958 856 


4,674,764 



262 



EEPOBT — 1893. 




ON MATHEMATICAL FUNCTIONS. 



263 



X 


I,x 


Difference 


r 


l,X 


Difference 


3-400 


5-670 102 192 


5,119,465 


4-450 

3-451 
3-452 
3-453 


5-931 870 019 


5,357,870 


3-401 
3-402 
3-403 


5-675 221 657 
6-680 345 782 
5-685 474 571 


5,124,125 

5,128,789 
5,133,457 


5-937 227 889 
5-942 590 641 
5-947 958 282 


5,362,752 
5,367,641 
5,372,531 


3-404 
3-405 
3-406 


5-690 608 028 
5-695 746 158 
5-700 888 965 


5,138,130 
5,142,807 
5,147,489 


3-454 
3-455 
3-456 


5-953 330 813 
5-958 708 240 
5-964 090 568 


5,377,427 
5,382.328 
6,387,234 


3-407 
3-408 
3-409 


5-706 036 454 
5-711 188 630 
5-716 345 496 


5,152,176 
5,156,866 
5,161,560 


3-457 
3-458 
3-459 


6-969 477 802 
5-974 869 945 
5-980 267 003 


5,392,143 
5,397.058 
6,401,977 


3-410 


5-721 507 056 


5,166,260 


3-460 


5-985 668 980 


5,406,900 


3-411 
3-412 
3-4] 3 


5-726 673 316 
5-731 844 280 
5-737 019 952 


5,170,964 
5,175,672 

6,180,383 


3-461 
3-462 
3-463 


5-991 075 880 
6-996 487 710 
6-001 904 471 


5,411.830 
5,416,761 
6,421,699 


3-414 
3-415 
3-416 


5-742 200 335 
5-747 385 436 
5-752 575 258 


5,185,101 
5,189,822 
5,194,547 


3-464 
3-465 
3-466 


6-007 326 170 
6-012 752 812 
6018 184 399 


5,426,642 
5,431,587 
5,436,540 


3-417 
3-418 
3-419 


5-757 769 805 
5-762 969 083 
5-768 173 094 


5,199.278 
5.204,011 
5,208,751 


3-467 
3-468 
3-469 


6023 620 939 
6-029 062 435 
6-034 608 890 


5,441,496 
5,446,455 
5,461,422 


3-420 


5-773 381 845 


5,213,494 


3-470 


6-039 960 312 


5,456,392 


3-421 
3-422 
3-423 


5-778 595 339 
6-783 813 580 
5-789 036 673 


5,218,241 
5,222,993 
5,227,751 


3-471 
3-472 
3-473 


6045 416 704 
6-050 878 068 
6056 344 413 


5,461,364 
5,466.345 
5,471,329 


3-424 
3-425 
3-426 


5-794 264 324 
5-799 496 835 
5-804 734 111 


5.232,511 
6,237,276 
5,242,047 


3-474 
3-475 
3-476 


6-061 815 742 
6067 292 058 
6-072 773 367 


5,476,316 
5,481.309 
5,486,308 


3-427 
3-428 
3-429 


5-809 976 158 
5-815 222 979 
5-820 474 580 


5,246,821 
5,251,601 
5,256,383 


3-477 
3-478 
3-479 


6-078 259 675 
6083 750 986 
6-089 247 303 


5,491,311 
5,496,317 
5,501.329 


3-430 


5-825 730 963 


5,261,170 


3-480 


6-094 748 632 


5,506,346 


3-431 
3-432 
3-433 


5-830 992 133 
6-836 258 096 
5-841 528 855 


5,265,963 
5,270,759 
5,275,562 


3-481 
3-482 
3-483 


6-100 254 978 
6-105 766 344 
6-111 282 736 


5,511,366 
5,516,392 
5,521,423 


3-434 
3-435 
3-436 


5-846 804 417 

5-852 084 784 
5-857 369 961 


6,280,.367 
5,285,177 
5,289,991 


3-484 
3-485 
3-486 


6-116 804 159 
6-122 330 617 
6-127 862 115 


5,526,458 
6,531,498 
5,536,543 


3-437 

3-438 
3-439 


5-862 659 952 
5-867 954 762 
5-873 254 396 


5,294,810 
6.299,634 
5,304,463 


3-487 
3-488 
3-489 


6-133 398 658 
6-138 940 250 
6-144 486 896 


5,541,592 
5,546,646 
6,561,705 


3-440 


5-878 558 859 


5,309,294 


3-490 


6-150 038 601 


5,556,767 


3-441 
3-442 
3-443 


6-883 868 153 
6-889 182 285 
5-894 601 259 


5,314,132 
5,318,974 
5,323,818 


3-491 
3-492 
3-493 


6-155 695 368 
6-161 157 205 
6-166 724 115 


5,561,837 
5,566,910 
5,671,987 


3-444 
3-445 
3-446 


5-899 825 077 
5-905 153 748 
5-910 487 275 


5,328.671 
5,333,527 
5,338,385 


3-494 
3-495 
3-496 


6-172 296 102 
6-177 873 172 
6-183 465 329 


5,577,070 
5,582.1.57 

5,587,248 


3-447 
3-448 
3-449 


6-915 825 660 
5-921 168 909 
5-926 517 028 


5,343,249 
5,348,119 
5,352,991 


3-497 
3-498 
3-499 


6-189 042 577 
6-194 634 923 
6-200 232 369 


6.592,346 
5,597,446 
6,602.553 


3-450 


5-931 870 019 


5,357,870 


3-500 


6-205 834 922 


5,607,664 



264 



BEPORT 1893. 



X 


l,x 


Difference 


X 


Iix 


Difference 


3-500 

3-501 
3-502 
3-503 

3-504 
3-505 
3-506 

3-507 
3-508 
3-509 


6-205 834 922 


5,607,664 


3-550 


6-492 579 585 


5,869,392 


6-211 442 586 
6-217 055 366 
6-222 673 267 

6-228 296 292 
6-233 924 448 
6-239 557 739 

6-245 196 168 
6-250 839 744 
6-256 488 468 


5,612,780 
5,617,901 
5,623,025 

5,628,156 
5,633,291 
5.638,429 

5,643,576 
5,648,724 
5,653,878 


3-551 
3-552 
3-553 

3-554 
3-555 
3-556 

3-557 
3-558 
3-559 


6-498 448 977 
6-504 323 730 
6-510 203 847 

6-516 089 335 
6-521 980 197 
6-527 876 440 

6-533 778 069 
6-539 685 087 
6-545 597 501 


5,874,753 
5,880,117 
5,885,488 

5,890,862 
5,896,243 
5,901,629 

5,907,018 
6,912,414 
5,917,814 


3-510 


6-262 142 346 


5,659,037 


3-560 


6-551 515 315 


5,923,219 


3-511 
3-512 
3-513 

3-514 
3-515 
3-516 

3-517 
3-518 
3-519 


6-267 801 383 
6-273 465 583 
6-279 134 953 

6-284 809 496 
6-290 489 217 
6-296 174 121 

6-301 864 212 
6-307 559 497 
6-313 259 979 


5,664,200 
5,669.370 
5,674,543 

5.679,721 
5,684,904 
5,690,091 

5,695,285 
5,700,482 
5,705,685 


3-561 
3-562 
3-563 

3-564 
3-565 
3-566 

3-567 
3-568 
3-569 


6-557 438 534 
6-563 367 165 
6-569 301 211 

6-575 240 677 
6-581 185 568 
6-587 135 889 

6-593 091 648 
6-599 052 847 
6-605 019 492 


6,928,631 
5,934,046 
5,939,466 

5,944,891 
5,950,321 
5,955,759 

6,961,199 
6,966,645 
6,972,097 


3-520 


6-318 965 664 


5,710,892 


3-570 


6-610 991 589 


5,977,651 


3-521 
3-522 
3-523 

3-524 
3-525 
3-526 

3-527 
3-5S8 
3-529 


6-324 676 556 
6-330 392 659 
6-336 213 979 

6-341 840 522 
6-347 572 292 
6-353 309 294 

6-359 051 531 
6-364 799 010 
6-370 551 736 


5,716,103 
5,721,320 
5,726,543 

5,731.770 
5,737,002 
5,742,237 

5,747,479 
5,752.726 
5,757,976 


3571 
3-572 
3-573 

3-574 
3-575 
3-576 

3-577 
3-578 
3-579 


6-616 969 140 
6-622 952 152 
6-628 940 632 

6-634 934 583 
6-640 934 Oil 
6-646 938 920 

6-652 949 315 
6-658 965 203 
6-664 986 587 


5,983,012 
5,988,480 
6,993,961 

5,999,428 
6,004,909 
6,010,395 

6,016,888 
6,021,384 
6,026,886 


3-530 


6-376 309 712 


5,763,233 


3-580 


6-671 013 473 


6,032,394 


3-531 
3-532 
3-533 

3-534 
3-535 
3-536 

3-537 
3-538 
3-539 


6-382 072 945 
6-387 841 439 
6-393 615 198 

6-399 394 230 
6-405 178 536 
6-410 968 122 

6-416 762 997 
6-422 563 159 
6-428 368 617 


5,768,494 
5,773,759 
5,779,032 

5.784,306 

5.789,586 
5,794,875 

5,800,162 
5,805,458 
5,810,760 


3-581 
3-582 
3-583 

3-584 
3-585 
3-586 

3-587 
3-588 
3-589 


6-677 045 867 
6-683 083 774 
6-689 127 198 

6-695 176 144 
6-701 230 618 
6-707 290 626 

6-713 356 172 
6-719 427 260 
6-725 503 897 


6,037,907 
6,043,424 
6,048.946 

6,064,474 
6,060,008 
6,065,646 

6,071,088 
6.076,637 
6,082,192 


3-540 


6-434 179 377 


5.816,064 


3-590 


6-731 586 089 


6,087,751 


3-541 
3-542 
3-543 

3-544 
3-545 
3-546 

3-547 

3-548 
3-549 


6-439 995 441 
6-445 816 815 
6-451 643 506 

6 457 475 517 
6-463 312 853 
6-469 155 519 

6-475 003 521 
6-480 856 863 
6-486 715 548 


5,821,374 
5,826,691 
6,832,011 

5,837,336 
6,842,666 
5,848,002 

5,853,342 

5.858,685 
5,864,037 


3-591 
3-592 
3-593 

3-594 
3-595 
3-596 

3-597 
3-598 
3-599 


6-737 673 840 
6-743 767 154 
6-749 866 037 

6-755 970 495 
6-762 080 533 
6-768 196 156 

6-774 317 369 
6-780 444 177 
6-786 576 586 


6,093,314 

6,098.883 
6,104,458 

6,110,038 
6,115,623 
6,121,213 

6,126,808 
6,132,409 
6,138,016 


3-550 


6-492 579 585 


5,869,392 


3-600 


6-792 714 601 


6,143,626 



ON MATHEMATICAL FDNCTIONS. 



265 



X 


Iir 


Difference 


X 


l,x 


Difference 


3-600 


6-792 714 601 


6,143,626 


3-650 


7-106 879 825 


6,430,965 


3-601 
3-602 
3-603 

3-604 
3-605 
3-606 

3-607 

3-G08 
3-609 


6-798 858 227 
6-805 007 469 
6-811 162 333 

6-817 322 824 
6-S23 488 946 
6-S29 660 705 

6-835 838 107 
()-S42 021 157 
6-848 209 860 


6,149,242 
6,154,864 
6,160,491 

6,166.122 
6.171,769 
6.177,402 

6,183,050 
6.188,703 
6,194,303 


3-651 
3-652 
3-653 

i 3-654 
3-655 
3-656 

' 3-657 

! 3-658 

3 659 


7-113 310 790 
7-119 747 639 
7-126 190 379 

7-132 639 015 
7-139 093 551 
7145 653 994 

7-152 020 349 
7-158 492 624 
7-164 970 821 


6,436.849 
6,442,740 
6,448,636 

6,454,536 
6,460,443 
6,466,355 

6,472,275 
6,478,197 
6,484,125 


3-610 


6-854 404 223 


6,200,026 


3-660 


7-171 454 946 


6,490,061 


3-611 
3-612 
3-613 

3-614 
3-615 
3-616 

3-617 
3-618 
3-619 


6-860 604 249 
6-866 809 944 
6-873 021 312 

6-879 238 360 
6-885 461 093 
6-891 689 516 

6-897 923 636 
6-904 163 456 
6-910 408 982 


6,205,695 
6,211,368 
6,217,048 

6,222,733 
6,228,423 
6,234,120 

6.239,820 
6,245.526 
6,251,237 

6,256.954 


i 3-661 

1 3-662 

3-663 

j 3-664 

1 3-665 

3-666 

3-667 

' 3-668 
3-669 


7-177 945 007 
7-184 441 007 
7-190 942 951 

7-197 450 848 
7-203 964 700 
7-210 484 516 

7-217 010 300 
7-223 542 056 
7-230 079 791 


6,496,000 
6,501,944 

6,507,897 

6,513,852 
6,519,816 
6,525,784 

6,531,756 
6,537,735 
6,543,719 


3-620 


6-916 660 219 


3-670 

3-671 
3-672 
3-673 

3-674 
3 675 
3-676 

3-677 
3-678 
3-679 


7-236 623 510 


6,549,709 


3-621 
3-622 
3-623 

3-624 
3-625 
3-626 

3-627 
3-628 
3-629 


6-922 917 173 
6-929 179 849 
6-935 448 253 

6-941 722 390 
6-948 002 265 
6-954 287 883 

6-960 579 251 
6-966 876 373 
6-973 179 254 


6,262,676 
6.268,404 
6,274,137 

6,279,875 
6,285,618 
6,291,368 

6,297,122 
6,302,881 
6,308,647 


7-243 173 219 
7-249 728 924 
7-256 290 631 
7-262 858 344 
7-269 432 070 
'7-276 Oil 814 

7-282 597 583 
7-289 189 380 
7-295 787 211 


6,555,705 
6,561,707 
6,567,713 

6,573,726 
6,579,744 
6,585,769 

6,591,797 
6,597,831 
6,603,873 


3-630 


6-979 487 901 


6,314,417 


3-680 


7-302 391 084 


6,609,919 


3-631 
3-632 
3-633 

3-634 
3-635 
3-636 

3-637 
3-638 
3-639 


6-985 802 318 
6-992 122 510 
6-998 448 484 

7-004 780 245 
7-011 117 798 
7-017 461 149 

7-023 810 301 
7-030 165 262 
7-036 626 038 


6,320,192 
6,325,974 
6,331,761 

6.337,553 
6,343,351 
6,349,152 

6,354,961 
6,360,776 
6,366,594 


3-681 
3-682 
3-683 

3-684 
3-685 
3-686 

3-687 

3-688 
3-689 


7-309 001 003 
7-315 616 973 
7-322 239 002 

7-328 867 094 
7-335 501 255 
7-342 141 490 

7-348 787 805 
7-355 440 205 
7-362 098 698 


6,615,970 
6,622,029 
6.628,092 

6,634,161 
6,640,235 
6,646,315 

6,652,400 
6.658,493 
6,664,590 


3-640 


7-042 892 632 


6,372,419 


3-690 


7-368 763 288 


6,670,694 


3-641 
3-642 
3-643 

3644 
3-645 
3-646 

3-647 
3-648 
3-649 


7-049 265 051 
7-055 643 299 
7-062 027 383 

7068 417 308 
7-074 813 079 
7-081 214 703 

7-087 622 185 
7-094 035 528 
7-100 454 740 


6,378,248 
6,384,084 
6,389,925 

6,395,771 
6,401,624 

6,407,482 

6,413,343 
6,419,212 
6,425,085 


3-691 
3-692 
3693 

3-694 
3-695 
3-696 

3-697 
3-698 
3-699 


7-375 433 982 
7-382 110 784 
7-388 793 700 

7-395 482 736 
7-402 177 898 
7-408 879 192 
7-415 586 623 
7-422 300 197 
7-429 019 920 


6,676,802 
6,682,916 
6,689,036 

6,695,162 
6,701,294 
6,707,431 

6,713,574 
6,719,723 
6,725,877 


3-650 


7-106 879 825 


6,430,965 


3-700 


7-435 745 797 


6,732,037 



266 



EEPOET 1893. 



X 


Iix 


Difference 


X 


I,X 


Difference 


3-700 


7-435 745 797 


6,732,037 


3-750 


7-780 015 230 


7,047,503 


3-701 
3-702 
3-703 

3-704 
3-705 
3-706 

3-707 
3-708 
3-709 


7-442 477 834 
7-449 216 037 
7-455 960 413 

7-462 710 9G7 
7-469 467 703 
7-476 230 628 

7-482 999 749 
7-489 775 070 
7-496 556 597 


6,738,203 
6,744,376 
6,750,554 

6,756,736 
6,762,925 
6,769,121 

6,775,321 
6,781,527 
6,787,740 


3-751 
3-752 
3-753 

3-754 
3-755 
3-756 

3-757 
3-758 
3-759 


7-787 062 733 
7-794 116 696 
7-801 177 128 

7-808 244 033 
7-815 317 416 
7-822 397 284 

7-829 483 643 
7-836 576 499 
7-843 675 859 


7,053,963 
7,060,432 
7,066,905 

7,073,383 

7,079,868 
7,086,359 

7,092,856 
7,099,360 
7,105,869 


3-710 


7-503 344 337 


6,793,958 


3-760 


7-850 781 728 


7,112,384 


3-711 

8-712 
3-713 

3-714 
3-715 
3-716 

3-717 
3-718 
3-719 

3-720 


7-510 138 295 
7-516 938 477 
7-523 744 888 

7-530 557 533 
7-537 370 422 
7-544 201 558 

7-551 032 947 
7-557 870 594 
7-564 714 505 


6,800,182 
6,806,411 
6,812,645 

6.818,889 
6,825,136 
6,831,389 

6,837,647 
6,843,911 
6.850,182 


3-761 
3-762 
3-763 

3-764 
3-765 
3-766 

3-767 
3-768 
3-769 


7-857 894 112 
7-865 013 017 
7-872 138 450 

7-879 270 417 
7-886 408 924 
7-893 553 977 

7-900 705 581 
7907 863 743 
7-915 028 470 


7,118,905 
7,125,433 
7,131,967 

7,138,507 
7,145,053 
7,151,604 

7,158,162 
7,164.727 
7,171,297 


7-571 564 687 


6,856,458 


3-770 


7-922 199 767 


7,177,874 


3-721 

3-722 
3-723 

3-724 
3-725 
3-726 

3-727 
3-728 
3-729 


7-578 421 145 
7-585 283 887 
7-592 152 916 

7-599 028 239 
7-605 909 862 
7-612 797 792 

7-619 692 032 
7-626 592 590 
7-633 499 472 


6,862.742 
6,869,029 
6,875,323 

6,881,623 
6,887.930 
6,894,240 

6,900,558 
6,906,882 
6,913,212 


3-771 

3-772 
3-773 

3-774 
3-775 
3-776 

3-777 
3-778 
3-779 


7-929 377 641 
7-936 562 097 
7-943 753 142 

7-950 950 782 
7-958 155 024 
7-965 365 873 

7-972 583 335 
7-979 807 417 
7-987 038 125 


7,184.456 
7,191,045 
7,197,6-iO 

7,204,242 
7,210,849 
7,217,462 

7,224,082 
7,230,708 
7,237,340 


3-730 

3-731 
3-732 
3-733 

3-734 
3-735 
3-736 

3-737 
3-738 
3-739 


7-640 412 684 


6,919,547 


3-780 

3-781 
3-782 
3-783 

8-784 

3-785 
3-786 

3-787 
3-788 
3-789 

3-790 


7-994 275 465 

8-001 519 442 
8-008 770 064 
8016 027 337 

8-023 291 267 
8-030 561 861 
8-037 839 123 

8-045 123 061 
8-052 413 681 
8-059 710 989 


7,243,977 


7-647 332 231 
7-654 258 118 
7-661 190 353 

7-668 128 941 
7-675 073 888 
7-682 025 200 

7-688 982 883 
7-695 946 942 
7-702 917 384 


6,925.887 
6,932,235 
6,938,588 

6,944,947 
6,951,312 
6,957,683 

6,964,059 
6,970,442 
6,976,832 


7,250,622 
7,257,273 
7,263,930 

7,270,594 
7.277,262 
7,283,938 

7,290,620 
7,297,308 
7,304,002 


3-740 


7-709 894 216 


6,983,227 


8-067 014 991 


7,310,703 


3-741 
3-742 
3-743 

3-744 
3-745 
3-746 

3-747 
3-748 
3-749 


7-716 877 443 
7-723 867 069 
7-730 863 103 

7-737 865 550 
7-744 874 414 
7-751 889 703 

7-768 911 424 
7-765 939 582 
7-772 974 182 


6,989,626 
6,996,034 
7,002,447 

7,008,864 
7,015,289 
7,021,721 

7,028.158 
7,034,600 

7,041,048 


3-791 
3-792 
3-793 

3-794 
3-795 
3-796 

3-797 
3-798 
3-799 


8-074 325 694 
8-081 643 104 
8-088 967 226 

8-096 298 067 
8-103 635 635 
8-110 979 936 

8-118 330 974 
8-125 688 756 
8-133 053 289 


7,317,410 
7,324,122 
7,330,841 

7,337,568 
7,344,301 
7,351,038 

7,357,782 
7,364,533 
7,371,290 


3-750 


7-780 015 230 


7,047,503 


3-800 


8-140 424 579 


7,378,054 



ON MATHEMATICAL FUKCTIONS. 



267 



X 


I,^- 


Difference 


X 


IlX 


Difference 


3-800 


8-140 424 


579 


7,378,054 


3-850 


8 517 745 677 


7,724,413 


3-801 
3-802 
3-803 


8-147 802 
8-155 187 
8-162 579 


633 

456 
056 


7,384,823 
7.391.600 
7,398.382 


3-851 
3-852 
3-853 


8-525 470 090 
8-533 201 596 
8-540 940 204 


7,731,506 

7.738,608 
7.745,715 


3804 
3805 
3-806 


S-ir.9 977 
8-177 382 
8-184 794 


438 
609 
575 


7,405,171 
7,411.966 
7,418,767 


3-854 
3-855 
3-856 


8-548 685 919 
8-556 438 746 
8-564 198 693 


7.752,827 
7,759,947 
7,767,074 


3-807 
3-808 
3-809 


8-192 213 
8-199 638 
8-207 071 


342 
918 
308 


7,425,576 
7,432,390 
7,439.210 


3857 
3-858 
3-859 


8-571 965 767 
8-579 739 975 
8-587 521 323 


7,774,208 
7,781,348 
7.788.495 


3-810 


8-214 510 


518 


7,446,037 


3-860 


8-595 309 818 


7,795,649 


3-811 
3-812 
3-813 


8-221 956 
8-229 409 
8-236 869 


555 
425 
135 


7,452,870 
7.459,710 
7,466,556 


3861 
3-862 
3-863 


8-603 105 467 
8-610 908 276 
8-618 718 251 


7,802,809 
7,809,975 
7,817,150 


3-814 
3-815 
3-816 


8-244 335 
8-251 809 
8-259 289 


691 
101 
369 


7,473,410 
7,480,268 
7.487,134 


3-864 
3-865 
3-866 


8-626 535 401 
8-634 359 731 
8-642 191 247 


7,824,330 
7,831,516 
7,838,711 


3-817 
3-818 
3-819 


8-266 776 
8-274 270 
8-281 771 


503 
508 
391 


7,494,005 
7,500,883 
7,507,768 


3-867 
3-868 
3-869 


8-650 029 958 
8-657 875 869 
8-665 728 987 


7,845,911 
7.853,118 
7,860,331 


3-820 


8-289 279 


159 


7,514,658 


3-870 


8-673 589 318 


7,867,553 


3-821 
3-822 
3-823 


8-296 793 
8-304 315 
8-311 843 


817 
373 
833 


7,521,556 
7,528,460 
7,535.370 


3-871 
3-872 
3-873 


8-681 456 871 
8-689 331 652 
8-697 213 666 


7,874,781 
7,882,014 
7,889,255 


3-824 
3-825 
3-826 


8-319 379 
8-326 921 
8-334 470 


203 
491 
702 


7,542,288 
7,549,211 
7,556,140 


3-874 
3-875 
3-876 


8-T05 102 921 
8-712 999 424 
8-720 903 181 


7,896.503 
7.903,757 
7,911,019 


3-827 
3-828 
3-829 


8-342 026 
8-349 589 
8-357 159 


842 
919 
939 


7.563,077 
7.570,020 

7,576,968 


3-877 
3-878 
3-879 


8-728 814 200 
8-736 732 487 
8-744 658 049 


7,918,287 
7,925,562 
7,932,844 


3-830 


8-364 736 


907 


7,583,925 


3-880 


8-752 590 893 


7,940,132 


3-831 
3-832 
3-833 


8-372 320 
8-379 911 
8-387 509 


832 
719 
575 


7,590,887 
7,597,856 
7,604,830 


3-881 
3-882 
3-883 


8-760 531 025 
8-768 478 452 
8-776 433 182 


7,947,427 
7,954,730 
7,962,038 


3-834 
3-835 
3-836 


8-395 114 405 
8-402 726 218 
8-410 345 019 


7,611,813 
7,618,801 
7,625,795 


3-884 
3-885 
3-886 


8-784 .395 220 
8-792 364 574 
8-800 341 251 


7,969,354 
7,976,677 
7,984,007 


3-837 
3-838 
-3-839 


8-417 970 
8-425 603 
8-433 243 


814 
611 
417 


7,632,797 
7,639,806 
7,646,819 


3-887 
3-888 
3-889 


8-808 325 258 
8-816 316 601 
8-824 315 286 


7,991,343 

7,998,685 
8,006,036 


3-840 


8.440 890 


236 


7,653,840 


3-890 


8-832 321 322 


8,013,393 


3-841 
3-842 
3-843 


8-448 544 
8-456 204 
8-463 872 


076 
945 

847 


7,660,869 
7,667,902 
7,674,944 


3-891 
3-892 
3-893 


8-840 334 715 
8-848 355 472 
8-856 383 599 


8,020,757 
8,028,127 
8,035,506 


3-844 
3-845 
3-846 


8-471 547 
8-479 229 
8-486 918 


791 

782 
827 


7,681,991 
7,689,045 
7,696,105 


3-894 
3-895 
3-896 


8-864 419 105 
8-872 461 995 
8-880 512 275 


8,042,890 
8,050,280 
8,057,680 


3-847 

3-848 
3-849 


8-494 614 
8-502 318 
8-510 028 


932 
104 
350 


7,703,172 
7,710,246 
7,717,327 


3-897 
3-898 
3-899 


8-888 569 955 
8-896 635 040 
8-904 707 536 


8,065,085 
8,072,496 
8,079,915 


3-850 


8-517 745 


677 


7,724,413 


3-900 


8-912 787 451 


8,087,342 



268 



REPORT 1893. 



X 


I,x 


Difference 


X 


IjX 


Difference 


3-900 


8-912 787 451 


8,087,342 1 


3-950 


9-326 397 737 


8,467,636 


3-901 
3-902 
3-903 

3-904 
3-905 
3-90G 

3-907 
3-908 
3-909 


8-920 874 793 
8-928 969 568 
8-937 071 784 

8-945 181 446 
8-953 298 561 
8-961 423 138 

8-969 555 183 
8-977 694 702 
8-985 841 703 


8,094,775 j 
8,102,216 
8,109,662 ; 

8,117,115 
8.124,577 
8,132,045 

8,139,519 
8,147,001 
8,154,490 


3-951 
3-952 
3-953 

3-954 
3-955 
3-956 

3-957 
3-958 
3-959 


9-334 865 373 
9-343 340 799 
9-351 824 021 

9-360 315 045 
9-368 813 881 
9-377 320 535 

9-385 835 013 
9-394 357 324 
9-402 887 475 


8,475,426 
8,483,222 
8,491,024 

8,498,836 
8,506,654 
8,514,478 

8,522,311 
8,530,151 
8,537,998 


3-910 


8-993 996 193 


8,161,985 


3-960 


9-411 425 473 


8,545,853 


3-911 
3-912 
3-913 

3-914 
3-915 
3-916 

3-917 
3-918 
3-919 


9-002 158 178 
9-010 327 666 
9-018 504 664 

9-026 689 179 
9-034 881 218 
9-043 080 788 

9051 287 895 
9-059 502 548 
9-067 724 753 


8.169,488 
8,176,998 
8,184,515 

8,192,039 
8,199,570 1 
8,207,107 ; 
8,214.653 
8,222,205 
8,229,764 


3-961 

3-962 
3-963 

3-964 
3-965 
3-966 

3-967 
3-968 
3-969 


9-419 971 326 
9-428 525 041 
9-437 086 624 

9-445 656 085 
9-454 233 429 
9-462 818 664 

9-471 411 800 
9-4S0 012 840 
9-488 621 793 


8,553,715 
8,561,583 
8,569,461 

8,577,344 
8,585,235 
8,593,136 

8,601,040 
8,608,953 
8,616,875 


3-920 


9075 954 517 


8,237,330 


3-970 


9-497 238 668 


8,624,804 


3-921 
3-922 
3-923 

3-924 
3-925 
3-926 

3-927 
3-928 
3-929 


9084 191 .S47 
9-092 436 751 
9-100 689 235 

9-108 949 305 
9-117 216 972 
9-125 492 238 

9-133 775 114 
9-142 065 606 
9-150 363 722 


8,244,904 
8,252,484 
8,260,070 

8,267,667 
8,275,266 

8,282,876 

8,290,492 
8,298,116 
8,305,745 


3-971 
3-972 
3-973 

3-974 
3-975 
3-976 

3-977 
3-978 
3-979 


9-505 863 472 
9-514 496 211 
9-523 136 894 

9-531 785 527 
9-540 442 117 
9-549 106 674 

9-557 779 204 
9-566 459 713 
9-575 148 211 


8,632,739 
8,640,683 
8,648,633 

8,656,590 
8,664,557 
8,672,530 

8,680,509 
8,688,498 
8,696,493 


3-930 


9-158 669 467 


8,313,382 j 


3-980 

3-981 
3-982 
3-983 

3-984 
3-985 
3-986 

3-987 
3-988 
3-989 


9-583 844 704 


8,704,495 


3-931 
3-932 
3-933 

3-934 
3-935 
3-936 

3-937 
3-938 
3-939 


9-166 982 849 
9-175 303 876 
9-183 632 554 

9-191 968 891 
9-200 312 ,S94 
9-208 664 571 

9-217 023 927 
9-225 390 970 
9-233 765 707 


8",321,027 1 
8,328,678 ; 
8,336,337 

8,344,003 
8,351.677 
8,359,356 

8,367,043 
8,374,737 
8,382.440 


9-592 549 199 
9-601 261 704 
9-609 982 229 

9-618 710 778 
9-627 447 359 
9-636 191 982 

9-644 944 652 
9-<;53 705 378 
9-662 474 166 


8,712,505 
8,720,525 
8,728,549 

8.736,581 
8,744,623 
8,752,670 

8,760,726 

8,768,788 
8,776,859 , 


3-940 


9-242 148 147 


8,390,150 


3-990 


9-671 251 025 


8,784,936 


3-941 
3-942 
3-943 

3-944 
3-945 
3-946 

3-947 
3-948 
3-949 


9-250 538 297 
9-258 936 163 
9-267 341 752 

9-275 755 071 
9-284 176 128 
9-292 604 930 

9-301 041 485 
9-309 485 800 
9-317 937 882 


8,397,866 
8,405,589 
8,413,319 

8,421,057 
8,428,802 
8,436,555 

8,444,315 

8,452,082 
8,459,855 


3-991 
3-992 
3-993 

3-994 
3-995 
3-996 

3997 
3-998 
3-999 


9-680 035 961 
9-688 828 984 
9-697 630 100 

9-706 439 316 
9-715 256 641 
9-724 082 081 

9-732 915 645 
9-741 757 341 
9-750 607 174 


8,793,023 
8,801,116 
8,809,216 

8,817,325 
8,825,440 
8,833,564 

8,841,696 
8,849,833 
8,857,980 


3-950 


9-326 397 737 


8,467,636 


4-000 


9-759 465 154 


8,866,134 



ON MATHEMATICAL FUNCTIONS. 



269 



.r 


I,x 


Difference 


.V 


Ii-r 


Difference 


4-000 


9-759 465 154 


8,866,134 


4-050 


10-212 921 103 


9,283,709 


4 001 
4-002 
4003 

4004 
4005 
4-006 

4-007 
4-008 
4-009 


9-768 331 288 
9-777 205 583 
9-786 088 047 

9-794 978 689 
9-803 877 515 
9-812 784 533 

9-821 699 751 
9-830 623 176 
9-839 554 817 


8,874,295 
8,882,464 
8,890,642 

8,898,826 
8,907.018 
8,915,218 

8,923,425 
8,931,641 
8,939,864 


4-051 
4-052 
4053 

4-054 
4-055 
4-056 

4-057 
4-058 
4-059 


10-222 204 812 
10-231 497 074 
10-240 797 895 

10-250 107 286 
10-259 425 253 
10-268 751 805 

10-278 086 948 
10-287 430 691 
10-296 783 045 


9,292,262 
9,300,821 
9,309,391 

9,317,967 
9,326,552 
9,335,143 

9,343,743 
9,352,354 
9,360,971 


4-010 


9-848 494 681 


8,948,093 


4-060 


10-306 144 016 


9,369,592 


4011 
4-012 
4013 

4-014 
4-015 
4-016 

4-017 
4018 
4019 


9-857 442 774 
9-866 399 106 
9-875 363 685 

9-884 336 516 
9-893 317 609 
9-902 306 972 

9011 304 611 
9-920 310 534 
9-929 324 751 


8,956,332 
8,964,579 
8,972,831 

8,981,093 
8,989,363 
8,997,639 

9.005,923 
9,014,217 
9,022,516 


i 4-061 

: 4062 

4063 

■ 4-064 
4-065 
4-066 

' 4-067 

4-068 

j 4-069 


10-315 513 608 
10-324 891 834 
10-334 278 701 

10-343 674 217 
10-353 078 391 
10-362 491 230 

10-371 912 742 
10-381 342 934 
10-390 781 817 


9,378,226 
9,386,867 
9,395,516 

9,404.174 
9,412,839 
9,421,512 

9,430,192 
9,438,883 
9,447,580 


4020 


9-938 347 267 


9,030,824 


4-070 

4-071 
4-072 
4-073 

4-074 

4-075 

; 4-076 

4-077 
1 4-078 
i 4-079 


10-400 229 397 


9,456,285 


4021 
4-022 
4-023 

4024 
4-025 
4026 

4027 
4-028 
4029 


9-947 378 091 
9-956 417 231 
9-965 464 694 

9-974 520 488 
9-983 584 623 
9-992 657 103 

10-001 737 938 
10010 827 135 
10019 924 702 


9,039,140 
9,047,463 
9,055,794 

9,064,135 
9,072,480 
9,080,835 

9,089,197 
9,097,567 
9,105,948 


10-409 685 682 
10-419 150 6S2 
10-428 624 404 

10-438 106 854 
10-447 598 046 
10-457 097 983 

10-466 606 673 
10-476 124 127 
10-485 650 354 


9,465.000 
9,473,722 
9,482,450 

9,491,192 
9,499,937 
9,508,690 

9,517,454 
9,526,227 
9,535,005 


4030 


10-029 030 650 


9,114,331 


j 4-080 


10-495 185 359 


9,543,792 


4031 
4032 
4033 

4-034 
4035 
4-036 

4-037 
4-038 
4039 


10038 144 981 
10-047 267 706 
10056 398 834 

10-065 538 372 
10074 686 325 
10083 842 703 

10-093 007 517 
10-102 180 769 
10-111 362 474 


9.122,725 

9,131,128 
9,139,538 

9,147,953 
9,156,378 
9,164,814 

9,173,252 
9,181,705 
9,190,160 


4-081 

. 4-082 

4-083 

4-084 

4-085 

1 4086 

4-087 
' 4-088 
' 4-089 

4-090 


10-504 729 151 
10-514 281 740 
10-523 843 133 

10-5.33 413 338 
10-542 992 363 
10-552 580 217 

10-562 176 907 
10-571 782 444 
10-581 396 834 


9,552,589 
9,561,393 
9,570,205 

9,579.025 

9,587,854 
9,596,690 

9,605,537 
9,614,390 
9,623,251 


4-040 


10-120 552 634 


9,198,625 


10-591 020 085 


9,632,122 

9,641,001 
9,649,887 
9,658,783 

9,667,686 
9,676,598 
9,685,518 

9,694,446 
9,703.383 
9,712,328 


4-041 
4042 
4 043 

4044 
4045 
4 046 

4047 
4048 
4049 


10-129 751 259 
10-138 958 355 
10-148 173 933 

10-157 397 999 
10-166 630 562 
10175 871 630 

10-185 121 209 
10-194 379 309 
10-203 645 938 


9,207,096 
9,215,578 
9,224,066 

9,232,563 
9,241,068 
9,249,579 

9,258,100 
9,266,629 
9,275,165 


j 4-091 
4-092 
4-093 

4-094 
4-095 
4096 

4097 
4-098 
4099 


10-600 652 207 
10-610 293 208 
10-619 943 095 

10-629 601 878 
10-639 269 564 
10-648 946 162 

10-658 631 680 
10-668 326 126 
10-678 029 509 


4050 


10-2] 2 921 103 


9,283,709 


4-100 


10-687 741 837 


9,721,281 



270 



REPORT 1893. 



X 


l,x 


Difference 


X 


Iix 


Difference 


4-100 


10-687 741 837 


9,721,281 


4-150 


11-184 950 646 


10,179,815 


4-101 
4-102 
4-103 

4-104 
4105 
4-106 

4-107 
4-108 
4109 


10-697 463 118 
10-707 193 363 
10-716 932 578 

10-726 680 771 
10-736 437 950 
10-746 204 126 

10-755 979 307 
10-765 763 499 
10-775 556 713 


9,730,245 
9,739,215 
9,748,193 

9,757,179 
9,766,176 
9,775,181 

9,784,192 1 

9,793,214 

9,802,243 


4-151 
4-152 
4-153 

4-154 

4-155 
4-156 

4-157 
4-158 
4-159 


11-195 130 461 
11-205 319 668 
11-215 518 275 

11-225 726 292 
11-235 943 726 
11-246 170 587 

11-256 406 883 
11-266 652 623 
11-276 907 815 


10,189,207 
10,198,607 
10,208,017 

10,217,434 
10,226,861 
10,236,296 

10,245,740 
10,255,192 
10,264,656 


4110 


10-785 358 956 


9,811,280 


4-160 


11-287 172 471 


10,274,127 


4-111 
4112 
4113 

4114 
4115 
4-116 

4-117 
4-118 
4-119 


10-795 170 236 
10-804 990 562 
10-814 819 943 

10-824 658 387 
10-834 505 903 
10-844 362 499 

10-854 228 184 
10-864 102 966 
10-873 986 855 


9,820,326 
9,829.381 
9,838,444 

9,847,516 
9,856,596 
9,865,685 

9,874,782 
9,883,889 
9,893,001 


4-161 
4-162 
4-163 

4-164 
4-165 
4-166 

4-167 
4-168 
4-169 


11-297 446 598 
11-307 730 204 
11-318 023 298 

11-328 325 889 
11-338 637 987 
11-348 959 600 

11-359 290 738 
11-369 631 408 
11-379 981 621 


10,283,606 
10,293,094 
10,302,591 

10,312.098 
10,321,613 
10,331,138 

10,340,670 
10,350,213 
10,359,763 


4120 


10-883 879 856 | 9,902,124 


4-170 


11-390 341 384 


10,369,323 


4121 
4-122 
4123 

4-124 
4-125 
4126 

4-127 
4-128 
4-129 


10-893 781 980 
10-903 693 238 
10-913 613 634 

10-923 543 177 
10-933 481 878 
10-943 429 745 

10-953 386 786 
10-963 353 009 
10-973 328 423 


9,911,258 
9,920,396 
9,929,543 

9,938,701 
9,947,867 
9,957,041 

9,966,223 
9,975,414 
9,984,615 


4-171 
4-172 
4-173 

4-174 
4-175 
4-176 

4-177 
4-178 
4-179 


11-400 710 707 
11-411 089 599 
11-421 478 069 

11-431 876 126 
11-442 283 778 
11-452 701 036 

11-463 127 907 
11-473 564 401 
11-484 010 525 


10,378,892 

10,388,470 
10,398,057 

10,407,652 
10,417,258 
10,426,871 

10,436,494 
10,446,124 
10,455,767 


4130 


10-983 313 038 j 9,993,824 


4-180 


11-494 466 292 


10,465,416 


4131 
4-132 
4-133 

4134 
4-135 
4-136 

4-137 
4-138 
4139 

4140 


10-993 306 862 
11-003 309 903 
11-013 322 169 

11-023 343 670 
11-033 374 414 
11-043 414 409 

11053 463 665 
11-063 522 190 
11-073 589 992 


10,003,041 
10,012,266 
10,021,501 

10,030,744 
10,039,995 
10,049,256 

10,058,525 
10,067.802 
10,077,089 


4-181 
4-182 
4-183 

4-184 
4-185 
4-186 

4-187 
4-188 
4-189 


11-504 931 708 
11-515 406 782 
11-525 891 524 

11-536 385 943 
11-546 890 049 
11-557 403 851 

11-567 927 354 
11-578 460 573 
11-589 003 513 


10,475,074 
10,484,742 
10,494,419 

10,.504,106 
10,513,802 
10,523,503 

10,533,219 
10,542,940 
10,552,671 


11-083 667 081 


10,086,385 


4-190 


11-599 556 184 


10,562,412 


4-141 
4-142 
4-143 

4-144 
4145 
4-146 

4-147 
4-148 
4-149 


11-093 753 466 
11-103 849 154 
11-113 954 156 

11-121 068 478 
11-134 192 130 
11-144 325 121 

11-154 467 459 
11-164 619 153 
11-174 780 212 


10,095,688 
10,105,002 
10,114,322 

10,123,652 
10,132,991 
10,142,338 

10,151,694 
10,161,059 
10,170,434 


4-191 
4-192 
4-193 

4-194 
4-195 
4196 

4-197 
4-198 
4-199 


11-610 118 596 
11-620 690 759 
11-631 272 681 

11-641 864 370 
11-652 465 836 
11-663 077 088 

11-673 698 136 
11-684 328 988 
11-694 969 654 


10,572,163 
10,581,922 
10,591,689 

10,601,466 
10,611,252 
10,621,048 

10,630,852 
10,640,666 
10,650,489 


4-150 


11-184 950 646 


10,179,815 


4-200 


11-705 620 143 


10,660,322 



ON MATHEMATICAL FUNCTIONS. 



271 



.r 


J,x 


Difference 


X 


Iix 


Difference 


4-200 

4-201 
4-202 
4-203 

4-204 
4-205 
4-206 

4-207 
4-208 
4-209 


11-705 620 143 


10,660,322 


4-250 


] 2-250 874 666 


11,163,862 

11,174,170 
11,184,494 
11,194,827 

11,205,169 
11,215,521 
11,225,883 

11,236,254 
11,246,635 
11,257,026 


11-716 280 465 
11-726 950 627 
11-737 630 640 

11-748 320 514 
11 -759 020 257 
11-769 729 877 

11-780 449 385 
11-791 178 791 
11-801 918 102 


10,670.162 
10,680,013 
10,689,874 

10.699.743 
10,709,620 
10,719,508 

10,729,406 
10,739,311 
10,749,226 


j 4-251 
4-252 
4-253 

4-254 
; 4-255 
1 4-256 

4-257 
4-258 
4-259 


12-262 038 528 
12-273 212 698 
12-284 397 192 

12-295 592 019 
12-306 797 188 
12-318 012 709 

12-329 238 592 
12-340 474 846 
12-351 721 481 


4-210 


11-812 667 328 


10,759,151 


4-260 


12-362 978 507 


11,267,427 


4-211 
4-212 
4-213 

4-214 
4-215 
4-216 

4-217 
4-218 
4-219 


11-823 426 479 
11-834 195 565 
11-844 974 594 

11-855 763 575 
11-866 562 519 
11-877 371 434 

11-888 190 329 
11-899 019 214 
11-909 858 099 


10,769,086 
10,779,029 

10,788,981 

10.798,944 
10,808,915 
10,818,895 

10,828,885 
10,838,885 
10,848,893 


4-261 
4-262 
4-263 

4-264 
4-265 
4-266 

4-267 
4-268 
4-269 


12-374 245 934 
12-385 523 770 
12-396 812 026 

12-408 110 713 
12-419 419 840 
12-430 739 416 

12-442 069 450 
12-453 409 953 
12-464 760 935 


11,277,836 
11,288,256 
11,298,687 

11,309,127 
11.319,576 
11,330,034 

11,340,503 
11,350,982 
11,361,471 


4-220 


11-920 706 992 


10,858,911 


4-270 


12-476 122 406 


11,371,969 


4-221 
4-222 
4-223 

4-224 
4-225 
4-226 

4-227 
4-228 
4-229 


11-931 565 903 
11-942 434 841 
11-953 313 817 

11-964 202 840 
11-975 101 918 
11-986 Oil 060 

11-996 930 277 
12-007 859 579 
12-018 798 973 


10,868,938 

10,878.976 
10,889,023 

10,899,078 
10.909,142 
10,919,217 

10,929,302 
10,939,394 
10,949,497 


4-271 

4-272 
i 4-273 

4-274 
' 4-275 
; 4-276 

^ 4-277 
4-278 
4-279 


12-487 494 375 
12-498 876 850 
12-510 269 846 

12-521 673 371 
12-533 087 432 
12-544 512 040 

12-555 947 206 
12-567 392 940 
12-578 849 252 


11,382,475 
11,392,996 
11,403,525 

11,414,061 
11,424,608 
11,435,166 

11,445,734 
11,456,312 
11,466,898 


4-230 


12-029 748 470 


10,959,610 


4-280 


12-590 316 150 


11,477,495 


4-231 
4-232 
4-233 

4-234 
4-235 
4-236 

4-237 
4-238 
4-239 


12-040 708 080 
12-051 677 812 
12-062 657 675 

12-073 647 679 
12084 647 833 
12-095 658 147 

12106 678 630 
12117 709 292 
12-128 750 142 


10,969,732 
10,979,863 
10,990,004 

11,000,154 
11,010,314 
11,020,483 

11,030,662 
11,040,850 
11,051,049 


4-281 
4-282 
4-283 

4-284 
4-285 
4-286 

4-287 
4-288 
4-289 


12-601 793 645 
12-613 281 748 
12-624 780 468 

12-636 289 815 
12-647 809 799 
12-659 340 429 

12-670 881 717 
12-682 433 672 
12-693 996 304 


11,488,103 
11,498,720 
11,509,347 

11,519,984 
11,530,630 
11,541,288 

11,551,955 
11,562,632 
11,573,318 


4-240 


12-139 801 191 


11,061,256 


4-290 


12-705 569 622 


11,584,015 


4-241 
4-242 
4-243 

4-244 
4-245 
4-246 

4-247 
4-248 
4-249 


12-150 862 447 
12161 933 919 
12173 015 619 

12-184 107 555 
12-195 209 737 
12-206 322 172 

12-217 444 875 
12-228 577 852 
12-239 721 112 


11,071,472 
11,081,700 
11,091,936 

11,102,182 
11,112,435 
11,122,703 

11,132,977 
11,143,260 
11,153,554 


4-291 
4-292 
4-293 

4-294 
4-295 
4-296 

4-297 
4-298 
4-299 

4-300 


12-717 153 637 
12-728 748 359 
12-740 353 799 

12-751 969 966 
12-763 596 870 
12-775 234 520 

12-786 882 927 
12-798 542 103 
12-810 212 056 


11,594,722 
11,605,440 
11,616,167 

11,626,904 
11,637,650 
11,648,407 

11,659,176 
11,669,953 
11,680,740 


4-250 


12-250 874 666 


11,163,862 


12-821 892 796 


11,691,537 



272 



KEPORT — 1893. 



X 


I,x 


Difference 


X 


I,.r 


Difference 


4-300 


12-821 892 796 


11,691,537 


4-350 


13-419 909 985 


12,244,526 


4-301 
4-302 
4-303 

4-304 
4-305 
4-306 

4-307 
4-308 
4-309 


12-833 584 333 
12-845 286 679 
12-856 999 843 

12-868 723 836 
12-880 458 666 
12-892 204 344 

12-903 960 881 
12-915 72S 286 
12-927 506 570 


11,702,346 
11,713,164 
11.723,993 

11,734.830 
11,745,678 
11,756,537 

11.767,405 
11,778,284 
11,789,173 


4-351 
4-352 
4-353 

4-354 
4-855 
4-356 

4-357 
4-358 
4-359 


13-432 154 511 
13-444 410 361 
13-456 677 550 

13-468 956 086 
18-481 245 981 
13-493 547 244 

13-505 859 886 
13-518 183 918 
13-530 519 351 


12,255,850 
12,267.189 
12,278,536 

12,289,895 
12,301,263 
12,812,642 

12,324,032 
12.335,433 
12,846,845 


4-310 


12-939 295 743 | 11,800,073 


4-360 


13-542 866 196 


12,858,267 


4-311 
4-312 
4-313 

4-314 
4-315 
4-316 

4-317 
4-318 
4-319 


12-951 095 816 
12-962 906 798 
12-974 728 700 

12986 561 532 
12-998 405 304 
13-010 260 026 

13-022 125 709 
13-034 002 364 
12-045 889 999 


11,810,982 
11,821,902 
11,832,832 

11,843,772 
11,854,722 
11,865,683 

11,876.655 
11,887,635 
11,898,627 


4-361 
4-862 
4-363 

4-364 
4-865 
4-366 

4-367 
4-368 
4-369 


13-555 224 463 
18-567 694 163 
13-579 975 306 

13-592 367 904 
18-604 771 966 
18-617 187 504 

13-629 614 529 
13-642 053 051 
13-654 503 081 


12,369,700 
12,881,143 
12,392,598 

12,404,062 
12,415,538 
12,427,025 

12,488,522 
12,450,030 
12,461,549 


4-320 


13-057 788 626 


11,909,629 


4-370 


13-666 964 630 


12,478,079 


4-321 
4-322 
4-323 

4-324 
4-325 
4-326 

4-327 
4-328 
4-329 


13-069 698 25^ 
13-081 618 897 
13-093 550 560 

13-105 493 257 
13-117 446 996 
13-129 411 789 

13-141 387 646 
13-153 374 577 
13-165 372 594 


11,920.642 
11,931,663 
11,942.697 

11,953,739 
11,964,798 
11,975,857 

11,986,931 
11,998,017 
12,009,111 

12,020,217 


4-371 

4-372 
4-373 

4374 
4-375 
4-376 

4-377 
4-878 
4-379 


13-679 437 709 
18-691 922 829 
13-704 418 499 

13-716 926 232 
18-729 445 538 
18-741 976 428 

13-754 518 912 
13-767 078 002 
13-779 638 709 


12,484,620 
12,496,170 
12,507,733 

12,519,306 
12,530,890 
12,542,484 

12,554,090 
12,565,707 
12,577,334 


4-330 


13-177 381 705 


4-880 


13-792 216 043 


12,588,972 


4-331 
4-332 
4-333 

4-334 
4-335 
4-336 

4-337 
4-388 
4-339 


13-189 401 922 
13-201 433 255 
13-213 475 714 

13-225 529 309 
13-237 594 052 
13-249 609 952 

13-261 757 020 
13-273 855 268 
13285 964 705 


12,031.333 
12,042,459 
12,053,595 

12.064.743 
12,075,900 

12,087,068 

12,098,248 
12,109,437 
12,120,6.35 


4-381 
4-382 
4-383 

4-384 
4-385 
4-386 

4-387 
4-388 
4-389 


13-804 805 015 
18-817 405 636 
13-830 017 918 

18-842 641 871 
13-855 277 505 
13-867 924 832 

13-880 583 863 
18-893 254 610 
13-905 937 082 


12,600,621 
12,612,282 
12,623,953 

12,635,634 
12,647,327 
12,659,031 

12,670,747 
12,682,472 
12,694,209 


4-340 


13-298 085 340 


12,131,845 


4-890 

4-391 
4-392 
4-393 

4-394 
4-395 
4-396 

4-397 
4-398 
4-399 


13-918 631 291 


12,705,957 


4-341 
4-342 
4-343 

4-344 
4-345 
4-346 

4-347 
4-348 
4-349 


13-310 217 185 
13-322 360 252 
13-334 514 549 

13-346 680 087 
13-358 856 878 
13-371 044 932 

13-383 244 259 
13-395 454 869 
13-407 676 776 


12,148,067 
12,154,297 
12,165,538 

12,176,791 
12,188.054 
12,199,327 

12,210,610 
12,221,907 
12,233,209 


13-931 337 248 
13-944 054 964 
13-956 784 450 

13-969 525 717 
13-982 278 775 
13-995 043 637 

14-007 820 314 
14020 608 815 
14033 409 153 


12,717,716 
12,729,486 
12,741,267 

12,753,058 
12,764,862 
12,776,677 

12,788,501 
12,800,338 
12,812,185 


4-350 


13-419 909 985 


12,244,526 


4-400 


14-046 221 338 


12,824,043 



ON MATHEMATICAL FUNCTIONS. 



273 



X 


If- 


Difference 


x 


I,r 


Difference 


4-400 


14-046 221 338 


12,824,043 


4-450 


14-702 184 510 


13,431,374 


4-401 
4-402 
4-403 

4-404 
4-405 
4-406 

4-407 
4-408 
4-409 


14-059 045 3Sl 
14-071 881 294 
14-084 729 088 

14-097 588 774 
14-110 460 363 
14-123 343 867 

14136 239 296 
14-149 146 662 
14-162 065 975 


12,S35,913 
12.847,794 
12,859,686 

12,871,589 
12,883,504 
12,895,429 

12,907,366 
12,919,313 
12,931,272 ; 


4-451 
4-452 
4-453 

4-454 
4-455 
4-456 

4-457 
4-458 
4-459 


14-715 615 884 
14-729 059 697 
14-742 515 961 

14-755 984 688 
14-769 465 889 
14-782 959 575 

14-796 465 761 
14-809 984 457 
14-823 515 672 


13,443,813 
13,456,264 
13,468.727 

13,481.201 
13,493,686 
13,506,186 

13,518,696 
13.531,215 
13,543,748 


4-410 

4-411 
4-412 
4-413 

4-414 
4-415 
4-416 

4-417 
4-418 
4-419 


14-174 997 247 


12,943,242 


4-460 


14-837 059 420 


13,556,293 


14-187 940 489 
14-200 895 714 
14-213 862 931 

14-226 842 151 
14-239 833 386 
14-252 836 648 

14-265 851 948 
14-278 879 298 
14-291 918 708 


12,955,225 
12,967,217 
12,979,220 

12,991,235 
13,003,262 
13,015,300 

13,027.350 
13,039,410 
13,051.481 


4-461 
4-462 
4-463 

4-464 
4-465 
4-466 

4-467 
4-468 
4-469 


14-850 615 713 
14-864 184 564 
14-877 765 984 

14-891 359 982 
14-904 966 573 
14-918 585 767 

14-932 217 578 
14-945 862 017 
14-959 519 094 


13,568,851 
13,581,420 
13,593,998 

13.606,591 
13,619,194 
13,631,811 

13,644,439 
13,657,077 
13,669,728 


4-420 


13-304 970 189 


13,063,564 


4-470 


14-973 188 822 


13,682,391 


4-421 
4-422 
4-423 

4-424 
4-425 
4-426 

4-427 
4-428 
4-429 


14-318 033 753 
14-331 109 412 
14-344 197 177 

14-357 297 058 
14-370 409 068 
14-383 533 218 

14-396 669 518 
14-409 817 981 
14-422 978 617 


13,075,659 
13,087,765 
13,099,881 

13,112,010 
13,124,150 
13,136,300 

13,148.463 
13.160,636 
13,172,823 


4-471 
4-472 
4-473 

4-474 
4-475 

4-476 

4-477 
4-478 
4-479 


14-986 871 213 
15-000 566 281 
15014 274 034 

15-027 994 485 
15-041 727 648 
15-055 473 533 

15-069 2.32 153 
16083 003 519 
15096 787 643 


13,695,068 
13,707,753 
13,720,451 

13,733,163 

13,745,885 
13,758,620 

13,771,366 
13,784,124 
13,796,^95 


4-430 


14-436 151 440 


13,185,020 


4-480 


15-110 584 538 


13,809,678 


4-431 
4-432 
4-433 

4-434 
4-435 
4-436 

4-437 
4-438 
4-439 


14-449 33(; 460 
14-462 533 688 
14-475 743 135 

14-488 964 814 
14-502 198 735 
14-515 444 912 

14-528 703 351 
14-541 974 070 
14-555 257 077 


13,197,228 
13,209,447 
13,221,679 

13,233,921 
13,246,177 
13,258,439 

13,270,719 
13,283,007 
13,295,307 


4-481 
4-482 
4-483 

4-484 
4-485 
4-486 

4-487 
4-488 
4-489 


15-124 394 216 
15-138 216 688 
15-152 051 965 

15-165 900 060 
15-179 760 987 
15-193 634 757 

15-207 521 382 
15-221 420 872 
15-235 333 240 


13,822,472 
13,835,277 
13.848,095 

13,860,927 
13,873,770 
18,886,625 

13,899,490 
13,912,368 
13,925,259 


4-440 


14-568 552 384 


13,307,619 


4-490 


15-249 258 499 


13,938,163 


4-441 
4-442 
4-443 

4-444 
4-445 
4-446 

4-447 
4-448 
4-449 


14-581 860 003 
14-595 179 946 
14-608 512 222 

14-621 856 845 
14-635 213 827 
14-648 583 178 

14-661 964 909 
14-675 359 035 
14-688 765 565 


13,319,943 
13,332,276 
13,344,623 

13.356,982 
13,369,351 
13,381,731 

13,394,126 
13,406,530 
13,418,945 


4-491 
4-492 
4-493 

4-494 
4-495 
4-496 

4-497 
4-498 
4-499 


15-263 196 662 
15-277 147 741 
15-291 111 745 

15-305 088 688 
15-319 078 582 
15-333 081 441 

15-347 097 275 
15-361 126 097 
15-375 167 919 


13,951.079 
13,964,004 
13,976.943 

13,989,894 
14,002,859 
14,015,834 

14,028.822 
14,041,8-22 
14,054,835 


4-450 


14-702 184 510 


13,431,374 


4-500 


15-389 222 754 


14,067,859 



iV>'d-6. 



274 



REPORT 1893. 



X 


\,z 


Difference 


X 


I,:r 


Difference 


4-500 

4-501 
4-502 
4-503 


15-389 


222 


754 


14.067,859 


4-550 


16-108 


828 


111 


14,734,909 


15-403 
15-417 
15-431 


290 
371 
465 


613 
509 
454 


14,080,896 
14,093,945 
14,107,005 


4-551 
4-552 
4-553 


16-123 
16-138 
16-153 


563 
311 
073 


020 

592 
841 


14,748,572 
14,762,249 
14,775,936 


4-504 
4-505 
4-506 


15-445 
15-459 
15-473 


572 
692 

825 


459 
538 
703 


14,120.079 
14,133,165 
14.146,262 


4-554 
4-555 
4-556 


16-167 
16-1S2 
16-197 


849 
639 
442 


777 
414 
766 


14,789.637 
14,803.352 
14,817,079 


4-507 
4-508 
4-509 


15-487 
15 502 
15-516 


971 
131 
303 


965 
338 
834 


14.159,373 
14,172.496 
14,185.630 


4-557 

, 4-558 
1 4-559 


16-212 
16-227 
16-241 


259 
090 
935 


845 
665 
237 


14,830,820 
14,844,572 
14,858.338 


4-510 


15-530 


489 


464 


14,198.778 


4-560 


16-256 


793 


575 


14,872.116 


4-511 

4-512 
4-513 


15-544 
15-558 
15-573 


688 
900 
125 


242 

180 
289 


14.211,938 
14.225,109 
14,238,293 


j 4-561 
i 4-562 
■ 4-563 


16-271 
16-286 
16-.S01 


665 
551 
451 


691 
599 
311 


14,885,908 
14,899,712 
14,913,531 


4-514 
4-515 
4-516 


15-587 
15-601 
15-615 


363 
615 

879 


582 
071 
770 


14,251,489 
14,264,699 
14,277,920 


4-564 
4-565 
4-566 


16-316 
16-331 
16-346 


304 
292 
233 


842 
202 
406 


14,927,360 
14,941.204 
14,955,060 


4-517 
4-518 
4-519 

4-520 


15-630 
15-644 
15-658 


157 690 
448 844 
753 245 


14.291.154 
14.304.401 
14.317.659 


4-567 
4-568 
4-569 

4-570 


16-361 
16-376 
16-391 


188 
157 
140 


4(56 
397 
209 


14,968,931 
14.9S2.812 
14.996,709 


15-673 


070 


904 


14,330.930 


16-406 


136 


918 


15,010.617 


4-521 
4-522 
4-523 


15-687 
15-701 
15-716 


401 
746 
103 


834 
048 
558 


14,344.214 
14,357,510 
14,370,819 


4-571 
4-572 
4-573 


16-421 
16-436 
16-451 


147 
172 
210 


535 
073 

547 


15,024,538 
15.038.474 
15,052,421 


4-524 
4-525 
4-526 


15-730 474 
15-744 858 
15-759 255 


377 
515 

987 


14,384,138 
14.397.472 
14.410,819 


4-574 
4-575 
4-576 


16-466 
16-481 
16-49(5 


262 
329 

409 


968 
350 
705 


15,066,382 
15,080,355 
15,094,343 


4-527 
4-5^8 
4-529 

4-530 


15-773 

15-788 
15-802 


666 
090 
528 


806 
983 
532 


14,424.177 
14.437,549 
14,450,932 


4-577 
4-578 
4-579 


16-511 
16-526 
16-541 


504 
612 
734 


048 
392 
749 


15,108,344 
15,122,357 
15,136,384 


15-816 


979 


464 


14,464,329 


4-.580 


16-556 


871 


133 


15.150.423 


4-531 
4-532 
4-533 


15-831 
15-845 
15-860 


443 
921 
412 


793 
530 

689 


14,477,737 
14,491,159 
14,504,592 


4-581 

4-582 
4-583 


16-572 
16-587 
16-602 


021 
186 
364 


556 
032 
574 


15,164,476 
15,178.542 
15,192,623 


4-534 
4-535 
4-536 


15-874 
15-889 
15-903 


917 
435 
966 


281 
321 
819 


14,518.040 
14.531,498 
14,544,970 


4-584 
4-585 
4-586 . 


16-617 
16-632 
16-647 


557 
763 
984 


197 
910 
731 


15.206.713 
15,220.821 
15,234,939 


4-537 
4-538 
4-539 


15-918 
15-933 
15-947 


511 

070 
642 


789 
243 
195 


14.558.454 
14.571,952 
14,585,462 


4-587 

4-588 
4-589 


16-663 

16-678 
16-693 


219 

468 
731 


670 
742 
958 


15,249,072 
15,263,216 
15,277,376 


4-540 


15-962 


227 


657 


14,598,984 


4-590 

4-591 
4-592 
4-593 


16-709 


009 


334 


15,291,547 


4-541 
4-542 
4-543 


15-976 
15-991 
16-006 


826 
439 
065 


641 
160 

228 


14,612,519 
14.626,068 
14,639,628 


16-724 
16-739 
16-754 


300 
606 
926 


881 
616 
547 


15.305,735 
15,319,931 
15.334,146 


4-544 
4-545 
4-546 


16-020 704 856 
16-035 358 057 
16-050 024 843 


14,653,201 
14,666,786 
14,680,387 


4-594 
4-595 
4-596 


16-770 
16-785 
16-800 


260 
609 
971 


693 
061 
671 


15.348,368 
15,362.610 
15,376,861 


4-547 
4 548 
4-549 


16-064 
16-079 
16-094 


705 
399 
106 


230 
229 

851 


14,693,999 
14,707,622 1 
14,721,260 


4-597 

4-598 
4-599 


16-816 
16-831 
16-847 


348 
739 
145 


532 
658 
064 


15,391,126 
15,405,406 
15,419,698 


4-550 


16-108 


828 


111 


14,734,909 


4-600 


16-862 


564 


762 


15,434,004 



ON MATHEMATICAL FUNCTIONS. 



■75 



X 


Ii-r 


Difference 


X 


I„r 


! Difl'erence 


4-600 

4-601 
4-602 
4-603 


16-862 564 762 


15,434,004 


j 4-650 


17-652 072 


549 


16,166,690 


16-877 098 766 
16-S93 447 088 
16-908 909 744 


15,448,322 
15,462,656 
15,477,001 


4-651 
4-652 
4-653 


17-668 239 
17-(;84 420 
17-700 617 


239 
939 
658 


16,181,700 
16,196,719 
16,211,758 


4-604 
4-605 
4-606