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ERE ROY A SOO i EY:

30TH NOVEMBER, 1895,

—

THE ROYAL SOCIETY. Nov. 30, 1895.

Her Sacrep Masesty QUEEN VICTORIA, Parron.

Date of Election.

1863. Feb. 12.) HIS ROYAL HIGHNESS THE PRINCE OF WALES, K.G.
1882. Mar. 16.) HIS ROYAL HIGHNESS THE DUKE OF EDINBURGH, K.G.

1893. June 8.| HIS ROYAL HIGHNESS THE DUKE OF YORK, K.G.

4

TH E

+2 Or

COUNCIL

OF

THE ROYAL

SOCIETY,

SIR JOSHPH LISTER, Barr., F.R.C.S., D.C.4.—Presipenr.

SIR JOHN EVANS, K.C.B., D.C.L., LL.D.—
TREASURER and VICt-PRESIDENT.

PROF. MICHAEL FOSTER,
SECRETARY.

THE LORD RAYLEIGH, M.A., D.C.l.—Secre-
TARY.

EDWARD FRANKLAND,
ForereN SECRETARY.

WILLIAM CROOKES, F.C.S.—Vics-PRESIDEN?.

SIR JOSEPH FAYRHER, K.C.S.I.

LAZARUS FLETCHER, M.A.

WALTER HOLBROOK GASKELL, M.D.

WILLIAM HUGGINS, D.C.L.—Vice-Preswenr.

THE LORD KELVIN, D.C.L.

MA. M.D—

D.C.L., LL.D.—

PROF.
Lu.D.

PROF. HORACE LAMB, M.A.

PROF. EDWIN RAY LANKESTER, M.A.—
Vice-PRESIDEN?.

PROF. CHARLES LAPWORTH, LL.D.

MAJOR PERCY ALEXANDER MacMAHON,
R.A.

PROF. JOHN HHNRY POYNTING, D.Sc.

PROF. ARTHUR WILLIAM RUCKER, M.A.

OSBERT SALVIN, M.A.

PROF. HARRY MARSHALL WARD, D.Sc.

ADML. WILLIAM JAMES LLOYD WHARTON,
C.B.

ALEXANDER 3B. W. KENNEDY,

** This Council will continue tll November 30, 1896.

Assistant-Secretary and Librarian.
HERBERT RIX, B.A.

Clerk.

THEODORE HE. JAMES.

Assistunt Inbrarian.

A. HASTINGS WHITH.

Ofice and Library Assistant.
RICHARD CHAPMAN.

Oraissions haying occasionally occurred in the Aunual List of Deceased Fellows, as announced from the
Chair at the Anniversary Meeting of the Royal Society, it is requested that any inforraation on that subject, as
also Notice of Changes of Residence, be addressed to the Assistant Secretary.

Date of Election.

June 7, 1860.

June 1, 1876.

Jan. 21, 1847.|’

June 6, 1872.) 82

June 7, 1883.

June 6, 1889.
June 3, 1880.

June 1, 1854.

June 12, 1884.

June 12, 1879.

Jnne 4, 1891.)

Servedon |

Council.

67-69 | R.
17-19 |

83-85 | Rm.

71-73 | R.

FELLOWS OF THE SOCIETY.
NOVEMBER 30, 1895.

(C) prefixed to a name indicates the award of the Copley Medal.
R) .. Q 2 00 Is

( : 3 Royal Medal.
(Rm) .. Sic a6 oo a x Rumford Medal.
(D) 30 ae 60 O0 a0 a0 Davy Medal.
(Dw.) .. 36 +e oe oo 90 Darwin Medal.
QD) bo + is able to an annual payment of £4.
re 00 50 oo 35 o6 op | bSBb

t Abel, Sir Frederick Augustus, Bart., K.C.B. D.C.L. (Oxon.) D.Se. (Camb.) V.P.C.S.
V.P.S. Arts. Hon. Mem. Inst. C.E., Inst. M.E., Ord. Imp. Bras. Rosae Eq.
Hon. Mem. Deutsch. Chem. Gesell., Mem. Soc. d’Encourag. Paris, Sec. and
Director of the Imperial Institute. 2 Whitehall-court, 8.W.; and Lnperial
Institute, Imperial Institute-road. S.W.

Abney, Wiliam de Wiveleslie, Capt. R.E. C.B. D.C.L. (Dunelm.) F.I.C. F.C.S.
F.R.A.S., Director for Science in the Science and Art Department. Rathmore
Lodge, Bolton-gardens South, Karl's Court, S.W.; and Atheneum Club. S.W.

Acland, Sir Henry Wentworth Dyke, Bart., K.C.B. A.M. M.D. LL.D. (Cantab.)
F.R.G.S., Coll. Reg. Med. Soc., Hon. Student of Ch, Ch., Radcliffe Librarian
and late Reg. Prof. of Medicine in the University of Oxford. Broad-streeé,

Oxford.

Adams, William Grylls, M.A. D.Se. F.G.S. F.C.P.S. Vice-President of Physical
Soc. Past Pres. Inst. Elec. Eng. Professor of Natural Philosophy and
Astronomy in King’s College, London. 43 Campden-hill-square. W.

* Aitchison, James Edw. Tierney, M.D. C.I.E., LL.D. (Adin.) F.R.S.E. F.L.S.
F.R.C.S. (Edin.) M.R.C.P. (Edin,) Corresp. Fell. Obstet. Soc. Edin. Brigade
Surgeon H.M. Bengal Army (retired). 20 Chester-street, Edinburgh.

* Aitken, John, F.R.S.E. Darroch, Falkirk. N.B.

* Allbutt, Thomas Chifford, M.A. M.D. LL.D. F.L.S. Regius Professor of Physic in
the University of Cambridge. St. Radegund’s, Cambridge.

Allman, George James, M.D. LL.D. F.R.S.E. F.R.C.S.1 F.L.S. M.R.LA. Cor.
Mem. Z.S. Emeritus Regius Professor of Natural History in the University of
Edinburgh, Ex-Pres. of the Linnean Society, Hon. Fell. Roy. Micros. Soc.,
Hon. Mem. Geol. Soc. Cormwall, Phil. Soc. Yorkshire, Lit. Antiq. Soc. Perth,
Trin. Hist. Soc. Dallas, Texas, Soc. Reg. Sci. Dan. Hafn. Soc. Honor. Soe. Zool.
Bot. Vindob. Socius Honor. Soc. Hist. Nat. Ind. Batay. Corr. Ardmore,
Parkstone, Poole, Dorsetshire; and Atheneum Club. S.W.

* Allman, George Johnston, LL.D. (Dubl.) D.Sc. Emeritus Professor of Mathe-
matics in Queen’s College, Galway, Member of Senate of the Royal Uni-
versity of Ireland. St. Mary’s, Galway.

Anderson, John, M.D. LL.D. (Edin.) F.R.S.E. F.S.A. F.L.S. F.Z.8, late Superm-
tendent, Indian Museum, and Professor of Comparative Anatomy in the
Medical College, Calcutta. 71 Harrington-gardens. S.W.

* Anderson, William, D.C.L. Past Pres. Inst. Mech.E., Mem. Inst. C.E., Director
General of Royal Ordnance Factories. Lesney House, Erith; and Royal

Arsenal, Woolwich.

6

Date of Election.

June 7, 1888.
June 3, 1875.

June 19, 1851.

June 12, 1873.

June

May 7,

Jane 3, 1880.

June

June 4, 1885.

June 5, 1890.

June

June 12, 1884.)

1846.

2, 1881.

6, 1878.) 85-84 |

Served on
Council.

55-56
83-84

*O1—62

89-91

79293 |

"92-94 |
|

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

* Andrews, Thomas, F.R.S.E. F.C.S. Mem. Inst. C.E., Telford Medallist and Prize-
man. Havencrag, Wertley, near Sheffield.

Archer, William, M.R.LA. National Library of Ireland; and 52 Lower Mount-
street, Dublin.

+ Argyll, George Douglas Clonal Duke of, K.G. K.T. D.C.L. (Oxon.) LL.D,
(Camb.) Trust. Brit. Mus. Hon. V.P.R.S. Edin. F.G.8. Argyll Lodge, Ken-
sington, W.; and Inverary Castle, Argyleshire.

+ Armstrong, Sir Alexander, K.C.B. M.D. LL.D. (Dubl.) F.R.G.S. late Director-
General of the Medical Department of the Navy, Hon. Physician to the
Queen and to H.R.H. The Prince of Wales. The Elms, Sutton Bonnington,
Loughborough, Leicestershire.

+ Armstrong, Henry Edward, Ph.D. (Lips.) LL.D. (St. Andr.) Pres. Chem. Soa
Professor of Chemistry at the City and Guilds of London Central Institute,
South Kensington, Hon. Mem. Pharm. Soc. Lond. 55 Granville-park,
Lewisham. §.E.

Armstrong, William George, Lord, C.B. D.C.L. (Oxon.) LL.D. (Cantab.) M.E.
(Dubl.) Ord.SS™™- Maur. et Lazar. Ital. Gr. Off. Ord. Dannebrog et Ord.
Jes. Christ Portog. Com. Ord. Fr. Jos. Austriae, Ord. Car. III. Hisp. et Ord.
Imp. Bras. Rosae Eq. Atheneum Club; Cragside, Rothbury; and Newcastle-
upon- Tyne.

* Attfield, John, M.A. Ph.D. (Tiib.) F.I.C. F.C.S. Professor of Practical Chemistry
to the Pharmaceutical Society of Great Britain, Hon. Mem. Amer, Pharm,

Pharm. Philad., New York, Mass., Chic., Ontario, and Pharm.

Assocs. Rivera Mare lana Virg., Georgia, New Hampshire, and

(Juebec, Hon. Corresp, Mem. Soc. Bhar. Paris, Hon. Mem. Pharm. Noe.

Gr, Brit., New South Wales, St. Petersb., Austria, Denmark, East Flanders,

Ashlands, Watford; and 17

Agsoc., Colls
Manch.,

Queensland, and Australasia.
Bloomsbury-sq. W.C.

* Ayrton, William Edward, Mem. Phys. Soc. and Inst. Elect. Eng., Professor of

Exxhibition-road. ©

Switzerland,

Applied Physics in the Guilds Central Technical College.
SW.
* Baird, Andrew Wilson, Lieut.-Colonel, R.E. Care of Messrs. Grindlay, Groom & Co.,

| Bombay, India.

| Baker, Sir Benjamin, K.C.M.G. LL.D. M.E. (Dubl.) Mem. Inst. C.E., Hon.
Mem. Amer. Soc. Mechan. Engs., Soc of Engs., and Mane. Lit. and Phil.
Soc. 2 Queen-square-place, Queen Anne's Mansions,
Athenwum Club. S.W.
it Baker, John Gilbert, F.L.S.
| Royal Herbarium, Kew.
it Balfour,

Westminster; and

Keeper of the Herbarium, Royal Gardens, Kew.

Right Hon. Arthur James, D.C.L. 4 and
| Whittinghame, Prestonkirk, N.B.

* Balfour, Isaac Bayley, D.Sc. M.D. (Edin.) M.A. (Oxon.) F.R.S.H#. F.LS. F.G.8.
| Keeper of the Royal Botanic Garden, Edinburgh, Queen’s Botanist in
Scotland, and Professor of Botany in the University of Edinburgh,
Corresp. Mem. Deutsch. Bot. Gesell., Soc. Nat, des Sci. Nat. et Math.
Cherbourg. Jnverleith House, Edinburgh ; S.W.

Carlton- gardens, S.W.;

and Atheneum Club.

Date of Election.

June 12. 1873.

June 6, 1889.

2, 1864.

June

June

Dec. 12, 1844.
June 13, 1895.
June 6, 1889.

June 4, 1868

Feb. 8, 183
June 7,189

June 11, 1857.

June 2, 1892.

June 12, 1873.

June 4, 1874.) ’8
June 12, 1884.
June 8, 1871.
June 12, 1879.
June 4, 1886.

April 6, 1843.
June 4, 1874.

6, 1850.

Served on
Council.

80-81

=o

ps

* Barry,

=

=

FELLOWS OF THE SOCIETY.

~

(Nov. 30, 1895.)

Ball, Sir Robert Stawell, Kt., Hon. M.A. (Cantab.) LL.D. M.R.I.A. Soc. Phil.
Cam. et Soc. Reg. Kdin. Soc. Honor. Lowndean Professor of Astronomy
and Geometry in the University of Cambridge.
Cambridge; and Athenevm Club, S. W.

Ballard, Edward, M.D. 6 Ravenscroft-park, High Barnet, Herts.

Barkly, Sir Henry, G.C.M.G. K.C.B. F.R.G.S.
S.W.

Barlow, William Henry,
Charlton, Kent.

Barrow, John, F.S.A., F.R.G.S.

The Observatory,

1 Bina-gardens, South Kensington,

F.R.S.E. Past Pres. Inst. C.E. igh Combe, Old
17 Hanover-terrace, Regent's Park. N.W.
John Wolfe, C.B. V.P. Inst. C.E. 23 Delahay-street, Westminster.
Basset, Alfred Barnard, M.A. Fledborough Hall, Holyport, Berks.
Bastian, Henry Charlton, M.A. M.D. F.L.S. Coll. Reg. Med. Soc. Professor of
the Principles and Practice of Medicine, University College, Physician
to University College Hospital, Fellow of Univ. Coll. London, Hon. Fellow
Roy. Coll. Phys., Ireland, Corr. Mem. Roy. Acad. Med. Turi and Soe.
Psychol. Physiolog. Paris. 8A AManchester-square. W.

Bateman, James, M.A. F.L.S. Home House, Worthing.

Bateson, William, M.A., Fellow of St. John’s College, Cambridge.
College, Cambridge.

Beale, Lionel Smith, M.B.Coll.Reg. Med. Socius. Prof. of the Principles and Practice
of Medicine, and formerly of Physiology and of General and Morbid
Anatomy, and of Pathological Anatomy im King’s College, London, and
Physician to the Hospital. Government Medical Referee for England. 61

S.W.

St. John’s

Grosvenor-street. W.

\* Beddard, Frank Evers, M.A. (Oxon.), F.R.S.E., F.Z.8., Lecturer on Comparative

Anatomy, Guy’s Hospital, Prosector to the Zoological Society. Zoological
Society's Gardens, Regent's Park. N.W.
Beddoe, John, M.D. LL.D. (Edin.) B.A., Officier de l'Instz. Publ. France; Vice-

"91-93 |

* Bessemer, Sir Henry, Hon. Mem. Inst. C.K. Denmark-hill.

Pres. Anthrop. Inst. Corresp. Mem. Anthrop. Soc. Berlin, Soc. Romana
di Antrop.; For. Mem. Soc. Anthrop. Paris; Hon. Mem. Anthrop. Socs.
Brussels and Washington, Acad. Anthrop. New York, Amer. Antiq. Soc.
and of Imp. Soc. Friends of Sci., Moscow. The Chaniry, Bradford-on-A von ;

and Atheneum Club. S.W.
+ Bell, Sir Lowthian, Bart. F.C.S. Mem. Inst. C.K. Rounton Grange, by
Northallerton.

* Bell, James, 0.B. D.Sc. (Dubl.) Ph.D. F.LC. Late Principal of the Inland Revenue

Laboratory, Somerset House. Howell Hill Lodge, Eweil, Surrey.
Besant, William Henry, D.Sc. F.R.A.S. Fellow of St. John’s College, Cambridge.
St. John’s College, and Spring lawn, Harvey-road, Cambridge.
S.E.

* Bidwell, Shelford, M.A.LL.B. Riverstone Lodge, Southfields, Wandsworth
Blake, Henry Wollaston, M.A. 8 Devonshire-place, Portland place. WwW,
+ Blanford, William Thomas, LL.D. (Univ. McGill) A.R.S.M. F.G.S. F-R.G.S.
F.Z.S. Ord. SS™:- Maur. et Lazar. Ital. Eq. Soc. Asiat. Beng. Soc. Honor.
72 Bedford-gardens,

S.W.

Campden-hill, Kensington. WV.

8
Served on
Date of Election. Council.
June 6, 1878.) 80-82
= 295
June 5, 1890.
June 7, 1888.
June 7, 1594
June 13, 1895
June 4, 1891
June 3, 1855
June 7, 1888
June 7, 1894
|
June 1882
June 12, 1873.|’77-78
June 3, 1875.|
June 12, 1879.) 91-92
June 6, 1889
June 7, 1883
June 4, 1874.|’82=84 |
June 13, 1895.)
|
Dec. 14, 1893.)
June 9, 1887
June 7, 1866.

FELLOWS OF THE SOCIETY. (Noy. 30, 1895.)

Bonney, Rev. Thomas George, D.Sc. LL.D. (Univ. McGill) Se.D. (Dubl.) F.S.A.
F.G.S. Soe. Phil. Cantab. Soc. et Ebor. Soc. Honor. Soc. Geol. Belg. et
Soc. Reg. Canad. Corresp. Corresp. Mem. Soc. Géol. du Nord de France,
Professor of Geology in University College, London. 23 Denning-road,
Hampstead. N.W.

* Bosanquet, Robert Holford Macdowall, M.A, Fellow of St. John’s College,
Oxford. Castillo Zamora, Realejo-Alto, Teneriffe; and New University
Club, St. James’s-street. S.W.

* Bottomley. James Thomson, M.A. D.Sc. F.R.S.E. F.C.S. Lecturer on
Natural Philosophy in the University of Glasgow. 13 University-gardens,
Glasgow.

* Boulenger, George Albert, F.Z.S. Corresp. Mem. Imp. Soc. Friends of Sci.
Moscow, Senckenb. Soc. Frankfort, Linn. Soc. Bordeaux, Sci. Soc. Boston.
8 Courtjield-road, South Kensington. S.W.

* Bourne, Alfred Gibbs, D.Sc. Professor of Biology in the Presidency College,
Madras. Fellow of University College, London. Presidency College,
Madras.

Bower, Frederick Orpen, D.Sc. (Camb.) F.L.S. F.R.S.E. Regius Professor of
Botany in the University of Glasgow. 45 Kerrsland-terrace, Hilihead,
Glasgow.

t Boxer, Edward Mounier, Major-General, R.A. Upton, near Ryde.

* Boys, Charles Vernon, A.R.S.M. Assistant Professor of Physics in the Royal College

| of Science, London, Officier de Instruction Publique, France. Royal College

of Science, South Kensington; and Glebe House, Glebe Place, Chelsea. S.W.

\* Bradford, John Rose, M.D. D.Sc. Assistant Professor of Clinical Medicine,

| University College, London. 52 Upper Berkeley-street. W.

* Brady, George Stewardson, M.D. LL.D. Professor of Natural History in
| the Durham College of Science, Neweastle. 2 Mowbray-villas, Sunderland.
| Bramwell, Sir Frederick Joseph, Bart., D.C.L. (Oxon. et Dunelm) LL.D.
(Cantab. et Uniy. McGill) M. Inst. C.E. 5 Great George-street, Westminster.
S.W.

it Brandis, Sir Dietrich, K.C.I.E. Ph.D. F.L.S., late Inspector-General of Forests to
the Government of India. 21 Kaiser Strasse, Bonn, Germany.

| Brown, Alexander Crum, D.Sc. LL.D. M.D. Professor of Chemistry in the Uni-
| versity of Edinburgh. 8 Belgrave-crescent, Edinburgh.

I* Brown, Horace T., F.C.S. F.LC.F.G.S. 52 Nevern-square, South Kensington. S.W.
Fe Browne, Sir James Crichton, Kt., M.D. LL.D. F.R.S.E. 61 Carlisle-place
| Mansions, Victoria-street. S.W.

|

f Brunton, Thomas Lauder, M.D. Sc.D. (Edin.) Hon. LL.D. (Aberdeen) Coll. Reg.
Med.Soc. 10 Stratford-place, Ouford-street, W.; and Atheneum Club.

'* Bryan, George Hartley, M.A. Fellow of St. Peter's College, Cambridge,

| Thornlea, Chaucer-road, Trumpington-road, Cambridge.

it Bryce, Right Hon. James, D.C.L. 54 Portland-place. W.

** Buchanan, John Young, M.A. F.R.S.E. F.C.8. F.R.G.S. 10 Moray-place, Edin-

| burgh.

Ht Bucknill, Sir John Charles, M.D. (Lond.) Coll. Reg. Med. Socius. Coll. Univ.
Lond. Soc. Kast Cliff House, Bournemouth.

Date of Election.

June 11, 1857,’ 1-6

June 12,

June
June

June

June

June

Dec.

June

June

Jan.

June

June

June
June

June

June

June

June

June

June

=I

ite)

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

| Buckton, George Bowdler, F.C.S. F.H.S. F.L.S. Corr. Acad. Nat. Sci. Philad.,
Mem. Soc. Entom. France. Weycombe, Haslemere, Surrey.

* Buller, Sa Walter Lawry, K.C.M.G. D.Sc. F.L.8. ZS. (Corr.) The Terrace,
Wellington, New Zealand.

* Burbury, Samuel Hawksley, M.A. 17 Upper Phillimore-gardens, Kensington. W.

ix Burnside, William, M.A. Professor of Mathematics, Royal Naval College,

| Greenwich. The Laurels, Hithergreen-lane. S.E.

* Callendar, Hugh Longbourne, M.A. — J.ate Fellow of Trinity College, Cambridge,
Protessor of Physics in McGill College, Montreal. McGill College, Montreal,

| Canada,

f Carruthers, William, V.P.L.8. F.G.S8. Keeper of the Botanical Department,

| British Museum. Central House, Central-hill, S..; and British Museum (Nat.

Fist.), Cromwell-road. S.W.

Cash, John Theodore, M.D. Regius Professor of Materia Medica in the

| University of Aberdeen. 25 Dee-street, Aberdeen.

+ Chamberlain, Right Hon. Joseph, LL.D, (Cantab.). 40 Prince’s-gardens ; and
Atheneum Ciub. S.W.

Chambers, Charles, Director of the Colaba Observatory, Bombay. Coldba Obser-

ratory, Bombay. é

* Cheyne, William Watson, M.B. C.M. (Edin.) F.R.C.S. (Eng.) Professor of

| Surgery in King’s College, London. 75 Harley-street. W.

f Childers, Right Hon. Hugh Culling Eardley, F.R.G.S. 6 St. George’s-place,
S.W.; Brocks’s and Athenewn Clubs. S.W.

* Christie, Wiliam Henry Mahoney, M.A. F.R.A.S. F.R. Met. Soc. Astronomer
Royal, Corr. Mem. Imp. Acad. Sci. St. Petersb. For. Memb. Roy. Acad.

Sc. Palermo, Corr. Mem. Soc. Spettros. Ital. Soc. Nationale des Sci.

| Nat. et Math. Cherbourg. Royal Observatory, Greenwich. S.E.

* Church, Arthur Herbert, M.A. (Oxon.) F.C.8S. F.LC. Professor of Chemistry in
the Reyal Academy of Arts, Lecturer on Organic Chemistry, Royal Indian

|
|
|
|
|

lye eens College, Cooper’s Hill. Shelsley, Kev.
* Clark, Latimer, Mem. Inst. C.E. F.R.A.S. 11 Victoria-street. S.W.

: - Clarke, Alexander Ross, Colonel, R.E. C.B. Hon. F.C.P.S. Hon. F.R.S.E.

Corr. Mem. Imp. Acad. Sci. St. Petersb. Polienaed Redhill, Surrey.
e Clarke, Charles Baron, M.A. (Cantab.) F.L.8S.F.G.8. 13 Kew Gardens-road, Kew.
Cleland, John, M.D. D.Sc. LL.D. Professor of Anatomy in the University of
| Glasgow. University, Glasgow.
t Clerk, Henry, Major-General, R.A. 40 St. Ermin’s Mansions, Caxton-street,
Westminster. S.W.
Clifford-Allbutt (sez Allbutt).
Clifton, Robert Bellamy, M.A. (Cantab. et Oxon.), F.R.A.S. Professor of
Experimental Philosophy in the University of Oxford, Soc. Lit, Phil. Mane.
Soc. Honor. 3 Bardwell-road, Banbury-road, Oxford ; and Atheneum Club.
* Colenso, Rev. William, F.L.S. Hon. Mem. N.Z. Inst., Mem. Penzance Nat. Hist.
and Antiq. Soc., Hon. Mem. Santa Barbara (Cal.) Soc. Nat. Hist. Napier,
New Zealand.
* Common, Andrew Ainslie, Treas. R.A.S. LL.D. (St. And.) D.Se. 63 Laton-rise,
Ealing. W.
B

10

Date of Election.

June 4, 1891.

June

June

June
June

June

Apr.

June

June

June

June

June 12, 1879.|’84-85

Jan. 24, 1895.

June

June

June

Served on
Council.

6, 1878.

6, 1878.) 78-79

4, 1863, ‘77-79
"94-95

3, 1879.) 80-81

8, 1882.) 94-95

36-87

6, 1867.) 89-91

4, 1891,
5, 1862.

eee!

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

* Conroy, Sir John, Bart., M.A. F.C.S. Fellow and Bedford Lecturer of
Balliol College, Oxford. Balliol College, Oxford.

} Cotterill, James Henry, M.A. Professor of Applied Mechanics, Royal Naval
College, Greenwich. 18 Gloucester-place, Greenwich. S.E.

+ Crawford, James Ludovic, Earl of, K.T. LL.D., Trustee of Brit. Mus., F.R.A.S.
Leg. Honor. Com. Ord. Imp. Bras. Rosae Com. Acad. Reg. Sci. Berol. Soe.
Honor. 2 Cavendish-square, W.; and Haigh Hall, Wigan.

* Creak, Ettrick William, Captain R.N. M. Inst. Elect. Eng. 386 Kidbrooke-park-
road, Blackheath. S.E.

t Crofton, Morgan William, D.Sc. Fellow of the Royal University of Ireland
15 Ambrose-place, Worthing.

ft Crookes, William—V1icEe-PRESIDENT—-Past Pres. Chem. Soc. and Inst. Elect.
Eng. 7 Kensington-park-gardens, W.; and Atheneum Club. S.W.

+ Cross, Right Hon. Richard Assheton, Viscount, G.C.B. G.C.S.I. D.C.L. LL.D.
12 Warwick-sq. and Atheneum Club, 8.W.; and Eecle Riggs, Broughton-in-

Furness, Lancashire.

* Cunningham, Daniel John, M.D. (Edin. and Dubl.), D.Sc. D.C.L. LL.D. Prof. of

Anatomy in the University of Dublin. 43 /% itzwilliam-place, Dublin.
Cunningham, David Douglas, M.B. C.M. (Edin.) C.IE. F.L.S. Brigade Surg.

es Lieut.-Col. Bengal Medical Service. Honorary Surgeon to the Viceroy of

India. Professor of Physiology in the Medical College, and Fellow of the

University of Calcutta. 9 Loudon-street, Calcutta.

* Dallinger, Rev. William Henry, LL.D. Se.D. (Dubl.) F.L.S. Vice-Pres. R.M.S.,
Hon. Mem. Amer. Micros. Soc. Ingleside, Newstead-road, Lee. S.E.

Darwin, Francis, M.A. and M.B. (Cantab.) F.L.S. F.Z.8. F.R.M.C.S. Fellow
of Christ’s College, and Reader in Botany in the Univ. of Cambridge.
Mem. Soc. Nat. Sci. et Math. de Cherbourg. Waychfield, Huntingdon-road,
Cambridge.

Darwin, George Howard, M.A. LL.D. (Glasc.) Se.D. (Dubl.) Ph.D. (Padua)
F.R.A.S. F.M.S. Hon. Mem.R.I.A. Fellow of Trinity College and Plumian
Professor of Astronomy and Expermental Philosophy in the University of
Cambridge. Hon. Fell. Astron. and Phys. Soc. Toronto. Newnham
Grange, Cambridge.

+ Davey, Right Hon. Horace, Lord, M.A. D.C.L. 86 rook-street, W.; and

Verdley-place, Fernhurst, Sussex.

t Dawkins, W. Boyd, M.A. (Oxon.) F.S.A. F.G.S. Assoc. Inst. C.E. Hon.
Fellow of Jesus Coll. (Oxford) Professor of Geology and Paleontology in the
Victoria University, Owens Coll., Manchester. Soc. Anthrop. Berol. Acad. Sci.
Nat. Philad. et Soc. Nat. Hist. Bost. Corresp. Soc. Phil. Amer. et Acad. Sci.
Noy.Ebor. et Soc. Geol. Belg. Soc. Honor. Woodhurst, Fallowfield, Manchester.

* Dawson, George Mercer, C.M.G. LL.D. F.G.S. A.R.S.M. F.R.S.C. Assistant

Director of the Geological Survey of Canada. Sussex-street, Ottawa, Canada.

| Dawson, Sir J. William, C.M.G. M.A. LL.D. F.G.S. Late Principal and Vice-
Chancellor of M‘Gill University, Montreal, Hon. Mem. Phil. Soc. Leeds,
Glasg., Prieeton, Soc. Nat. Hist. Boston, Maryland Academy. Corresp.
Fell. Geol. Soc. Edin., Fell. Roy. Soc. Canada, Amer. Acad. Arts and

| Sciences, Amer. Phil. Soc. Corr. Mem. Acad. Nat. Sci, Philad. 293

| University-street, Montreal.

Date of Election.

June 6, 1861.
Mar. 3, 1892
June 7, 1877

June 4, 1885.

June

June

Feb.

Feb.

June

June 1, 1893.

June

June

June 13, 1895.

June 12, 1873.

Served on
Council.

70-72
*S1-83

3, 1880.) 86-88

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) i3t

7 Debus, Heimrich, Ph.D. F.C.S. Late Prof. of Chemistry at the Royal Naval
College, Greenwich, Lecturer on Chemistry at Guy's Hospital. 4
Schlangenweg, Cassel, Hessen, Germany.

+ Devonshire, Spencer Compton Cavendish, Duke of, K.G. M.A. LL.D. Hon. Mem.
Inst. C.E. Chancellor of the University of Cambridge. Devonshire House,
Piccadilly, W.; and Chatsworth, Derbyshire.

Dewar, James, M.A. F.C.8S. F.R.S.E. Hon. LL.D. (Glase. and St. And.) Jack-
sonian Prof. of Natural Experimental Philosophy in the University of
Cambridge, Fullerian Prof. of Chemistry in the Royal Institution. 1

Nie

Divers, Edward, M.D. Professor of Chemistry in the Imperial University, Japan.

Scroope-terrace, Cambridge; and Royal Institution, Albemarle-street.

Hongo, Tokyo, Japan.

* Dixon, Harold B., M.A. F.C.S. Prof. of Chemistry and Director of the Chemical

| Laboratories in Owens College, Manchester. Birch Hall, Rusholme,
Manchester.

Douglass, Sir James Nicholas, M. Inst. C.E. M. Inst. M.E. M. Inst. E.K. Late
Engineer-in-Chief to the Hon. Corporation of Trinity House. Stella House,
Dulwich. SE.

Ducie, Heury John Reynolds-Moreton, Earl of, F.G.S.

Falfield, Gloucestershire.

Dufferm and Ava, Frederick Temple Blackwood, Marquis of, K.P. G.C.B.
G.C.M.G. G.C.S.I. G.M.IE. D.C.L. (Oxford) LL.D. (Camb. and Dubl.)
F.R.G.S. Clandeboye, Co. Down, Ireland.

+ Dunkin, Edwin, F.R.A.S. Formerly Chief Assistant, Royal Observatory, Green-

wich. Kenwyn, Kidbrooke Park-road, Blackheath. 8.H.

* Dunstan, Wyndham R., M.A. (Oxon.) Sec. Chem. Soc. F.L.C. Professor of

| Chemistry to, and Director of the Research Laboratory of, the Pharma-

Tortworth Court,

|
|
|
|

ceutical Society of Great Britain. Lecturer on Chemistry at St. Thomas’s
| 3 Percy-villas, Campden Hill, Kensington. W.

if Dupré, August, Ph.D. F.C.S. Lecturer on Chemistry at the Westminster
| Hospital. Westminster Hospital Medical School, Caxton-street, Westminster,
S.W.; and Cliftonville, Sutton, Surrey.

* Dyer, William Turner Thiselton, C.M.G. C.I.E. M.A. (Oxon.) B.Se. (Lond.) Ph.D.
| F.L.S. Director, Royal Gardens, Kew; late Fellow Univ. of London; Hon.
Fellow, King’s Coll., Lond.; Bot. Soc. Edin.; Hon. Mem. Roy. Bot. Soc.
Lond., Pharm. Soc. Gt. Britain; Cam. Phil. Soc. ; Lit. Phil. Soc. Manchester ;
Soc. Néerland d’Hort. et de Bot., Amsterdam and New Zealand Institute ;
Corresp. Acad. Sci. Philad.; Boston Soc. Nat. Hist.; Hort. Soc. Berlin
and Massachusetts; Soc. Nat. Sci. et Math. de Cherb.; and Botan. Soe.
Copenhagen ; Mitg. Kais.-Leop. Deutsch. Acad. der Naturf. in Halle.

Hospital.

|

| royal Gardens, Kew.

* Eliot, John, M.A. Meteorological Reporter to the Government of India. Indian
Meteorological Office, Simla.

+ Ellery, Robert Lewis John, C.M.G. F.R.A.S. Late Government Astronomer,
| and Director of the Observatory. Melbourne, Victoria.

bo

B

12

Date of Election.

June Fa 1891,

June

June

June

June

June

June

June

June

June

June

June

June

June

June
June

1, 1893.

|
12, 1879.|

|
1, 1893,

Served on |
Council.

FELLOWS OF THE SOCIETY. (Noy. 30, 1895.)

¥%

*

* *K

3K

+

Elliott, Edwin Bailey, M.A. F.R.A.S. Waynflete Professor of Pure Mathematics
in the University of Oxford; Fellow of Magdalen College, Oxtord. 4
Bardwell-road, Oxford.

Ellis, William, F.R.A.S. F.R. Met. Soc. Memb. Inst. Elect. Eng. Late Super-
intendent of the Magnetical and Meteorological Department, Royal
Observatory, Greenwich. 12 Vanbrugh-hill, Blackheath. S8.E.

Erichsen, Sir John Eric, Bart., F.R.C.S. LL.D. (Hdin.) Surgeon Extraordinary to
the Queen, Pres. of and Emeritus Prof. of Surgery to University College, and
Consulting Surgeon to the Hospital. 6 Cavendish-place, Cavendish-square. W.

Esson, Wilham, M.A. F.C.S. F.R.A.S. Deputy Savilian Professor of Geometry
in the University of Oxford, Fellow, and Mathematical Tutor of Merton
College. Aerton College; and 13 Bradmore-road, Oxford.

{ Etheridge, Robert, F.R.S.E. F.G.S. Hon. Memb. Geol. Soc. Belg. N.Z. Inst.

Roy. Geol. Soc. Cornwall, Phil. Soc. York, Bristol, Corresp. Imp. Geol.
Inst. Vienna. 14 Carlyle-square, Chelsea. S.W.

Evans, Sir John—TREASURER and VIcE-PRESIDENT—K.C.B. D.C.L. (Oxon.)
LL.D. (Dubl.) Sc.D. (Camb.) Trustee, Brit. Mus. F.S.A. F.L.8. F.G.S. F.C.S.
F.Z.8. Assoc. LC.E. Pres.Num.Soc. Hon. M.R.LA. Hon. F.S.A.(Scot.) Comm.
of the Ord. of St. Thiago of Port., Cor, of Inst. de France (Acad. des Inscrip.),
Hon. Mem. of the Amer. Phil. Soc., Amer. Acad. Arts and Sciences, Amer.
Ethnol. Soc., Num. and Ant. Soc, of Philadelphia, Amer. Num. and
Archeol. Soc., Soc. France. de Numism., Soc. Ital. d’Anthrop., Soc. Roy.
Gr. Duc. de Luxembourg, Soc. Anthrop. de Brux. et de Lyons, Soc. de
Borda. Dax., Soc. Polym. du Morbiban, and Soc. Suisse de Numism., For,
Mem. of the Soc. Ant. of Sweden, Soc. Anthrop. de Paris, and the Numism.
Soc. of the Netherlands, and Corr. Mem. of the Soc. Géol. de Belg., Inst.
di Corr. Arch., Acad, Valdarn., Anthrop. Soc. of Berlin, and Soe. d’Emui.
d Abbeville. Nash Mills, Hemel Hempstead; and Atheneum Club.

Everett, Joseph David, M.A. D.C.L. F.R.S.E. Professor of Natural Philosophy in
Queen’s College, Belfast. Derryvelgie Avenue, Belfast.

Ewart, James Cossar, M.D. Professor of Natural History in the University of
Edinburgh. The University, Mdinburgh.

Ewing, James Alfred, Hon. M.A. (Camb.) B.Se. (Edin.) F.R.S.E. M. Inst. C.E.
Professor of Mechanism and Applied Mechanics in the University of Cam-
bridge. Langdale Lodge, Cambridge.

Farrar, Very Rey. Frederic William, M.A. D.D. (Cantab.) Dean of Canterbury.

Fayrer, Sir Joseph, K.C.S.1. M.D. LL.D. (Edin. and St. And.) F.R.C.P. (Lond.)
F.R.C.S. F.R.S.E. Honorary Physician to the Queen. 16 Devonshire-street,
Portland-place. AV.

Ferrers, Rey. Norman Macleod, D.D. Master of Gonville and Caius College,
Cambridge. The Lodge, Gonville and Caius College, Cambridge.

Ferrier, David, M.A. (Aberd.) M.D. (Edin.) LL.D. F.R.C.P. Professor of
Neuro-pathology, King’s College, London. 384 Cavendish-square. W.
Festing, Edward Robert, Major-General, R.E. (retired). Science Museum

Director, South Kensington Museum. South Kensington. S.W.

* Fitzgerald, Prof. George Francis, M.A. D.Sc. 40 Trinity College, Dublin.
'* Fleming, John Ambrose, M.A. (Camb.) D.Sc. (Lond.) Late Fellow of St. John’s

|
|

College, Cambridge, Fellow and Professor of Electrical Engineering in
University College, London. University College, Gower-street. W.C.

Date of Election.

June

June

June

June

June

June

June

June

|
June 4, 1891.|

}

Served on |
Council.
6, 1889.
2, 1864.) 68-70
76-78
84-86
9, 1887.
4, 1886.| 93-95
2, 1892.
|
3, 1869, "70-72
"77-78
Poe
91-93
re. low --
6, 1872.) 76-77
781-95
2, 1853.| 57-59
| 65-67
"75-17

Rs |

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 13
|

Fletcher, Lazarus, M.A. (Gxon,) F.G.8. F.C.8.

British Museum. Natural History Museum, Cronvwell-road; and 36 Wood-

| ville-road, Kaling. W.

| Flower, Sir William Henry, K.C.B. D.C.L. (Oxon. et Dunelm.) LL.D. (Edin.

| et Dubl.) Se.D. (Camb.) Ph.D. (Utrecht) F.R.C.S. P.Z.S. F.L.S. F.G.S. V.P.
Anthrop. Inst. Hon. Fell. Roy. Med. Chir. Soc. Hon. Memb. Asiat. Soc.
Bengal, Camb. Phil. Soc., Manchester Lit. Phil. Soc. N.Z. Inst. Zool. Soc.
Amsterdam and France, Acad. Sci. New York, Anthrop. Soc. Washington,
Memb. Amer. Phil. Soc. Imp. Soc. Nat. Moscow, Corresp. Memb. Inst. Fr.
(Acad. Sci.) Acad. Sci. Bologna, Acad. Sci. Turin, Acad. Nat. Sci. Philad.,
Soc. Nat. Hist. Boston, Soc. Anthrop. Ethnol. and Prehist. Arch. Berlin,
Anthrop. Soc. Rome, For. Assoc. Anthrop. Soc. Paris, Director of the Nat.
Hist. Departments, British Museum.
road; and 26 Stanhope-gardens. S.W.

* Forbes, George, M.A. F.R.S.E. F.R.A.S. Mem. Inst. C.E. M.I.E.E. Chev. Lég
Honor. Memb. Astron. Gesell. Vienna, Amer. Phil. Soc., and Franklin Inst.
Formerly Professor of Nat. Phil. in Anderson’s College. Glasgow. 84 Great
George-street. S.W.

* Forsyth, Andrew Russell, M.A. Sc.D. F.C.P.S.
Mathematics in the University of Cambridge, Fellow of Trinity College,
Cambridge. Trinity College, Cambridge.

* Foster, Clement Le Neve, B.A. D.Sc. (Lond.) F.G.S., A.R.S.M., Professor of
Mining in the Royal College of Science, and H.M. Inspector of Mines.

Keeper of Minerals in the

Natural History Museum, Cromacell-

Sadlerian Professor of Pure

Min-y-don, Llandudno.

Foster, George Carey, B.A. F.C.S.
London. 18 Daleham-gardens, South Hampstead, N.\W.; and Athenwum
Club. S.W.

T Foster, Michael—SrcreTtary—M.D. B.A. (Lond.) Hon. M.A. (Cantab.) D.C.L.
(Oxon.) LL.D. (Glasg. and St. And.) Se.D. (Dubl.) F.L.S. F.C.S. For.
Mem. R. Accad. dei lLincei, Roma, R. Accad. delle
Torino, Hon. Mem. Roy. Ivish Acad., Lit. and Pihil. Soc. Mane.,
| Roy. Soc. N. 8. Wales, Med. Chir. Soc., and Pharm. Soc. Lond.,
Professor of Physiology in the University of Cambridge. Great Shelford,

Professor of Physics in University College,

Scienze,

| Cambridge.

| Frankland, Edward—ForbiGN SECRETARY—D.C.L. (Oxon.) Ph.D. (Marp.) M.D.
(Wiirzburg) LL.D. (Edin. et Univ. McGill) V.P.C.S. Hon. Mem. Inst. C.E.,
Assoc. Etrang. Inst. Fr. (Acad. Sci.) Par., Imp. Sci. Petrop. et Vindob.
Reg. Sci. Berol. Soc. pro fov. Indust. Nat. Corresp., Soc. Reg. Sci.
Gott. et Upsal, Soc. Nat. Scrutat Helvet., Acad. Reg. Monac. Socius
Honor., Soc. Reg. Edin. Acad. Reg. Hib., Soc. Lit. Phil. Mane., Soc.
Chem. Berol. et Acad. Sci. Amer. Nov. Ebor, Lehigh Univ. U.S. Soe.
Ree. Sci. Boie. Marob. et Nat. Sanit. Dresd., Chem. Amer. Nov. Ebor.
Soc. Reg. Med. Chi. Lond. et Adsoc. Intern. pro Hyg. promov. Brux.
Soc. Asiat. Beng. Honor. The Yews, Reigate-hill, Reigate; and
Atheneum Club.

* Frankland, Percy Faraday, Ph.D., B.Sc., A.R.S.M. Professor of Chemistry in

Mason College, Birmingham.

Soc.

the Mason College, Birmingham.

14 FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

Served on

Date of Election. Council.

June 4, 1874. } Franks, Sir Augustus Wollaston, K.C.B. D.C.L. (Gxon.) P.S.A. F.G.S. Trust. Brit.
Mus. Keeper of British and Medieval Antiquities, and of Ethnography at
the British Museum. British Museum, W.C.; and 123 Victoria-street, West-
minster. S.W.

June 7, 1877. } Fraser, Thomas Richard, M.D. (Edin.) F.R.C.P. & R.S. (Edin.) LL.D. (Aberdeen)
Professor of MateriaMedica and Clinical Medicine in the University, Edin-
burgh. 13 Drumsheugh-gardens, Edinburgh.

June 7, 18383. * Frost, Percival, Sc.D. Fitzwilliam-street, Cambridge.

June 7, 1894. * Froude, Robert Edmund. Superintendent of the Admiralty Experimental
Works, Gosport. 1 Claremont, Alverstoke, Gosport.

Dec. 13, 1883. Fry, Right Hon. Sir Edward, B.A. (Lond.) D.C.L. (Oxon.) LL.D. (Edin.)

F.S.A. F.L.S. Fellow of the University of London, and of University
College, London, and Hon. Fellow, Bailiol Coll. Oxon. Failand House,
Fuiland, near Bristol.

June 2, 1892. * Gadow, Hans Friedrich, Ph.D. (Jena) Hon. M.A. (Camb.) Strickland Curator
and Lecturer on the Advanced Morphology of Vertebrata in the University
of Cambridge. Zoological Laboratory, Cambridge.

June 1, 1893. * Gairdner, William Tennant, M.D. (Edin.) Hon. M.D. (Dubl.) Hon. TbibyID, (Edin.)
F.R.C.P. (Edin.) Hon. F.R.C.P. (Irel.) Professor of Medicine in the Uni-
versity of Glasgow. Physician in Ordmary to the Queen in Scotland.
The University, Glasgow.

June 9, 1859.) 61-63 Galton, Sir Douglas, K.C.B. D.C.L. LL.D. (Univ. McGill and Durham) F.G.S.
67-69 F.L.S. F.C.S. F.R.G.S. Hon. Memb. Inst. C.E. 12 Chester-street, Grosvenor-
94-95 ;
place. S.W.
June 7, 1860.) 65-66 R. | Galton, Francis, M.A. (Cantab.) D.C.L. (Oxon.) Sc.D. (Camb.) Officier de
70-72 l'Instruction Publique, France; Corresp. Memb. of the Geograph.
Ines | Societies of Berlin and Vienna, and of Anthrop. Soc. of Rome. Hon,

Memb. of Geograph. Soc. of Italy, and Inst. Internat. de Statistique.
42 Rutland-gate. S.W.

June 6, 1872.) 86-88 t Gamgee, Arthur, M.D. M.R.C.P. (Lond.) & F.R.C.P. (Edin.) 8 Avenue de la
| Gare, Lausanne, Switzerland.
June 5, 1890. Gardiner, Walter, M.A. F.L.S. Fellow of Clare College, Cambridge, and
| | University Lecturer in Botany. 45 Hills-road, Cambridge.
June 38, 1858. | + Garrod, Sir Alfred Baring, M.D. Coll. Reg. Med. Socius, Physician Extraordinary

to the Queen, Consulting Physician to King’s College Hospital. 10 Harley-
| | oP aaa Wo i

R. |* Gaskell, Walter Holbrook, M.A. M.D. (Cantab.) LL.D. (Edin.) Lecturer in
Physiology at Cambridge. The Uplands, Great Shelford, near Cambridge.
June 1, 1865.) 85-87 | t Geikie, Sir Archibald, Knt. Sc.D. (Cantab. et Dubl.) LL.D. (Kdin. et St. And.)
89-13 F.R.S.E. F.G.S. F.Z.S. Director-General of the Geological Survey of the
| United Kingdom, and of the Museum of Economic Geoloae London,—
Inst. France. (Acad. Sci.) Acad. Reg. Berol. Acad. Imp. Sci. Vindob. Acad.
| Reg. Bavar. Monach. Soc. Cor.; Soc. Reg. Sci. Géttmgen; Caesar. Leop.
| | Carol. Acad. Sci. Nat.; Soc. Imp. Mineral. Petropol; Soc. Imp. Nat. Sci.
Mosquen; Acad. Reg. Weller del Poggio; Soc. Geogr. Ital. et Batav. ;
| Soc. Geol. Edin. Glasc. Liverp. Manehect Franc. Belg. Stockholm; Soe.
Phil. Ebor. et Americ., Soc. Sci. Christiania, Socius. (Geological Survey Office,
28 Jermyn-sireet, S.W.; 10 Chester-terrace, Regent's Park. N.W.

= |
June 8, 1882.

. Served on
Date of Election. | Gansta
June 3, 1875.!
|
June 2, 1892
June 7, 1860.) °86-88
|

June

June

June |

Jan.
June

June

June

June

June

June

Jan.
June

June

Feb.

4, 1891
7, 1883.)
2, 1853.) 63-64
"66-68
13, 1881.
7, 1849,|
3, 1875.) 83-84
90-92
8, 1882, "92-94 |
|
8, 1882.|’91-93 |
3, 1880
1, 1865,
18, 1872.
2, 1892,
9, 1887.|
3, 1881.

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 15

Tt Geikie, James, D.C.L. (Dunelm.) LL.D. F.R.S.E. F.R.G.S. F.G.S. Murchison,
Professor of Geology and Mineralogy in the University of Edinburgh, Hon.
Memb. Phil. Soc. York, Geol. Soc. Stockholm, Vidensk.-Selsk. Christiania,
Geol. Paleont. Hydrol. Belg., Soc. Geol. Neuchatel, Memb. Amer.
Phil. Soc. Corresp. Memb. Acad. Sci. Philadelphia. 31 Merchiston-avenue,
Edinburgh.

Giffen, Sir Robert, K.C.B. LL.D. (Glase.) 44 Pembroke-road, Kensington. W.

Gilbert, Sir Joseph Henry, M.A. (Oxon.) Sc.D. (Camb.) Ph.D. (Giessen) LL.D.
(Edin. et Glasc.) Sc.D. (Cantab.) V.P.C.S. F.L.S. Soc. Reg. Agric. Engl.
Soc. Honor. Inst. Fr. (Acad. Sci.) Mem. Cor. Soc. Chem. Agric. Ult. et
Acad. Agric. et Sylv. Petrovsk. et Soc. Reg. Agric. Hannoy. Soc. Honor.
Soe. pro. fov. Ind. Nat. Par. Soc. Agric. Franc. et Inst. Agron. Gorigoretsk.
Mem. Corr. Acad. Reg. Agric. Sued. Soc. Late Sibthorpian Professor of
Rural Economy in the Univ. of Oxford. Harpenden, St. Alban’s ; and
Atheneum Club.

Gilchrist, Perey Carlyle, A.R.S.M. Frognal Bank, Finchley-road, Hamp-
stead. N.W.

* Gill, David, LL.D. (Aberd. et Edin.) Hon. F.R.S.E. F.R.A.S. F.R.G.S. Her
Majesty's Astronomer at the Cape of Good Hope, Trustee, S. African
Museum, Corresp. Mem. Imp. Acad. Sci. 8. Petersb., and Roy. Acad. Sci
Berl., For. Mem. Soc. Holl. des Sci., Haarlem; Corresp. Mem. Soc. degh
Spettroscop. Ital. Rome, Soc. Nationale des Sci. Nat. et Math. Cherbourg,
Geogr. Soc. Lisbon. Royal Observatory, Cape of Good Hope.

Gladstone, John Hall, Ph.D. Se.D. (Dubl.) V.P.C.S. 17 Pembridge-square.
W.

Gladstone, Right Hon. William Ewart, D.C.L. Hawarden, Chester.

Glaisher, James, F.R.A.S. Ord. Bras. Rosae Eq. he Shola, Heathfield Road,
South Croydon.

Glaisher, James Whitbread Lee, Sc.D. (Camb. and Dubl.) V.P.R.A.S. F.C.P.S.
Trinity College, Cambridge.

* Glazebrook, Richard Tetley, M.A. Treas. C.P.S. Fellow of Trinity College, Cam-

bridge. 7 Harvey-road, Cambridge.
Godman, Frederick Ducane, F.L.S. F.G.S. F.E.S. 10 Chandos-street, Cavendish-
square, W.; and South Lodge, Horsham.

* Godwin-Austen, Henry Haversham, Lieut.-Col. F.G.S. F.Z.S. F.R.G.S. Shal-

| ford House, Guildford.

Gore, George LL.D. (Kdin.). Inst. Set. Research, 67 Broad-street, Birmingham.

Goschen, Right Hon. George Joachim, M.A. 6% Portland-place. W.

* Gotch, Francis, B.A. B.Sc. (Lond.) Hon. M.A. (Oxon.) M.R.GS. Waynflete
Professor of Physiology in the University of Oxford. The Lawn, Banbury-
road, Oxford.

Gowers, William Richard, M.D. F.R.C.P. Fellow of University College,
London, Consulting Physician to University College Hospital. Physician
to the National Hospital for the Paralysed and Epileptic. 50 Queen Anne-

street. W.

+ Grant Duff, Right Hon. Sir Mountstuart Elphinstone, G.C.S.I. V.-P.R.G.S.

Atheneum Club; and York House, Twickenham.

“=HSE

3K

16

Date of Election.

June

June

June
June

June
Noy.

June
June
June

June

Jan.

June

Dec.

June

June

June

June

| Served on |
Council.

4, 1886.) °93-95

|

13, 1895.)

7, TAS,
6, 1878.
13, 1895.
26, 1840.) "45-50
|’56-58
|’?61-62 |
| 66-67 |
"78-79
7, 1883.
7, 1883. |
6, 1867. 74-76 |
|
4, 1891, |
15, 188%.)
|.
4, 1868. 78-80
15, 1881, |
meal
1, 186 |
4, 1863.)
12, 1884,
3, 1858.| |
2, 1864.

R.
|

|

|
|

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

™ Green, Alexander Henry, M.A. Professor of Geology in the University

of Oxford. University Museum, Oxford.

* Green, Joseph Reynolds, M.A. B.Sc. (Lond.) D.Se. (Camb.) F.L.S8. Professor

of Botany to the Pharmaceutical Society of Great Britain. <Arneliffe,
Grange-road, Cambridae.

* Greenhill, Alfred George, M.A. Professor of Mathematics in the Artillery College,

Woolwich. 10 New Inn. W.C.

it Greenwell, Rev. William, M.A. D.C.L., Canon of Durham, F.S.A. | Durham.
* Griffiths, Ernest Howard, M.A. 12 Parkside, Jambridge.

Grove, Right Hon. Sir William Robert, Knt., M.A. D.C.L. (Oxon.) LL.D,
(Cantab.) Hon. F.R.S.E. Hon. Mem. Inst. C.E. Ord. Imp. Rose Brazil
Eq. Acadd. Reg. Sci. Taurin., Lync. Rome, Soc. Phil. Basil. et Soc.
Imp. Carob. Corresp. 115 Harley-street. W.

* Groves, Charles Edward, F.C.S. F.1.C. 352 Kennington-road. S.E.

.

Grubb, Sir Howard, F.R.A.S. 51 Kenilworth-square, Rathaar, Dublin.

Giinther, Albert C. L. G., M.A. M.D. Ph.D. F.L.S. F.Z.S. Late Keeper of the
Zoological Department in the British Museum, Reg. Scient. Soc. Upsal
Soe. Phys.-Med. ad Rhenum infer. Soc. Zool-Rot. Vindob. Socius
ord. Reg. Acad. Panormit. Scient. Soc. Asiat. Bengal. Instit. Nov. Zel.
Soc. Linn. Noy. Gall. Soc. Nat. Scrutat. Basil. Soc. Zool. Gall. Soc.
Lit. et Phil, Liverpool Soc. Roman. Zoolog. Socius Honor. Imp. Aca.
Scient. Petropcl. Reg. Acad. Scient. Taurin. Reg. Acad. Scient. Suec.
Soc. Senckenb. Nat. Scrutat. Francci, Acad. Scient. nat. Philad. Acad.
Scient. nat. Californ. Soe. Scient. nat. Cherbourg Soc. Human. et Scient.
Gall. Merid. Orient. Soc. extran. Lichfield Moxd, Kew Gardens,

Surrey.

* Halliburton, William Dobinson, M.D. B.Se. Professor of Physiology in King’s

College, London. 9 Ridgmount-gardens, Gower-street. W.C.

if Halsbury, Right Hon. Hardinge Stanley Giffard, Lord, M.A. D.C.L. 4 Lanis-

more-gardens. WV.

Harcourt, Augustus George Vernon, M.A. (Oxon.) D.C.L. (Dunelm.) LL.D.
(Univ. McGill) F.C.S., Lee’s Reader in Chemistry at Christ Church. Corley
Grange, Oxford; and Athencum Club. S.W.

t Harcourt, Right Hon. Sir William George Granville Venables Vernon, Knt., M.A.

Malwood, Lyndhurst, Hants.

Harley, George, M.D. F.R.C.P. F.C.S. Acad. Sci. Monach. et Soc. Phys. Med.
Herbip. et Acad. Med. Chir. Madrit. Corr. Mem. 25 Harley-street. W.
Harley, Rey. Robert, M.A. (Oxon.) F.R.A.S. Lit. et Phil. Soc. Mane. Soe. Reg.

Queensl. Soc. Honor, Rosslyn, Westlourne-road, Forest-lill. 8.1.

* Hartley, Walter Noel, F.R.S.E. F.1.C. Professor of Chemistry in the Royal College

of Science for Ireland. Joyal College of Science, Stephen’s-green, Dublin ;
and 386 Waterloo-road, Dublin.

Haughton, Rev. Samuel, M.D. (Dubl. et Bonon.) D.C.L. (Oxon.) LL.D. (Cantab.
et Edin.) Fellow of Trinity College, Dublin. Trinity College, Dublin.

Hay, Right Hon. Sir John Charles Dalrymple, Bart., Admiral, K.C.B. D.C.L.
(Oxon.) F.R.G.S. V.P. Inst. Naval Architects. 108 St. George’ s-square, S.W.
and Craigenveoch, Wigtownshire, N.B.

Date of Election.

June 1, 1876.
June 4, 1891.
June 7, 1866.

June 6, 1889.

June 3, 1875.

June 3, 1858.

June © 4, 1874.

June 2, 1892.

June 12, 1884.

June 8, 1871.
Jan.- 21, 1892|
June 13, 1895.
Feb. 7, 1839.
June 4, 1885,|
June 5, 1862.

June 4, 1885

June 13, 1495.

Served on
Council.

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 17

+ Hayward, Robert Baldwin, M.A. Ashcombe, Shanklin, Isle of Wight.
* Heaviside, Oliver, Hon. Mem. Lit. Phil. Soc. Manchester. Paignton, Devon.
Hector, Sir James, K.C.M.G. Ord. Cr. Pruss. M.D. F.G.S. F.L.S. F.R.S.E.

C.M.Z.S., Hon. Mem. of the Royal Societies of Victoria, New South Wales,
South Australia, and Tasmania; For. Mem. Amer. Acad. Sci., Amer. Inst.
Mining Engs., and K. Leop. Carol. Acad.; Director of the Geological
Survey, Colonial Laboratory, Meteorological and Weather Depaitments,
and of the New Zealand Institute; Chancellor of the New Zealand
University. Wellington, New Zealand.

* Hemsley, William Botting, A.L.S. Hon. Memb. Nat. Hist. Soc. Mexico, Principal
Assistant in the Herbarium, Royal Gardens, Kew. Herbarium, Royal

Gardens, Kew.

Hennessey, John Baboneau Nickterlien, C.I.E. M.A. F.R.A.S. F.R.G.S. late
Deputy Surveyor-General m charge of the Trigonometrical Surveys,
Survey of India. Merrimu, 18 Alleyn-park, West Dulwich, 8.E.; and
Athenewn Club. S.W.

Hennessy, Henry G., M.R.I.A. Professor of Applied Mathematics and Mechanism
in the Roy. Coll. of Science for Ireland. Clarens, Montreux, Switzerland.

Henrici, Olaus Magnus Friedrich Erdmann, Ph.D. LL.D. (St. And.) Professor of
Mechanics and Mathematics in the City and Guilds of London Institute.
Central Technical College, Exhibition-road, S.W.; and 34 Clarendon-road,
Nottinghill. W.

* Herdman, William Abbott, D.Sc. F.R.S.E. F.L.S. Professor of Natural History
in University College, Liverpool. University College, Liverpool.

Herschel, Alexander Stewart, M.A. Hon. D.C.L. (Durham), F.R.A.S. Honorary
Professor of Physics and Experimental Philosophy in the Durham
College of Science, Newcastle-on-Tyne. Observatory House, Slough,
Bucks.

Herschel, John, Col. R.E. F.R.A.S. Late Deputy Superintendent, Great
Trigonometrical Survey of India. Observatory House, Slough, Bucks.

Herschell, Right Hon. Farrer, Lord, G.C.B. D.C.L. LL.D. Chancellor of the
University of London. 46 Grosvenor-gardens. S.W.

Heycock, Charles Thomas, M.A.- Lecturer on Natural Science, King’s College,
Cambridge. 24 Fitzwilliam-street, Cambridge.

Heywood, James, M.A. F.G.S. F.S.A. 26 Kensington Palace-gardens, W.: and
Atheneum Club. S.W.

* Hicks, Henry, M.D. M.R.C.S. F.G.S. Corresp. Memb. Acad. Nat. Sai. Philad..

Geol. Soc. Liverpool. LHendon-grove, Hendon. N.W.

it Hicks, John Braxton, M.D. (Lond.) F.L.S. Coll. Reg. Med. Soc. “he Brackens,

| Lymington, Hunts.

* Hicks, William Mitchinson, M.A. D.Sc. Late Fellow of St. John’s College,
Cambridge, Principal and Professor of Physics in Firth College, Sheffield.
Dunheved, Hndcliffe-crescent, Sheffield.

Hickson, Sidney John, D.Sc.(Lond.) M.A.(Camb.) Hon. M.A. (Oxon.) F.L.S.

| Fellow of Downing College, Cambridge; Professor of Zoology in Owens

College, Manchester. _Lllesmere House, Wilmslow Road, Fallowjield, Man-

chester.

=

+

+

OF

Cc

18
| Served on
Date of Election. | Council.
—
June 7, 1894.
|
June 6, 1872.
June 4, eos | Ue
June 7, 1855.
June i, 1893.
June 13, 1895.
Apr. 22, 1847.) 53-54. |
1756-58 |
| 62-64
°70—-80
84-86
|
|
|
}
|
June 6, 1878. 86-87
*91—93
June 4, 1886
June 1, 1893
June 12, 1884
June 6, 1889.
June 1, 1865.) °66_68
69-71
"80-82
88-89
June 3, 1880

| R.
| R.

Rm.

RR

R.

R.

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

|

* Mill, Micaiah J. M., M.A., D.Sc. Professor of Mathematics, University College,

London. 27 Parliament-hill-road, Hampstead. N.W.

Tt Hincks, Rey. Thomas, B.A. (Lond.) Stokeleigh, Leigh Woods, Clifion, Bristol.

t Hind, John Russell, LL.D. (Glasc.) F.R.A.S. Inst. Fr. (Acad. Sci.) Par.

et Acad. Imp. Sci. Petrop. Corr., late Supermtendent of the Nautical

Almanae. 3 Cambridye Park-gardens, Twickenham.

+ Hippisley, John, F.R.A.S. Athenewn Club, S.W.; and Stoneaston Park, Bath.

* Hobson, Ernest William, D.Sc. Fellow of Christ's College, Cambridge. The

Gables, Mount Pleasant, Cambridge.

* Holden, Henry Capel Lofft, Major, R.A. The Haves, Belvedere, Woolwich.

Hooker, Sir Joseph Dalton—Pasr PREsSmENT—K.C.S.I. C.B. M.D. D.C.L.
LL.D. P.L.S. F.G.S. F.R.G.S. Hon. Mem. Roy. Bot. Soc. and Roy. Med.
Chir. Soc., London; Bot. and Med. Socs., Edin.; Nat. Hist. Soc. Newcastle;
Camb. Philos. Soc.; Asiat. Soc. Beng. ; and New Zeal. Institute. Corresp.
Mem. of Acad. Sci., Paris (Sect. Botan.). Member of Acad. Imp. Sci., St.
Petersb.; K. Akad. der Wissensch., K. K. Geogr. Gesell., and Hort. Soe. of
Vienna; K. Akad. der Wissensch. Berlin; Accad. delle Sci. dell’ Istit.

| Bologna; Acad. Roy. des Sci. Brussels; Reale Accad. dei Georgofili,
Florence ; Kong. Dansk. Vidensk. Selsk. Copenh.; K. Gesell. der Wiss.
Gott.; K. Danske Vidensk. Seiskab., Stockholm ; K. Vetensk. Soc., Upsala ;
K. Phys-oekonom. Gesell. Konigsb.; Soc. Vellosiana, Rio de Janeiro;
K. Leopeld.-Carol. Deut. Akad. der Naturf., Halle ; Senck. Naturf. Gesell.
Frankf. a M.; K. Baier. Bot. Gesell., Ratisb.; R. Accad. dei Lincei, Rome;
Amer. Acad. of Sci., Boston. Corresp. Mem. of Dubl. Nat. Hist. Soc. and
Agricult. Soc. of Paris. For. Mem. of Acad. de Méd., Paris and Nat. Acad.
of Sci., Washington. The Camp, Sunningdale, Berkshire.

Hopkinson, John, M.A. D.Sc. Holmwood, Wimbledon. S.W.

* Horsley, Victor Alexander Haden, B.S. F.R.C.S. M.D. (Halle) Professor of
Pathology in University College, London. 25 Cavendish-square, W.; and
Atheneum Club. S.W.

* Howorth, Sir Henry Hoyle, K.C.LE. D.C.L. 30 Collingham-place, Cromwell-road.

| S.W.

* Hudleston, Wilfrid H., M.A. F.G.8S. F.C.S. 8 Stanhope-gardens, South Kensington.
S.W.

* Hudson, Charles Thomas, M.A. LL.D. (Camb.). 2 Barton-terrace, Dawlish.

Huggins, William—VIcE-PRESIDENT—D.C.L. (Oxon.) LL.D. (Cantab. Edin.
Dubl. et St. And.) Ph.D. Lugd. Bat. Hon. F.R.S.E. F.R.A.S. Ord. Imp. Bras.
Rosae Com. Inst. Fr. (Acad. Sci.) Soc. Reg. Sci. Gott. et Soe. Spettros. Ital.
Mem. Corr. Acad. Lync. Rome Soc. Acad. Amer. Art. et. Sci. Boston. Reg.
Sci. Hafn. Physiogr. Lund. Reg. Boie. Marob. Acad. Reg. Sci. Acad. Reg.
Hib. Soc. Reg. Dubl. Lit. Phil. Mane. Soc. Astr. de France, Soc. Astr. et
Phys. Toronto, Soc. Hist. Dallas et Soc. Reg. Nov. Camb. Austr. Soc. Honor.
90 Upper Tulse-hill; and Atheneum Club. S.W.

* Hughes, David Edward, Com. of the Leg. dHonn. Fr. and Com. of Ords. of

Charles IIT. Spain, Iron Crown Austr., SS. Anne Russ., Mich. Bay., Maur. et

Lazar. Ital. and Medijie Turkey, Past-Pres. Soc. Teleg. Eng. 40 Langham-

street, Portland-piace. W.

Date of Election. |

June 6, 1889.

June

June

June

June

June

Feb.

June

June

June

June

June

June

June

6, 1878.
5, 1891.
4, 1885.

2, 1864.

Served on |
Council.

|
|
9.)°70-71 |
|

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 19

* Hughes, Thomas McKenny, M.A. Trin. Coll. Camb. F.G.S. F.S.A. Professorial
Fellow of Clare College, Camb., Chev. Ord. SS™- Maur. et Lazar. Ital. Corresp.
Memb. Soc. Géol. de Belg. Memb. Soc. Géol. de Fr. Woodwardian Professor

of Geology in the University of Cambridge. 18 Hills-road, Cam-
bridge.

+ Hull, Edward, M.A. F.G.S. LL.D. (Glase.) late Director of the Geological Survey
of Treland, and Professor of Geology in the Royal College of Science,
Master in Engineering (Hon. Caus. Dubl.) Hon. Mem. Acad. Sci. Amer.
Philad. Corresp. Soc. Geol. Belg. Soc. Extr. Hon. Mem. Geol. Soc. Edin.,
Glasg., Manch. 20 Arundel-gardens, Notting-hill. W.

Humphry, Sir George Murray, Knt., M.D. LL.D. (Edin.) Se.D. (Dubl.) Prof. of

Surgery in the Univ. of Cambridge, Fellow of King’s Coll. Hon, Fellow of

| Downing Coll. Grove Lodge, Cambridge.

‘* Hutchinson, Jonathan, LL.D. (Glase. and Camb.) M.D. (Dubl.) F.R.C.S. Corr.

Mem. Soe. Chir. Paris, Hon. Mem. Soc. Dermat. Nov. Ebor. Formerly

| President of and Professor of Pathology and Surgery in the Royal College

| of Surgeons. 15 Cavendish-square. W.

* Hutton, Frederick Wollaston, Captain. F.G.S. C.M.Z.8. Curator of the Canter-

| bury Museum, Christchurch, Cor. du Mus. dHist. Nat. Paris, Cor. Mem.

Roy. Soc. Tas. Hon. Mem. Roy. Soc. N.S.W. Cor. Acad. Nat. Sci. Philad.

Cor. Ornith. Ver. Wien, Cor. K. K. Geol. Reichsanst. Wien. Canterbury

Museum, Christchurch, New Zealand.

+ Jackson, John Hughlings, M.D. Coll. Reg. Med. Soc., Consulting Physician to

the London Hospital. 8 Manchester-square. W.

Jackson, Right Hon. William Lawies. 27 Cadogan-square, S.W.; and Allerton

| Fall, Chapel Allerton, Leeds.

* Japp, Francis Robert, M.A. Ph.D. LL.D. (St. And) He Ce ECS Rots on

Chemistry in the University of Aberdeen. University, Aberdeen.

| Jenner, Sir William, Bart., G.C.B. M.D. D.C.L. (Oxon.) LL.D. (Cantab. et Edin.)
Physician in Ordinary to the Queen, and to H.R.H. the Prince of Wales.
Greenwood, Durley, Bishop's Waltham.

* Jervois, Sir William Francis Drummond, Lient.-Gen., R.E., G.C.M.G. C.B.

Merlewood, Virginia Water.

{ Johnson, Sir George, Kt. M.D. (Lond.) Coll. Reg. Med. Soc., Physician Extra-

ordinary to the Queen, Emeritus Professor of Clinical Medicine in King’s

| College, London, and Consulting Physician to King’s College Hospital.

| 11 Savile-row. W.

* Joly, John, M.A. B.E. D.Se. 39 Waterloo-road, Dublin.

* Jones, John Viriamu, M.A. (Oxon.) B.Sc. (Lond.) Principal and Professor of

| Physics in the University College of South Wales and Monmouthshire.
Fellow of University College, London. 42 Park-place, Cardiff.

Jones, Thomas Rupert, F.G.S. Hon. Mem. Gesell. Isis, Dresden, Soe. Belg. de

Microse., and Soc. Geol. Hydrol. Paleeontol. Brux., Geol. Assoc. Lond.,
Geol. Socs. Edin. and Glasg., Roy. Irish Geol. Soc., and Anthrop. Inst.
Lond, Corresp. Mem. of the K.-K. Geolog. Reichsanst. Wien, and Acad.
Nat. Sci. Philad. 17 Parson’s Green, Pulham. S.W.

|

ca

20

Date of Election.

June

June

June

June

June

June

June

June

June

June

June

June

June

Council. |

Served on |

7, 1877.|°87-89

5, 1851.) 90-95

is)
=
(7)
[o7)
~I

5, 1890.

9, 1887.|

12, 1884.) 94-95

ma

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

[ie

Judd, John Wesley, C.B. F.G.S. Professor of Geology in the Royal College
of Science, London, and Dean of the College, Soc. Phil. Ebor. et Sci. Nat.
Deva. Soc. Honor, Acad. Sci. Nat. Philad. Soc. Geol. Belg. Brux. Inst.
Imp. Geol. Vindob. Corresp. 16 Cumberland-road, Kew; Royal College of
Science, South Kensington; and Atheneum Club. S.W. .

Kelvin, Wiliam Thomson, Lord, Past PrEsipENtT—D.C.L. (Oxon) LL.D. (Camb.
Dubl. Edin.) F.R.S.E. Hon. Mem. Inst. C.E., and Elect. Eng. Professor of
Natural Philosophy im the University of Glasgow, and Fellow of St. Peter’s
College, Cambridge, Trust. Brit. Mus. Grand Officier of the Legion of
Honour of France. Ord. Boruss. “Pour le Mérite” Eq. Comm. Ord. of
Leopold, Belgium, Comm. Imp. Ord. of the Rose, Brazil. Assoc. Etrang.
Inst. Fr. (Acad. Sci.) Par.; Corresp. Mem. R. Inst. Lomb., R. Acad. dei
Lincei; For. Mem. Soe. Roy. Sci. Gétt., Soc. Ital. delle Scienze, Soc. Reale
di Napoli, Acad. Nat. Sci. Philad.; Hon. Mem. Acad, Imp. Sci. Vienna,
Acad. Nov. Lyne. Rom., United Service Inst. Lond., Lit. and Phil. Soc.
Manch., Phil. Soc. Glasg., Roy. Irish Acad. University, Glasgow; and
Atheneum Club. S.W.

Kempe, Alfred Bray, M.A. 2 Paper-buildings, Temple, E.C.; and 23 Gilbert-
street, Brook-street. W.

Kennedy, Alexander B. W., LL.D. Mem. Inst. C.E. Pres. Inst. M.E. Emeritus
Professor of Engineering and Mechanical Technology in University College,
London. 2 Gloucester-place, Portman-square. W.

Kerr, Rey. John, LL.D. Mathematical Lecturer in the Free Church Traming
College, Glasgow. 113 Hill-street, Glasgow.

King, George, M.B. LL.D. C.1.E. F'.L.8. Superintendent of the Royal Botanical
Gardens, Calcutta, and of the Government Cinchona Plantations, Darjeelmg.
Seebpore, Calcutta.

Kingsburgh (see Macdonald).

Kirk, Sir John, G.C.M.G. K.C.B. M.D. LL.D. F.L.S. F.R.G.S. Waveriree,
Sevenoaks. Kent; and Atheneum Club. S.W.

Klein, Edward Emanuel, M.D. Lecturer on General Anatomy and Pbysi-
ology in the Medical School, St. Bartholomew’s Hospital. 19 Harl’s Court-
square. §.W.

Lamb, Horace, M.A. (Cantab.) Professor of Mathematics in the Owens College,
Manchester. Burton-road, Didsbury, Manchester.

* Langley, John Newport, M.A. Fellow and Lecturer of Trinity College,

Lecturer on Histology in the University of Cambridge. Trinity College,
Cambridge.

Lankester, Edwin Ray—Vicr-PREsSmENT—M.A. (Oxon.) LL.D. (St. And.) Linacre
Professor of Human and Comparative Anatomy in the University of Oxford,
Fellow of Merton College, Honorary Fellow of Exeter College, Oxford;
Hon. Mem. Camb. Phil. Soc. and Roy. Phys. Soc. Edin.; Corr. Acad. Nat,
Sci., Philadelphia. 2 Bradmore-road, Oxford; and Atheneum Club. S8.W.

Lapworth, Charles, LL.D. (Aberd.), F.G.S. Professor of Geology m the Mason
Science College, Birmingham. 13 Duchess-road, Edgbaston, Birmingham.

Larmor, Joseph, M.A. D.Sc. (Lond.) Fellow of St. John’s College, Cambridge ,
late Professor of Natural Philosophy in Queen’s College, Galway, and
Fellow of the Royal University of Ireland. St. John’s College, Cambridge.

Served on

Date of Election. Council.
June 1, 1854.
June 5, 1890.
June. 3, 1880.

June 7, 1860.|’81-83

: 793

|

June 12, 1879. 91-92
June 8, 1882.
|
|

June 3, 1869. ’74-76

| "85-87

|°91—-93
|

June 9, 1887.) 93-94
June 7, 1894.
June 6, 1867.)

June 3, 1858. 61-63

"70-72

"78-719

193-94.

4

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 21

Lawes, Sir John Bennet, Bart., D.C.L. (Oxon.) LL.D. (Edin.) Sc.D. (Cantab.)
F.C.S. Inst. Fr. (Acad. Sci.) Corr. Rothamsted, St. Albans.

* Lea, Arthur Sheridan, Sc.D. Fellow, Lecturer in Physiology, and Assistant

Tutor of Gonville and Caius College, Assistant Lecturer of Trinity

College, and University Lecturer, Cambridge. Gonville and Caius College,

Cambridge.
* Limerick, Charles Graves. Lord Bishop of, D.D., D.C.L. he Palace, Limerick,
Ireland.
Lister, Sir Joseph, Bart.——PREsIDENT—F.R.C.S. D.C.L. (Oxon.) Hon. M.D.

(Dubl. Wiirzburg, Bologna) LL.D. (Camb. Edin. Glase.) Emeritus
Professor of Clinical Surgery, King’s College, London, Surgeon Extraor-
dinary to the Queen. Knt. Comm. Ord. Danebrog. Knt. Pruss. Ord. “ Pour
le Mérite.” Inst. Fr. (Acad. Sci.) Mem. Assoc, Hon. Mem. Amer, Acad. Arts
and Sei. 12 Park-crescent, Portland-place. W.

Liveing, George Downing, M.A. Se.D. (Dubl.) Professor of Chemistry. Fellow
of St. John’s College, Cambridge. Newnham, Cambridge.

* Liversidge, Archibald, M.A. (Camb.) F.G.8. F.C.8. FEC. F.R.G.S., Assoc.

R.S.M. V.P. Roy. Soc. N.S.W. Memb. Phys. Soc. Lond. Mim. Soc. Gr. Brit.
Min. Soc. Fr. Corr. Mem. Roy. Soc. Tasm. Roy. Soc. Queensland, Soc.
dAcclimat. Maur. Senck. Naturf. Gesell. Frankf. Hon. Mem. Roy. Soe.
Vict. New Zeal. Inst. and K. Leop. Carol. Acad. Halle. Corresp. Edin.
Geol. Soc. Professor of Chemistry im the University of Sydney. The
University, Sydney, New South Wales.

Rm.|f Lockyer, Joseph Norman, O.B, F.R.A.S. Phys. Soc. Lond., Ord. Imp. Bras. Rosae.

Eq. Inst. Fr. (Acad. Sci.) Soc. pro fov. Indust. Nat. Par. Soc. Reg. Sct.
Gott. Frank. Inst. Philad. Soc. Phys. Soc. Reg. Med. Brux. Soc. Spettros.
Ital. Reg. Sci. Panorm. et Hist. Nat. Genev. Mem. Corr. Acad. Reg. Line.
Rome. et Soc. Phil. Amer. Philad. Socius. Soc. Lit. et Phil. Mane. Acad.
Gioen. Sci. Nat. Catan. Soc. Phil. Ebor. et Univ. Lehigh Soc. Honor. 16
Penywern-road, S.W.; Observatory House, Westgate-on-Sea ; and Royal College
of Science, South Kensington: S.W.

be Lodge, Oliver Joseph, D.Sc. LL.D. (St. And.) Professor
University College, Liverpool. 2 Grove-park, Liverpool.

* Love, Augustus Edward Hough, M.A. Fellow of St. John’s College; Cambridge.
St. John’s Colleye Cambridge.

t Lowe, Edward Joseph, F.R.A.S. F.L.S. F.G.S. FMS. Soc. Lit. et Phil.
Mane. et Lyc. Hist. Nat. Nov. Ebor. Mem. Corr. Shirenewton Hall, near
Chepstow, Monmouthshire.

Lubbock, Right Hon. Sir John, Bart., D.C.L. (Cx: )) LED: eae Dubl. et
Edin.) M.D. (Wiirzb.) V.P.L.S. F. G. §. F.Z.S. F.S.A. F.E.S. Trust. Brit. Mus.,
Assoc. Acad. Roy. des Sci. Brux., Hon. ‘een Amer. Bthnol Soc. Anthrop.
Soce. Wash. (U.S.), Brux., Firenze., Anthrop. Verein, Graz., Soc. Entom. de
France, Soc. Géol. de la Suisse, and Soc. Helvét. des Sci. Nat., Mem. Amer.
Phil. Soc. Phiiad. Corresp. Mem. Soc. Nat. des Sci. Nat. de Cherb., Berl. Gesell.
fiir Anthrop., Soc. Romana di Antrop., Soc. d’Emul. d’Abbeville, Soc. d’Ethn.
de Paris, Soc. Cient. Argentina, Soc. de Géog. de Lisb., Acad. Nat. Sci.
Philad., Numis. and Ant. Soc. Philad., For. Assoc. Mem. Soc. d’Anthrop. de
Paris, For. Mem. Amer. Antiq. Soc. High Elms, Down, Keni.

ot Physics in

22

Date of Election.

17, 1894.

June

June

June

June

June

June

May

June

June

June

June

June
June
June

June

13, 1895.)

| Served on |
| Council.

|

2, 1881.)

|

1, 1865,

3, 1880.|

cir)

Or
—
(os)
PY)
Ss

June 11, 1857.

June 12, 1873.

2, 1884.) 92-93

FELLOWS OF THE SOCIETY. (Noy. 30, 1895.)

* Lydekker, Richard, B.A. (Camb.). The Lodge, Harpenden, Herts.

* Macalister, Alexander, M.A. M.D. (Dubl. & Camb.) M.D. Se.D. (Dubl.) LL.D.
(Glasg.) Professor of Anatomy in the University of Cambridge. Torrisdale,
Cambridge.

McClean, Frank, M.A. LL.D. (Glasg.) F.R.A.S. M. Inst. C.E. Rusthall House,
Tunbridge Wells.

McClintock, Sir Francis Leopold, Admiral, K.C.B. D.C.L. L.L.D. 8 Atherstone-
terrace, Gloucester-road. S.W.

* MCoy, Sir Frederick, K.C.M.G. M.A. D.Se. (Cantab.) F.G.S. Professor of Natural

Sciences in the University, Melbourne, Soc. Phil. Cantab. Soc. Honor.

Melbourne, Australia.

ft Macdonald, John Denis, M.D. Inspector-General of Hospitals and Fleets,

R.N. 82 Messina-avenue, West Hampstead. N.W.

lf Macdonald, Right Hon. John Hay Athole, C.B. LL.D. F.R.S.E. M.I.E.E. Lord

Justice-Clerk of Scotland, and Lord President of the Second Division of

the Court of Session. 15 Abercromby-place, Edinburgh.

* Macewen, William, M.D. (Glasg.) Hon. LL.D. (Glasg.). Professor of Surgery
in the University of Glasgow. 38 Woodside-crescent, Glasgow.

McIntosh, William Carmichael, M.D. (Edin.) LL.D. (St. And.) F.L.S. F.R.S.E.
L.R.C.S.E. C.M.Z.S. Professor of Natural History in the University of
St. Andrews; Director of the University Museum, and of the Marine
Laboratory, St. Andrews; Mem. Fishery Board for Scotland; Hon.
Mem. Psychol. Soc. Paris and Soc. Centrale d’Aquicult. de France.

| 2 Abbotsford-crescent, St, Andrews, Scotland.

* MeKendrick, John Gray, M.D. LL.D. F.R.S.E. F.R.C.P.E. Professor of
Physiology in the University of Glasgow. 2 Florentine-gardens, Glasgow.

McLachlan, Robert, F.L.S. F.Z.S. F.E.S. Soc. Imp. Ami. Sci. Nat. Mosq. Inst.
Noy. Zel. Soe. pro Faun. et Flo. Fenn. Soc. Entom. Batav. Soc. Entom. Belg.
Soc. Entom. Helvet. Soc. Nat. Hist. Glasc. Soc. Honor. Soc. Reg. Sci.
Leodii. Corresp. Westview, 23 Clarendon-road, Lewisham. §.E.

McLeod, Herbert, F.LC. F.C.S. Professor of Chemistry in the Royal Indian
Engineering College, Cooper’s Hill. The College, Cooper’s-hill, Staines.

* MacMahon, Percy Alexander, Major, R.A. Pres. Lond. Math. Soc. Artillery
College, Woolwich ; and Regency-mansions, 40 Shaftesbury-avenue. W.

Malet, John Christian, M.A. Assistant Commissioner of Intermediate Education,
Ireland. Carbery, Silchester-road, Kingstown, Co. Dublin.

Mallet, John William, Ph.D. (Gétt.) M.D. LL.D. F.C.S. Mem. of the Chem. Soes.
of Paris, Berlin, and New York, and of the Amer. Phil. Soc. Philad. Fellow
of the Coll. Phys. Philad. and Hon. Fellow of the Med. Chir. Faculty of
Maryland. University of Virginia, Albemarle Co., Virginia, United States.

Marcet, William, M.D. F.C.S. Past Pres. Royal Meteorol. Soc. Flower-mead,
Wimbledon-park, S.W.; and Atheneum Club, 8.W.

Markham, Clements Robert, C.B. P.R.G.S. F.S.A. Acad. Caes. Nat. Cur.
Socius Soc. Geog. Par. Berol. Vindob. Hist. Philad. et Univ. Chil. Soc. Honor.
Atheneum Club; and 21 Eceleston-square. 8.W.

a5

ea

%#

as

—{-

Date cu EG Election.

June

June

June

June

June

4, 7, 1801,
|
|

13, 1895.|

June 12, 1879

June

June

June

June

June

June

June

June

June

June

June

3, 1880.

) Servedon |
| Gaaen

=

=

ok

5

3k

=>

ft

ae

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 23

Marr, John Edward, M.A. F.G.S. Fellow and Lecturer of St. John’s College,
Cambridge, and University Lecturer in Geology. St. John’s College,
Cambridge.

Martin, Henry Newell, M.A. (Camb.) M.B.and D.&e. (ond.) (Hon.) M.D, Univ.
of Georgia. Physiological Laboratory, Unixersity, Cambridge.

Martin, Sidney, M.D. B.S. B.Sc. F.R.C.P. Assistant Ihysician in University
College Hospital, and in the Hospital for Consumption, Brompton.
10 Mansjield-street, Cavendish-square. W.

Maskelyne, Nevil Story, M.A. F.G.8. Late Professor of Mineralogy in the
University of Oxford, Hon. Fellow Wadham Coll. Oxon. Soc. Reg. Geol.
Cornub. Soc. Imp. Min. Petrop. et Soc. Hist. Nat. Bost. Soc., Acad. Reg.
Bavar. Monach. Soc. Cor. Basset Down House, Swindon.

Masters, Maxwell Tylden, M.D. M.R.C.S. F.L.8. Ord. Leopold Eques. Inst. Fr.
(Acad. Sci.), Acad. Sci. Nat. Philad., Soc. Reg. Li¢ge et Soc. Sci. Nat.
Cherbourg Soe. Corr. Mount Avenue, Faling. W.

Matthey, George, F.C.S. Assoc. Inst. C.E. Leg. Honor. (France), Ord. Franz
Josef (Austria), Great Gold Medal for Artsand Science (Germany). Cheyne
House, Chelsea Embankment. S.\V.

Medlicott, Henry Benedict, M.A. (Dubl.) F.G.. Late Director (1876-87) of
the Geol. Survey of India. 48 St. John’s-road, Clifton, Bristol.

Meldola, Raphael, For. Sec. C.S. F.L.C. F.R.A.S. F.E.S. Professor of Chemistry
in the Finsbury Technical Colles City and Guilds of London Institute.
6 Brunswich-square, W.C.

Meldrum, Charles, C.M.G. M.A. LL.D. F.R.A.S. FR. Met. Soc. Director of the
Royal Alfred Observatory, Mauritius. J/auritius.

Miall, Louis Compton, F.L.S. F.G.S. Professor of Biology in the Yorkshire
College, Leeds. Crag Foot, Ben Rhydding, Leeds.

Mills, Edmund James, D.Sc. F.C.S. FIC. Young Professor of Technical
Chemistry in the Glasgow and West of Scotland Technical College,
Glasgow. 60 John-street, Glasgow.

Milne, John, F.G.S. Assoc. and Hon. Fellow of King’s College, London, Late
Professor of Ming and Geology in the Imperial College of Engineering,
Japan. Shide Hil House, Shide, Newport, Isle of Wight.

Minchin, George M., M.A. (Dubl.). Professor of Mathematics in the Royal
Indian Engineering College, Cooper’s-hill. The College, Cooper’s-hill, Staines.

Mivart, St. George, Ph.D. M.D. F.L.S. F.Z.S. Acad. Sci. Philad. Corr.
Mem. Professor of the Philosophy of Biology in the University of
Louvain. 15 Duke-street, St. James's. S.\W.

Moncrieff, Sir Alexander, Colonel (late R.A.), K.C.B. 15 Viearage-gute, Ken-
sington, W.; and Atheneum Club. S.W.

Mond, Ludwig, Ph.D. F.LC. F.C.S. The Poplars, 20 Avenue-road, Regent’s-park,
N.W. ; and Winnington Hall, Northwich.

Moore, John Carrick, M.A. F.G.S. 113 Eaton-square, S.W.; and Corswall,
Stranraer, Wigtonshire.

Morley, Right Hon. John, M.A. (Oxon.) Hon. LL.D. (Camb. and Glasg.) 95
Elm Park Gardens; and Atheneum Club. S.W.

Moulton. John Fletcher, M.A.Q.C. 57 Onslow-square. S.W.

24

Date of Election.

June 6, 1861.

June

Mar.

June

June

June

June

June

June

June

Jan.

June

June

June

June
June

June

June

7,

Or

>,

1866.

18638.)’75

1868.|

2.) "92-94

| 84-85
89-90

Served on
Council.

"83-85 |
89-91

|
|
|
|
|

"79-81
89-91

*§4—66
9 =o

4704-56 |

| 60-62 |

THE
79-81
"88-89 |

=

*

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

Mueller, Baron Ferdinand von, K.C.M.G. M.D. Ph.D. Hon. LL.D. (Uniy.
McGill) F.L.S. F.C.S. F.G.S. F.R G.S. OM.Z.S. Corr. Mem. Geol. Soe.
Edin., Bot. Soe. Lond. and Edin., and Pharm. Soc. Lond. Hon. Mem.
Soc. of Arts, Roy. Hort. Soc., Roy. Iish Acad., Roy. Hist. Soc., Inst.
Egypt, Inst. Nat. Genevois, R. Scott. Geogr. Soc. and Geogr. Soc. Manch.
For. Mem. of the Academies of Stockholm, Copenhagen, Boston, Munich,
and Halle. Corr. Mem. K. Gesell. der Wiss. Gottingen. Pres. Roy.
Geogr. Soc. Austr. (Vict. Branch), Government Botanist, and Director of
the Botanic Museum, Melbourne. Melbourne, Victoria.

Miiller, Hugo, Ph.D. LL.D. (St. And.) V.P.C.S. Ord. SS"™ Lazar. et Maunit.
Eq. 13 Park-square, N.W.; Crosby-hill, Camberley, Surrey ; and Atheneum
Club. S.W.

Mundella, Right Hon. Anthony John. 16 Elvasten-place; and Atheneum and
Reform Clubs. S.W.

Nares, Sir George Strong, Vice-Admiral, K.C.B. 1 Beaufort-villas, Surbiton.

Newton, Alfred, M.A. F.L.S. V.P.Z.8. Professor of Zoology and Comparative
Anatomy in the University of Cambridge. Magdalene College, Cam-
bridge.

Newton, Edwin Tulley, F.G.S. F.Z.8. Geological Museum, Jermyn-street. S.W.

Niven, Charles, M.A.-F.R.A.S., Professor of Natural Philosophy in the University,
Aberdeen. 6 Chanonry, Old Aberdeen.

Niven, William Davidson, M.A., Director of Studies in the Royal Naval College,
Greenwich. Greenwich. S.E.

Noble, Sir Andrew, Capt., K.C.B. F.R.A.S. F.C.8. Ord. Coron. Ital. et Ord.
Jes. Christ Portog. Com., Ord. Imp. Bras. Rosae Gr. Off. et Ord. Car. III.
Hisp. Eq. Jesmond Dene House, Newcastle-upon-Tyne; and Atheneum
Club. S.W.

* Norman, Rev. Alfred Merie, M.A. D.C.L. F.L.S. Hon. Canon of Durham.

efor

Burnmoor Rectory, Fence Houses, Co. Durham.

Northbrook, Thomas George Baring, Earl of, LL.D. D.C.L.G.C.S.I. 4 Hamilton-
place, W.; and Stratton, Micheldever Station, Hants.

Odling, William, M.B. Coll. Reg. Med. Socius. V.P.C.8. Hon. Math. Phys. Doct.
(Lugd. Bat.) Waynflete Professor of Chemistry in the University of Oxford.
Museum; and 15 Norham-gardens, Oxford.

Oliver, Daniel, LL.D. (Aberd.) F.L.S. late Keeper of the Herbarium and Library,
Royal Gardens. Kew, Emeritus Professor of Botany, University College,
London. 10 Kew Gardens-road, Kew.

Ommanney, Sir Erasmus, Admiral, Knt., C.B. LL.D. (Univ. McGill} F.R.A.S.
F.R.G.S. Cross of Grand Comm. of Royal Ord. of the Saviour, Greece. 29
Connaught-square, Hyde Park, W.: and United Service Club.

Osler, Abraham Follett. South Bank, Edgbaston, Birmingham.

* O'Sullivan, Cornelius, F.I.C. F.C.S. 140 High-street, Burton-on-Trent.

Paget, Sir James, Bart., D.C.L. (Oxon.) LL.D. (Cantab. et Edin.) Hon. M.D.
(Dubl.) Corr. Mem. Inst. Fr. (Acad. Sci.) Late Vice-Chancellor of the
University of London, Serjeant-Surgeon to the Queen, Surgeon in Ordinary
to H.R.H. the Prince of Wales. 5 Park-square West, Regent's Park. N.W.

Palgrave, Robert Harry Inglis, F.S.8. Belton, Great Yarmouth.

Served on

Date of Election. Council.

June

June
June

June

June

June
June

June

June

June

JI ine

June
April

June

June

June

June

June

June

7, 1888.

7, 1866.°79-81
1792-94

4, 1868.)

9, 1887,
5, 1890.
4, 1889,

1, 1876,

9, 1848.| 56-58

13, 1895.

7, 1888.|’94-95

ws

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 25

* Parker, T. Jeffery, D.Sc. (Lond.), A-R.S.M. A.L.S. C.M.Z.S. F.R.M.S. Mem.
Imp. Soc. Nat. Moscow, Corr. Mem. Linn. Soc. N.S.W. Professor of
Biology at the University of Otago. Dunedin, New Zealand.

+ Parsons, R. Mann, Major-General R.E. Hyde-vale, Blackheath. S.E.

if Pavy, Frederick William, M.D. (Lond.) LL.D. (Glasc.) Coll. Reg. Med. Socius,

Consulting Physician and formerly Lecturer on Physiology and Comparative

Anatomy and Zoology, and on Medicine, at Guy’s Hospital. 35 Grosvenor-

| street. W.

ES Peach, Benjamin Neeve, F.R.S.E. F.G.S. Geological Survey Office, Sheriff Court-

buildings, Edinburgh.

Pedler, Alexander, F.C.S. F.LC. Fellow of the University of Calcutta;

Professor of Chemistry, Presidency College, Calcutta ; and Meteorological
| Reporter to the Government of Bengal. Presidency College, Calcutta.

* Penrose, Francis Cranmer, M.A. F.R.A.S. Honorary Fellow of Magdalene

| College, Cambridge. Colebyfield, Copse Hill, Wimbledon. S.W.

Perkin, William Henry, V.P.C.S. LL.D. (St. And.) Ph.D. The Chestnuts, Sudbury,
Harrow.

* Perkin, William Henry, junior, Ph.D. F.R.S.E. FIC. F.C.S. Professor of
Organic Chemistry in Owens College, Manchester. Fairview, Wilbraham-

| road, Fallowfield, Manchester.

* Perry, John, D.Sc. Professor of Mechanical Engineering and Applied Mathematics
in the City and Guilds of London Technical College, Finsbury. 31 Brunswick-
square. W.C.

Pettigrew, James Bell, M.D. and F.R.C.P. (Edin.), LL.D. (Glasg.) Professor of
Medicine and Anatomy and Dean of the Medical Faculty in the University
of St. Andrews; Laureate Inst. Fr. St. Andrews. N.B.

* Pickard-Cambridge, Rev. Octavius, M.A. Bloxworth, Wareham, Dorset.

* Pickering, Spencer Percival Umfreville, M.A. F.C.S. F.I.C. Mem. Phys. Soc.
Lond. Deutsch. Chem. Gesell. Berlin. Harpenden, Herts.

{ Pirbright, Right Hon. Baron Henry de Worms, Lord. 42 Grosvenor-place, S.W. ;
Henley-park, Guildford.

+ Pitt-Rivers, Augustus Henry Lane-Fox, Lieut.-General, D.C.L. (Oxon.) V.P.
Anthrop. Inst. F.S.A. F.G.8. 4 Grosvenor-gardens, S.W.; and Rushmore,
Salisbury.

+ Playfair (of St. Andrew’s), Right Hon. Lyon, Lord, G.C.B. LL.D. Ph.D. V.P.C.S,
& R.S.E. Comm. Leg. Honor. and of Ord. Fran. Joseph Austr., Stell. Bor. Suec.
Eq. 68 Onslow-gardens. S.W.

Pole, William, Mus. Doc. Oxon., Knt. Commander, Imp. Ord. of the Rising Sun,
Japan. Mem, and Hon. Sec. Inst. C.E. Soc. Reg. Edin, Soc. Atheneum Club.
S.W.

* Poulton, Edward Bagnall, M.A. (Oxon.) F.L.S. F.Z.S. F.G.8. Hope Professor
of Zoology in the University of Oxford. Wykeham House, Banbury-road,
Oxford; and St. Helen’s Cottage, St. Helen's, Isle of Wight.

* Power, William Henry, Assistant Medical Officer, Local Government Board.
Glenbrook, Greenhithe ; and Local Government Board, Whitehall. S.W.

* Poynting, John Henry, D.Sc. Professor of Physics at the Mason College,
Birmingham. Fowhill, Alvechurch, Worcestershire.

|

|
|
|
|

D

26

Date of Election.

June 2, 1881.

- June 2, 1853.

June 3, 1852.

June 13, 1895.

June 4, 1886.) ¢

June 8, 1871.

June 7, 1888.

June 2, 1870,

June 12, 1884.

June 12, 1873.

June 1, 1876.

June 7, 1883

June 3, 1880.

June 3, £869

Served on
Council,

"8789

"17-19
84-95

R.

FELLOWS OF THE SOCIETY. (Noy. 30, 1895.)

* Preece, William Henry, C.B. Fellow of King’s College, London, M. Inst. Electr.

Eng. Mem. Inst. C.E. Hon. Mem. Inst. E.E. (America) Officier Lég. Honor,
France. Telegraph Department, General Post Office; and Gothic Lodge,
Wimbledon.

. |f Prestwich, Joseph, D.C.L. (Oxon.) F.G.S. F.C.S. Assoc. Inst. C.E. Inst. Fr.

(Acad. Sci.) Corresp. Soc. Geol. Fr. Socius. Inst. Imp. Geol. Vindob. Acad.
Lync. Rome. Acad. Reg. Sci. Belg. Soc. Anthrop. Brux. Soc. Phil. Amer.
Philad. Pont. Acad. Rome. Sci. Nat. Helvet. Soc. Vaud. Hist. Nat. et Soe.
Lit. Phil. Manc. Soc. Honor. Soc. Reg. Geol. Cornub. Soc. Hist. Nat. Bost.
Mem. Corr. Darent-Hulme, Shoreham, Sevenoaks.

Price, Rev. Bartholomew, D.D. F.R.A.S., Master of Pemb. Coll., Sedleian Prof.
of Nat. Phil., and Hon. Fellow of Queen’s College, Oxford. Canon of
Gloucester. Master's Lodge, Pembroke College, Oxford; and Atheneum Clib.
S.W.

* Purdie, Thomas, B.Sc. Ph.D. A.R.S.M. Professor of Chemistry in the University

of St. Andrews. The University, St. Andrews.

Pye-Smith, Philip Henry, M.D. B.A. F.R.C.P. Physician to Guy’s Hospital,
late Lect. on Physiol. at Guy’s Hospital. 48 Brook-street. W.

Quain, Sir Richard, Bart., M.D. (Lond.) Hon. M.D. (Dubl. and Roy. Univ.
Trel.) Hon. LL.D. (Edin.) F.R.C.P. Hon. F.R.C.P. Irel. President of the
General Medical Council, Physician Extraordinary to the Queen, Fellow of
the University of London. 67 Harley-street, W.; and Atheneum and Union
Clubs. S.W.

. * Ramsay, Wiliam Ph.D. (Tiib.) F.C.S. F.1.C. Professor of Chemistry in University

College, London. Corresp. Inst. Fr. (Acad. Sci). 12 Arundel-gardens,
Yotting-hill. W.
Ransom, William Henry, M.D. Coll. Reg. Med. Soc. Consulting Physician to
the General Hospital. Nottingham. The Pavement, Nottingham.

* Ransome, Arthur, M.A. M.D. Professor of Public Health im Owens College.

Examiner in Sanitary Science in Cambridge and Victoria Universities.
Sunninghurst, Dean-park, Bournemouth.

Rayleigh, John William Strutt, Lord—Srcretary—M.A. D.C.L. (Oxon.) Se.D.
(Camb. and Dubl.) LL.D. (Edin. Glasg. and Univ. McGill) Ph.D. (Heidel.)
Hon. Fellow of Trinity College, Cambridge, Hon. Mem. Inst. C.E. F.R.A.S.
Soc. Reg. Edin. Soc. Lit.et Phil. Mane. Acad. Reg. Sci. Monach. Soc. Honor.,
Inst. Fr. (Acad. Sci.). Par. Corresp., Soc. Reg. Sci. Gott. Corr. Soc., Professor
of Natural Philosophy in the Royal Institution. Terling Place, Witham,
Essex.

‘+ Reed, Sir Edward James, K.C.B. Broadway-chambers, Westminster. S.W.

|
Je

Reinold, Arnold William, M.A. Professor of Physics in the Reyal Naval College,
Greenwich. 28 Belmont Hill, Lee. 3S.E.

i Reynolds, J. Emerson, M.D. Se.D. (Dubl.) M.R.LA. F.C.S. Professor of

Chemistry, University of Dublin. 70 Morehampton-road, Dublin.

if Reynolds, Sir John Russell, Bart., M.D. Pres. R.C.P. Emeritus Professor of

|

Medicine in University College, London, Acad. Caes. Leop. et Soe.
Neurol. Nov. Ebor. Socius. Soc. Psychol. Physiol. Par. Soc. Corresp.,
Physician in Ordinary to Her Majesty’s Household. 38 Grosvenor-street. W.

Date of Election.
June 7, 1877.)
|
June 7, 1866.
June 6, 1867.

Jan. 13, 1842.
June 4, 1885.

May 24. 1860.)

June 5, 1890.
June 6, 1878.
June 7, 1877.)
June 3, 1875.)
June 4, 1863.

|
June 10, 1888,
Dec. 19, 1867.)

June 6, 1872.)

June 12, 1884.)

Served on
Council.

*82-84

68-70

790-91 |

.|’90-92

72-73
81-83
"38-90

(1-712
87-88

88-90

bo
ot

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

Reynolds, Osborne, M.A. (Cantab.) LL.D. (Glasgow), Mem. Inst. C.E. Hon. Fellow,
Queen’s Coll. Camb. Professor of Engineering in Owens College, Victoria
University, Manchester. 23 Lady Barn-road, Fallowfield, Manchester.

+ Richards, Sir George Henry, Admiral, K.C.B., F.R.G.S. Inst. Fr. (Acad. Sci.)
Par. Corresp. Soc. Geog. Berol. et Soc. Geog. Ital. Flor. Inst. Nov. Zel.
Soc. Honor. The Cottuge, Fetcham, Leatherhead; and Atheneum Club.
S.W.

+ Richardson, Sir Benjamin Ward, M.D. LL.D. M.A. F.S.A. Coll. Reg. Med. Soc.
Honorary Physician to the Royal Literary Fund. Mem. Acad. Caes. Leop.
Nat. Cur. Dresd.: Amer. Phil. Soc. Philad.; Acad. Phys. Med. Stat. Milan ;
Phil. Soc. St. And. Soc. Ital. d’Hygiéne, and Soc. Franc. d’Hygitne. 25
Manchester-square. W.

Riddell, Charles James Buchanan, Major-Gen. C.B.
Devonshire.

* Ringer, Sydney, M.D. (Lond.) Holme Professor of Clnical Medicine, University

College, London. 15 Cavendish-place. W.

{| Ripon, George Frederick Samuel Robinson, Marquis of, K.G. G.C.S.1. CLE.
D.C.L. (Oxon.) F.L.8. F.R.G.S. 9 Chelsea Embankment, 8.W.; and Studley
Royal, Ripon, Yorkshire. :

Roberts, Isaac, Sc.D. (Dubl.) F.R.A.S. F.G.S. Starfield, Crowborough, Sussex.

t Roberts, Samuel, M.A. (Lond.). 34 Lady Margaret-road, St. John’s College Park.
N.W.

Roberts, Sir William, B.A. M.D. (Lond.) Coll. Reg. Med. Soc.
square. W.

Roberts-Austen, William Chandler, C.B. F.C.S. Prof. of Metallurgy, Royal
College of Science, Chemist of the Royal Mint, Chev. Lég. Hon. France,
Mem. Chem. Soe. Berlin. Royal Mint, Tower-hill, E.; Chilworth, Guildford ;
and Atheneum Club. S.W.

Roscoe, Sir Henry Enfield, Knt., B.A. D.C.L. (Oxon.) LL.D. (Cantab. et
Dubl. et Montr.) Hon. M.D. (Heidelb.) Ph.D. V.P.C.S. Officier Lég. Hon.
France, Inst. Fr. (Acad. Sci.) Fellow of Univ. of Lond., Univ. Coll., and
Eton College, Emeritus Professor of Chemistry in Victoria University
(Owens College), Vice-President of Literary and Phil. Soc. Manchester,
For. Mem. Acad. Sci. Paris. Hon. Mem. of the New York Acad. Sci. Berlin
Chem. Soc. of the Verein fiir Naturwiss. Brunswick, and of the Physikal.
Verem, Frankfort-on-Main, Acad. Sci. Monach. Acad. Reg. Sci. Gott. et Soc.
Sci. Catan. Corresp. Acad. Cees. Leop. Soc. Reg. Physiogr. Lund. Soc. 10
Bramham-gardens, South Kensington, S.W.; and Atheneum Club.

Rosebery, Right Hon. Archibald Philip Primrose, Earl of, K.G. D.C.L. 38
Berkeley-square, W.; and Dalmeny Park, Linlithgowshire.

Rosse, Laurence Parsons, Earl of, K.P. B.A. D.C.L. (Oxon.) LL.D. (Dubl.) F-R.A.S.
Chancellor of the University of Dublin. irr Castle, Parsonstown, Ireland.

Routh, Edward John, D.Sc. (Cantab. et Dubl.) LL.D. (Glasc.) M.A. (Lond.)
Fellow of the University of London, Hon. Fellow St. Peter’s College,

| Cambridge, F.R.A.S. F.G.S. Newnham Cottage, Queen’s-road, Cambridge.

* Roy, Charles Smart, M.D. (Edin.) Professor of Pathology in the University of

Trinity College, Cambridge.

Oaklands, Chudleigh,

8 Manchester-

Cambridge.
D2

28
Date of Election.
June 12, 1884.
June 4, 1886
June 6, 1872.
June 1, 1876.
Jan. 28, 1869.
June 4, 1863
|
|
June 4, 18638
June 12, 1873.
June 2, 1881.|’
June 6, 1867
June 6, 1878
June 6, 1850.|
June 12, 1879. |

June 6, 1861.|’

June 7, 1894.

June 2, 1870 |

Served on
Council.

87-89
94-95

69-70
82-83

92-94

WO

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

- * Riicker, Arthur William, M.A. (Oxon.) D.Sc. (Vict.) Professor of Physics, Royal

College of Science, London, Hon. Fellow of Brasenose Coll. Oxford, Fellow

of the University of London, Treasurer, British Association, Corr. Mem.

Leeds Lit. and Phil. Soc. Hon. Mem. Royal Cornwall Polytechnique Society.

19 Gledhow-gardens, South Kensington, 8.W.; and Atheneum Club. S.W.

* Russell, Henry Chamberlame, C.M.G. B.A. (Sydn.) F.R.A.S. F.R. Met. Soc.

Government Astronomer of New South Wales.

N.S. Wales.

+ Russell, William James, Ph.D. V.P.C.S. Lecturer on Chemistry at the Medical

School of St. 34 Upper Hamilton-terrace.

N.W.

t Rutherford, Wiliam, M.D. F.R.S.E. Professor of Physiology in the Univ. of

Edinburgh. The University; and 14 Douglas-crescent, Edinburgh.

+ Salisbury, The Mest Hon. Robert Arthur Talbot Gascoigne-Cecil, Marquis of,
K.G. M.A. D.C.L. (Oxon.) Chancellor of the University of Oxford. 20
Arlington-street, S.W.; and Hatfield House, Hatjield, Herts.

Salmon, Rey. George, D.D. (Dubl. et Edin.) D.C.L. (Oxon.) LL.D. (Cantab.
Provost of Trin. Coll. Dubl. Inst. Fr. (Acad. Sci.) Paris, Acad. Imp. Sci.
Berol. Soc. Reg. Sci. Gott. Corresp. Soc. Reg. Sci. Hafn. Soc. Extr. Trinity
Colleyz, Dublin.

Salter, Samuel James Augustus, M.B. London, Hon. Fellow King’s College,
London, F.L.S. Atheneum Club; and Basingjield, near Basingstoke, Hants.

Salvin, Osbert, M.A. F.L.S. F.Z.8. Hawksfold, Fernhurst, Haslemere.

The Observatory, Sydney,

Bartholomew’s Hospital.

* Samuelson, Right. Hon. Sir Bernhard, Bart. Mem. Inst. C.E. 56 Princes-gate.

S.W.

Sanderson, J. S. Burdon, M.A. (Oxon.) M.D. LL.D. Se.D. (Dubl.) LL.D.

(Edin.) D.C.L. (Dunelm.) F.R.S.E. F.R.C.P. Regius Professor of Medicine

in the University of Oxford, Hon. Fellow of Magdalen College. Physio-
logical Laboratory ; and 64 Banbury-road, Oxford.

t Schiifer, Edward Albert, M.R.C.S. Jodrell Professor of Physiology, University
College, London. Croxley Green, Rickmansworth.

+ Schunck, Edward, F.C.S.

Kersal, Manchester.

. |* Schuster, Arthur, Ph.D. F.R.A.S. Professor of Physics in Owens College,

Victoria University, Manchester. 4 Anson-road, Victoria-park, Manchester.

Sclater, Philip Lutley, M.A. Ph.D. (Bonn) Hon. Fellow of Corpus Christi
College. F.L.S. F.G.S. F.R.G.S. Secretary of the Zoological Society
of London. 38 Hanover-square, W.; and Odiham Priory, Winchield,
Hants.

* Scott, Dukinfield Henry, M.A. (Oxon.) Ph. D. (Wiirzb.) F.L.S. F.G.S. Honorary
Keeper of the Jodrell Laboratory, Royal Gardens, Kew. Old Palace,
Richmond, Surrey.

t Scott, Robert Henry, M.A. F.R. Met. Soc. Secretary to the Meteorological
Council. Ord. Coron. Ferr. Austr. Eq. Acad. Cees. Leop. Soc. Soc. Met.
Fr. Par. Soc. Imp. Reg. Zool. Bot. Soc. Met. Austr. Vindob. Soe. Met.
Germ. Berol. et Soc. Nat. Scrutat. Emb. Soc. Honor. Inst. Geol. Imp.
Vindob. et Soc. Isis Dresd. Mem. Corr. Meteorological Office, 63 Victoria-

street ; and 6 Elm-park-gardens. S.W.

Date of Election.

June

4, 1886.

June 12, 1879.

June

June

June

June

June

June

June

June

7, 1894.

9, 1837.|

6, 1889.

11, 1857.

| Served on
Council.

92-94

eRe

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 29

* Sedgwick, Adam, M.A. Fellow and Lecturer of Trin. Coll, Cambridge, and
Reader of Animal Morphology in the University. Whitefield, Great Shelford,
Cambridge.

Seeley, Harry Govier, F.L.S. F.G.S. F.Z.S. F.R.G.S. Professor of
Geography and Lecturer on Geology in King’s College, London, Inst.
Imp. Reg. Geol. Vindob. et Acad. Sci. Nat. Philad. Corresp. Soc. Phil.
Ebor. Soc. Imp. Sci. Nat. Hist. Mosq. Soc. 25 Palace-gardens-terrace,
Kensington. W.

Selwyn, Alfred Richard Cecil, C.M.G. F.G.S. Late Director of the Geological
Survey of Canada. Susscw-séreet, Ottawa, Canada.

* Sharp, David, M.B. C.M. (Edin.) Hon. M.A. (Camb.) F.L.8. F.Z.8. Hon. Mem.
New Zealand Inst. Museum of Zoology, Cambridge; and Hawthorndene,
Lills-road, Cambridge.

Sharp, William, M.D. F.G.S. Horton House, Rugby.

Shaw, William Napier, M.A. Fellow and Senior Tutor of Emmanuel
College, Cambridge. Hmmanuel College, Cambridge.

Sherrington, Charles Scott, M.A. M.D.(Camb.) Professor of Physiology in
University College, Liverpool. 16 Grove-road, Liverpool.

Simon, Sir John, K.C.B. F.R.C.S. D.C.L. (Oxon.) LL.D. (Cantab. et Edin.) M.D.
(Dubl). M.Chir.D. (Munich), Consulting Surgeon to St. Thomas’s Hospital.
40 Kensington-square. W.

Simpson, Maxwell, B.A. M.B. M.D. & LL.D. (Hon. Dubl.) F.C.S. D.Se. F.LC. Hon.
F.K.Q.C.P. (Dubl.) Late Professor of Chemistry in Queen’s College, Cork.
Late Fellow of the Royal University of Ireland, 9 Barton-street, West Ken-

—1

x

sington. W.

* Smith, Rev. Frederick John, M.A. (Oxon.) University Lecturer in Mechanics and
Millard Lecturer in Experimental Mechanics, Trinity College, Oxford. 28
Norham-gardens, Oxford.

\* Snelus, George James, F.C.S. A.R.S.M. Mem. Inst. M.K. Vice-Pres. Iron and

Steel Inst. Hnnerdale Hall, Frizington, Cumberland.

* Sollas, William Johnson, D.Sc. (Camb.) LL.D. (Dubl.) F.R.S.E. F.G.S. Pro-
fessor of Geology in the University of Dublin. Lisnabin, Dartry-park-road,
Rathgar, Dublin.

Sorby, Henry Clifton, LL.D. (Cantab.) F.L.S. F.G.8. F.Z.S. F.S.A. F.R.MLS.
Soc. Min. Petrop. Soc. Holland. Harl. Socius., Acad. Lyne. Rome. Adsoc.
Extr., Amer. Acad. Arts et Sci. Soc. Honor. Acad. Sci. Nat. Philad. et Lyc.
Hist. Nat. Nov. Ebor. Corr. Mem. Broomfield, Sheffield.

t Sprengel, Hermann Johann Philipp, Ph.D. (Heidelb.) F.C.S. Royal Prussian
Professor (titular). Savile Club, 107 Piccadilly. W.

Stirling, Edward Charles, C.M.G. M.A. M.D. (Camb.) F.R.C.S. C.M.Z.S. Senior
Surgeon, Adelaide Hospital; Lecturer on Physiology in the University of
Adelaide; Hon. Director of the South Australian Museum. The University,
Adelaide, South Australia.

*

30 FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

Date of Election. “Connell.
June 5, 1851.)"54-92 | C. | Stokes, Sir George Gabriel, Bart—Pasr PresmEnT— M.A. D.C.L. “(Oxon.)
Rm. LL.D. (Dubl. Edin. et Cant.) D.Sc. Lucasian Professor of Mathematics

in the University of Cambridge, F.C.P.S. F.R.S.E., Hon. Memb. Iust. C.E.,
Soc. Reg. Hib. Lit. et Phil. Mane. et Med. Chi. Lond. Soc. Honor.
Ord. Boruss. “Pour le Mérite” Eq. Acad. Imp. Sci. Vindob. Inst. Fr.
(Acad. Sci.) Par. Acad. Sci. Berol. Soc. Reg. Sci. Gott. Corresp. Soc.
Gall. Phys. Reg. Sci. Upsal. Acad. Sci. Bavar. et Acad. Nov. Lyne. Rom.
Soc. Extr. Soc. Phil. Amer. et Soc. Batavy. Roterod. Socius et Acad. Amer.
Bost. Soc. Philos. Glase. et Mach. Civ. Inst. et Soc. Asiat. Beng. Soc. Honor.
Lensfield Cottage, Cambridge; and Atheneum Club. 8.W.

June 4, 1868.) 81-83 + Stone, Edward James, M.A. F.R.A.S. Radcliffe Observer., Ph.D. (Padua) Hon.
Fellow Queen’s Coll. Camb., Hon. Mem Lit. Phil. Soc. Mane. Corresp.
Mem. Soc. Nat. Sci. Nat. Cherbourg. Radeliffe Observatory, Oxford ; and
Atheneum Club. S.W.

June 2, 1881.) ** Stoney, Bindon Blood, LL.D. M. Inst. C.E. M.R.LA. M.LN.A. 14 Higin-road,
Dublin.
June 6, 18611! { Stoney, George Johnstone, M.A. D.Sc. Vice-President R.D.S. F.R.A.S. 8
Upper Hornsey-rise. N.
June 1, 1854.)’72-74 t Strachey, Richard, Lieut.-General, R.E. C.S.I. LL.D. (Cantab.) V.P.R.G.S.
|’80-81 | F.G.S. F.L.8, Chairman Meteorological Council. 69 Lancaster-gate, Hyde-
eaten park. W.

Mar. 22, 1888. + Sudeley, Charles Douglas Richard Hanbury-Tracy, Lord. Ormeley Lodae, Ham
| | Common, Surrey.

June 7, 1894.) * Swan, Joseph Wilson, M.A. (Durh.) F.C.S. F.LC. M. Inst. Elec. Eng. 58
| Ffolland-park. W.

P Sylvester, James Joseph, M.A. D.C.L. (Oxon.) Hon. Se.D. (Camb.) LL.D.
| (Dubl. et Edin.) F.R.S.E. Hon. Fellow of St. John’s Coll. Camb. and
|

Fellow of New Coll. Oxford, Savyilian Professor of Geometry m the

Apr. 25, 1839.| 62-64
184-85

WO

| University of Oxford, Officer of the Legion of Honour, Inst. Fr. (Acad. Sei.)
| et Soc. Philom. Par. Acad. Imp. Sci. Petrop. Reg. Sci. Berol. Ist. Lomb.
| Mediol. Soc. Sci. Nat. Carob. et Soc. Philom. Par. Mem. Corr. Acad.
Reg. Sci. Rome. Acad. Imp. Sci. Vindob. Soc. Reg. Sci. Gott. Reg. Sci.
Neapol. Acad. Sci. Amer. Bost. et Acad. Nat. Sci. Wash. et Philad. et Soc.
Ital. Sci. Adsoc. Extr. Soc. Reg. Edin. Acad. Reg. Hib. Lit. Phil. Mane. et
Univ. Kasan Soc. Honor. Atheneum Club, S.W.; and New College,
Oxford.

June 6, 1878. t Symons, George James, Sec. Roy. Met. Soc., Mem. of the Scot. Met. and
| | Soc. Met. de Fr., Corresp. Mem. of the Deutsche Met. Gesell. and of the
Soc. Reg. de Méd. Pub. de Belg., Registrar of the Sanitary Institute,
Chey. de la Légion dHonneur. 62 Camden-square. N.W.

June 7, 1888. * Teale, Thomas Pridgin, M.A. F.R.C.8. 38 Cookridge-street, Leeds.
June 5, 1890.) * Teall, J. J. H., M.A. F.G.S. 2 Sussea-gardens, West Dulwich, 8.E.; and
| Geological Museum, Jermyn-street. S.W.

| :
June 3, 1869.| | | ‘Tennant, James Francis, Lieut.-General, R.E. C.I.E. V.P.R.A.S. 11 Clifton-
gardens, Maida-hill. W.

Served on
Date of Election. Council.

June 4, 1891.

June 12, 1884.|’89-91

June 5, 1890.

June 1, 1893,
June 1, 1876,/"90-91 |

June 3, 1869.)

June 3, 1880.|’92—94

June 4, 1891,

June 6, 1889.

June 6, 1878.

June 6, 1867.
June 6, 1889.
June 1, 1892.

June 2, 1881.

June 7, 1888. |

June 7, 1883.

June 4, 1868

|
|

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.) 31

* Thompson, Silvanus Phillips, B.A. D.Sc. (Lond.), F.R.A.S. M.D. (Regiomont),
Reg. Acad. Sci. Suec. Soc. Phys. Verein, Francof. ad Mcenum. Soc. Honor.
Principal and Professor of Physics in the City and Guilds of London
Technical College, Finsbury. Morland, Chislett-road, West Hampstead.
N.W.

. * Thomson, Joseph John, M.A. Se.D. (Dubl.) Fellow of Trinity College and Caven-

dish Professor of Experimental Physics. Cambridge. Trinity College, Cam-

bridge.

be Thorne, Richard Thorne, U.B. M.B. (Lond.) F.R.C.P. Medical Officer to

H.M. Local Government Board, Vice-President of the Epidemiological
Society, Lecturer on Public Health at the Medical Schoo of St. Bartholo-
mew’s Hospital. 45 Jnverness-terrace. W.

Thornycroft, John Isaac, M. Inst. CE. Hyot Villa, Chiswick Mall, Chiswick.

Thorpe, Thomas Edward, B.Sc. (Vict.) Se.D. (Dubl.) Ph.D. (Heid.) LL.D.
(Glasg.) Treas. C.S. Principal of the Government Laboratories, Somerset
House, Fellow of the University of London, Soc. Chym. Berol. Socius.
Soe. Phil. Glase. Mem. Corr. Soc. Phil. Leeds, Lit. Phil. Mane. Soc. Honor.
Government Laboratories, Somerset House, W.C.; and Atheneum Club.

S.W.

it Thuilher, Sm Henry Edward Landor, General, R.A. CSI. F.R.G.S. Tudor

House, Richmond, Surrey ; and Oriental Club. W.

* Tilden, William Augustus, D.Sc. (Lond. and Dubl.) F.C.S. F.LC. Professor of
Chemistry in the Royal College of Science, London. Hon. Mem. Pharm.
Soc., Soe. Pub. Anal., Soc. Nat. Bristol, Coll. Pharm. Philad. 9 Ladbroke-
gardens, Notting-hill. W.

* Tizard, Thomas Henry, Staff-Captain R.N., F.R.G.S. Hydrographic Depart-

ment, Admiralty, Whitehall. S.W.

* Todd, Sir Charles, M.A. (Camb.) K.C.M.G. F.R.A.S. Postmaster-General
Superintendent of Telegraphs and Government Astronomer, South
Australia. The Observatory, Adelaide, South Australia.

Tomes, Charles Sissmore, M.A. (Oxon.). 9 Park-erescent, Portland-place. W.

f Tomlinson, Charles, F.C.S. 7 North-road, Highgate. N.

* T'omlinson, Herbert, B.A. (Oxon.). 88 Oakley-street, Chelsea. S.W.

* Trail, James William Helenus, A.M. M.D. C.M. (Aberd.) F.L.S. Regius Professor of

Botany in the University of Aberdeen. The University, Aberdeen. N.P.

* Traquair, Ramsay H., M.D. LL.D. F.R.S.E. F.G.S. Keeper of the Natural History
Collections in the Museum of Science and Art, Edinburgh. 8 Dean LPark-
crescent, Ldinburgh.

* Trimen, Henry, M.B. F.L.S. Director of the Royal o tanic Gardens, Ceylon.
Peradeniya, Ceylon; and Union Club. S.W.

* Trimen, Roland, F.L.S. F.Z.S. F.E.S. Late Curator of the South African Museum.
9, Osborne Mansions, Northumberland-street, Marylebone-road, W.; and
Oriental Club. W.

Tristram, Rev. Henry Baker, M.A. (Oxon.) LL.D. (Edin.) D.D. C.M.Z.S. Canon of
Durham. College, Durham.

32

Date of Election.

June 7, 1877.

June

June

June

June
June

June

June

June

June

June

Nov.

June

June

June

=

k

2k

+

==

sk

FELLOWS OF THE SOCIETY. (Nov. 30, 1895.)

Tumer, Sir William, M.B. (Lond.) D.C.L. (Dunelm. et Oxon.) LL.D. (Glasg.)
Se.D. (Dubl.) F.R.C.S. (Edin.) F.R.C.8. F.R.S.E. Professor of Anatomy in
the University of Edinburgh, Hon. Prof. Anat. Roy. Scot. Acad., Hon.
Member Roy. Irish Acad., Hon. Fellow Roy. Med. Chir. Soc. London, Fos.
Assoc. Anthrop. Soc. Paris, Cor. Member Soc. Anthrop. Ethnol. and
Prehist. Arch. Berlin. 6 Eton-terrace, Edinburgh; and Athenewn Club.
S.W.

Tylor, Edward Burnett, D.C.L. (Oxon.) LL.D. (St. And. Aberd. and McGill)
Assoc. Acad. Reg. Belg. Professor of Anthropology in the University of
Oxford. Museum House, Oxford.

* Unwin, W. Cawthorne, B.Sc. Mem. Inst. C.E. Mem. Inst. M.E. Mem.

Amer. Phil. Soc. Professor of Engineering at the Central Technical
College of the City and Guilds of London Institute. 7 Palace Gate-
mansions, Kensington. W.

* Veley, Victor Herbert, M.A. F.C.8S. University College; and 22, Norham-road,

Oxford.

* Venn, John, Sc.D. 3 St. Peter’s-terrace, Cambridge.
t Verdon, The Hon. Sir George Frederic, C.B. K.C.M.G. The Melbourne Club,

Melbourne, Australia; and Atheneum Club. S.W.

* Vines, Sydney Howard, M.A. (Oxon.) D.Sc. (Camb. and Lond.) F.L.S. Sherardian

Professor of Botany in the University of Oxford, Fellow of the University
of London, Hon. Mem. Mane. Lit. Phil. Soc. and Roy. Phys. Soc. Edin.,
Corr. Mem. Soc. Nat. Sci. et Math. de Cherb. and Soc. Nat. Hist. Bost.
Headington Hill, Oxford.

Walker, James Thomas, General, C.B. R.E. LL.D. F.R.G.S. 13 Cromwell-road,
South Kensington. S.W.

Walker, John James, M.A. Mem. Lond. Math. Soc. and Mem. Phys. Soc. 12
Denning-road, Hampstead. N.W.

* Wallace, Alfred Russel, LL.D. D.C.L. F.L.S. F.Z.8. Corfe View, Parkstone,

Dorset.

Waller, Augustus Désiré, M.D. Lecturer on Physiology at St. Mary’s Hospital
Medical School. 16 Grove End-road. N.W.

Walpole, Right Hon. Spencer Horatio, M.A. D.C.L. LL.D. Q.C. Trust. Brit.
Mus. 109 Haton-square, 8.W.; and Ealing.

is Walsingham, Thomas de Grey, Lord, M.A. LL.D., High Steward of the Univer-

sity of Cambridge, Trust. Brit. Mus. F.L.S. F.Z.S. F.E.S., Mem. Soe.
Ent. de France, Ent. Ver. zu Berlin, Nederlands Ent. Ver., Soc. Ent. de
Russie, Linn. Soc. N.S.W. Merton Hall, Thetford, Norfolk.

Ward, Harry Marshall, D.Sc. F.L.S. Late Fellow of Christ's College, Cambridge,
Professor of Botany in the University of Cambridge. Botanical Laboratery, —
New Museums, Cambridge.

* Warington, Robert, M.A. (Oxon.) F.C.S. Sibthorpian Professor of Rural

Economy in the University of Oxford. High Bank, Harpenden,
St. Albans.

* Warren, Sir Charles, Major-General, R.E. K.C.B. G.C.M.G. Government

House, Chatham; and Athenewn Club. S.W.
* Watson, Rey. Henry William, D.Sc. The Rectory, Berkeswell, Coventry.

Date of Election. Served on
ase Council.
June 5, 1890.
June 4, 1886.) 88-89
June 9, 1887
June 7, 1888.) 94-95
June 4, 1886.
June 2, 1870.
June 5, 1862.
June 7, 1855.|’59-61
69-71
73-90
June 12, 1879.
Jane 4, 1874,|’89-90 |
June 7, 1855
June 12, 1873
June 1, 1893.
June 6, 1889.
June 1, 1893.
June 3, 1852)

FELLOWS OF THE SOCIETY. (Noy. 30, 1895.) 33

* Weldon, Walter Frank Raphael, M.A. Fellow of St. John’s College, Jodrell
Professor of Comparative Anatomy and Zoology at University College,
London. 380A Wimpole-street. W.

* Wharton, William James Lloyd, Rear-Admiral, C.B. F.R.A.S. F.R.G.S. Hydro-
grapher of the Admiralty. Florys, Prince’s-road, Wimbledon Park; and
Atheneum Club. S.W.

* Whitaker, William, B.A. F.G.S. Assoc. Inst. C.E. Geological Survey of
England and Wales. Corr. Acad. Nat. Sci. Philad. 33 East Park-terrace,
Southampton; and Geological Survey Office, 28 Jermyn-street. S.W.

* White, Sir William Henry, K.C.B. LL.D. (Glasg.) F.R.S.E. Mem. Inst. C.E.
Fellow Royal School of Naval Architecture, V.P. Inst. Naval Architects,
Assistant Controller and Director of Naval Construction. The Admiralty,
Whitehall, S.W.; and Athenewn Club. S.W.

Wilde, Henry, Pres. Lit. Phil. Soc. Manch. The Hurst, Alderley Edge, Cheshire.

j Wilks, Samuel, M.D. LL.D. Coll. Reg. Med. Soc. Consulting Physician to Guy’s
Hosvital. 72 Grosvenor-street. W.

Williams, C. Greville, F.C.S. F.LC. Castlemaine, Oakhill-road, Putney. S.W.

Wilhamson, Alexander William, Ph.D. (Giessen) D.C.L. (Dunelm.) LL.D.
(Dubl. et Edin.) F.R.S.E. V.P.C.S. Hon. Mem. R.LA. Fellow of Univ.
Lond. Emeritus Prof. of Chemistry in Uniy. Coll. Lond. Soc. Inst. Fr.
(Acad. Sci.) Par. Acad. Reg. Sci. Berol. Acad. Reg. Sci. Taurin. Soc.
Biol. Paris, Corr. Mem. Acad. Lync. Rome. Soc. Chem. Berol. et Amer.
Nov. Ebor. Soc. Lit. Phil. Mane. Soc. Honor. Soc. Reg. Sci. Gott. Soe.
Extr. High Pitfold, Shottermill, Haslemere.

* Williamson, Benjamin, M.A. D.Se. D.C.L. (Oxon.) M.R.I-A. Fellow and Senior
Tutor of Trinity College, Dublin. Trinity College, Dublin.

‘ft Wilson, Sir Charles William, Major-General R.E. K.C.B. K.C.M.G. D.C... (Oxon.)
LL.D. (Edin.) M.E. (Dubl.) F.R.G.S. Atheneum Club. S.W.

Wilson, George Fergusson, F.C.8. F.L.8. Heatherbank, Weybridge Heath, Surrey.

+ Woodward, Henry, LL.D. (St. And.) P.G.S. F.Z.S. F.R.M.S. Lye. Hist. Nat. Nov.
Ebor. et Soc. Phil. Amer. Philad. Soc. Soc. Phil. Ebor. Assoc. Geol. Lond.
Soce. Geol. Edin.. Glase. Liverp. et Nordov. Soc. Honor. Soce. Geol. Belg.
Imp. Nat. Hist. Mosq. Hist. Nat. Montreal et Malacol. Belg. Corresp., Keeper
of the Department of Geology, British Museum (Natural History), Cromwell-
road, S.W. 129 Beaufort-street, Chelsea. S.W.

* Worthington, Arthur Mason, M.A. F.R.A.S. Headmaster and Professor of
Physics, Royal Naval Engineering College, Devonport. 6 Osborne Villas,
Devonport.

* Yeo, Gerald Francis, M.D. (Dublin) F.R.C.S. Emeritus Professor of Physiology
in King’s College, London. Bowden, Totnes, South Devon.

'* Young, Sydney, D.Sc. (Lond.) F.C.S. F.LC. Professor of Chemistry in

University College, Bristol. 13 Aberdeen - road, White Ladies’ - road,
Bristol.

f Younghusband, Charles Wright, Lieut.-General, 0.B. Palace-court-mansions,
Bayswater-road, W.; and Atheneum Club. S.W.

Rm.

Rm

Rm.

C.

FOREIGN MEMBERS.

——$H+# OO —

Agassiz, Alexander ...... Camb. (Mass.). 1891.
Auwers, Georg Friedrich

Julius Arthur ........... Berlin. 1879.
Baeyer, Adolf von.......... Munich. 1885. |
Berthelot, Marcellin ........ Paris. 1877.
Bertrand, Joseph Louis

IMINO cacoohon va du00 Paris. 1875.
Bunsen, Robert Wilhelm .... Heidelberg.1858.
Cannizzaro, Stanislao ...... Rome. 1889.
Chauveau, Jean Baptiste

AMUSE 9.50.0005 60000600 Paris. 1889.

4| Corman, “NbineGh Segoe no o8oc Paris. 1884.
Cremonaslouio iret te Rome. 1879. |
Daubrée, Gabriel Auguste .. Paris. 1881. |
Des Cloizeaux, Alfred Lows

Olivas Ne oisooddocosedddc Paris 1875. |
Du Bois-Reymond, Emil Hein-

HI Cla rewessrereustaievatcronsven env evs Berlin. 1877
Fizeau, Hippolyte Louis .... Paris. 1875
Cecenbaurs Carlier ssmeieee Heidelberg. 1884
Gould, Benjamin Apthorp Camb.(Mass.). 1891
Hermite. Charlestayscn ice Paris. 1873
Janssen, Pierre Jules César.. Paris. 1875.
Kekulé; Auoust... 2.20... Bonn, 1875.
Kilenm AWG Ltxce fages stetmuencts veers Géttingen. 1885

eorscoee

Kolliker, Albert von Wiirzburg. 1860.
Kowalewski, Alexsandr. . .. St. Petersburg. 1885.
Kiihne, Willy .............. Heidelberg.1892.
Leuckart, Rudolph Leipsic. 1877.
Mascart, Eleuthére Elie Nicolas Paris. 1892.
Mendeleeff, Dmitri Ivanovitch

St. Petersburg.1892.

seceoeeere

Newcomb, Simon ......... . Washington1877.
Newton, Hubert Anson...... New Haven.1892.
Pfliiger, Eduard Friedrich

Whlkvelin reer Bonn. 1888.
Poincaré srenriisen eee Paris. 1894,

Quincke, Georg Hermann,... Heidelberg. 1879.

Rowland, Henry A. ...... .. Baltimore. 1889.
Sachs, Julius von .......... Wirzburg. 1888.
Steenstrup, Johannes Japetus
SNE N56 Baginod5 000 ce .-.- Copenhagen.1863.
Strasburger, Eduard........ Bonn. 1891.
Struve, Otto Wilhelm . .. Pulkowa. 1873.
SLESA Lu GUancdseee eerie .. Vienna. 1894,
.| Tacchini, Pietro.. Reeieeluonees 1891.
Warchowss hid oleae .2- Berlin. 1884.
Weierstrass, Carl ......; oe. Lerlin. 1881.
Wiedemann, Gustav.....,.. Seipsic. 1884.

FELLOWS DECEASED SINCE THE LAST ANNIVERSARY (Nov. 30, 1894).

On the Home List.

Aberdare, Henry Austin Bruce, Lord, G.C.B. Hawkins, Bisset, M.D.

Babington, Charles Cardale, M.A. Hulke, John Whitaker, P.R.C.S.

Ball, Valentine, C.B. Huxley, Right Hon. Thomas Henry, D.C.L.
Beetham, Albert William. Kirkman, Rev. Thomas Penyngton, M.A.
Bristowe, John Syer, M.D. Rawlinson, Sir Henry Creswicke, Bart., G.C.B.
Buchanan, Su George, M.D. Savory, Sir William Scovell, Bart.

Carter, Henry John, Surgeon-Major. Selborne, Roundell Palmer, Earl of.

Cayley, Arthur, D.C.L- Tomes, Sir John F.R.C.S.

Cockle, Sir James, M.A. Williamson, William Crawford, Lh.D

Dobson, George Edward, M.A.

On the Foreign List.

Baillon, Henri Ernest. | Neumann, Franz Ernst.
Dana, James Dwight. | Pasteur, Louis.
Lovén, Sven Ludwig. Tchebitchef, Pafnutij.

Ludwig, Carl.

Change of Name and Title.

Worms, Baron Henry de, to Lord Pirbright.

FELLOWS ELECTED SINCE THE LAST ANNIVERSARY.

1895. June 13.)*Barry, J. Wolfe, C.B. |1895. June 13.|*Hickson, Prof. Sydney John,
1895. June 13. *Bourne, Prof. Alfred Gibbs, D.Sc. | | D.Se.
1895. June 13. *Bryan, George Hartley, M.A. | 1895. June 13. *Holden, Major Henry Capel Lofft.
1395. Jan. 24. |{Davey, Right Hon. Horace, Lord,| R.A.

DECra: 1895. June 13. *McClean, Frank, M.A., LL.D.
1895. June 13.'*Eliot. John, M.A. 1895. June 13, *Macewen, Prof. William, M.D.
1895. June 13.*Green, Prof. Joseph Reynolds,|1895. June 13. /*Martin, Sidney, M.D.

D.Se. 1895. June 13 |*Minchin, Prof. George M., M.A.
1895. Jone 13. *Griffiths, Ernest Howard, M.A. | 1895. June 13.\*Power, William Henry
1895. June 13.| Heycock, Charles Thomas, M.A. 1895. June 13.|*Purdie, Prof. Thomas, B.Sc.

NAMES OF PERSONS TO WHOM THE MEDALS

OF

THE ROYAL SOCIETY HAVE BEEN AWARDED.

. Stephen Gray.

2. Stephen Gray.
34, John Theophilus Desaguliers.

. John Theophilus Desaguliers.
. John Belchier.

. James Valoue.

. Stephen Hales.

. Alexander Stuart.

. John Theophilus Desaguliers

2. Captain Christopher Middle-

ton.

3. Abraham Trembley.
44, Henry Baker.
5. Sir William Watson.

. Benjamin Robins.

. Gowin Knight.

. Rey. James Bradley.
. John Harrison.

. George Edwards.
51. John Canton.

2. Sir John Pringle.

3. Benjamin Franklin.

. William Lewis.

. John Huxham.

. Lord Charles Cavendish.
. John Dollond.

. John Smeaton.

. Benjamin Wilson.

. John Canton.

56. William Brownrigy.

Edward Delaval.
Hon. Henry Cavendish.
. John Ellis.

08, Peter Woulfe.

COPLEY MEDAL.

1769.
1770.
1771.
1772.
1773.
1775.
1776.
1777.
1778.
1780.
| 1781.
1782.
| 1783.

William Hewson.

Sir William Hamilton.
Matthew Raper.
Joseph Priestley.
John Walsh.

Rev. Nevil Maskelyne.
Captain James Cook.
John Mudge.

Charles Hutton.

Rev. Samuel Vince.
Sir William Herschel.
Richard Kirwan.
John Goodricke.
Thomas Hutchins.

84. Edward Waring.
. Major-General William Roy.

. John Hunter.

. Sir Charles Blagden.

1789. Wiliam Morgan.

. dames Rennell.

John Andrew De Luc.

. Benjamin Count Rumford.
. Professor Volta.

. Jesse Ramsden.

. George Attwood.

. Sir

George Shuckburgh |

Evelyn.
Charles Hatchett.

. Rey. John Hellins.

. Edward Howard.

. Sir Ashley Paston Cooper.
. William Hyde Wollaston.
. Richard Chenevix.

. Smithson Tennant.

. Sir Humphry Davy.

1806.
1807.
1808.
1809.
1811.
1813.
1814.
1815.
1817.
1818.
1820.
1821.

Thomas Andrew Knight.
Sir Everard Home.
William Henry.
Edward Troughton.
Benjamin Collins Brodie.
William Thomas Brande.
James lvory.
David Brewster.
Captain Henry Kater.
Sir Robert Seppings.
John Christian Oersted.
Captain Edward Sabine.
John Frederick William
Herschel.

. Rey. William Buckland.
. John Pond.
. John Brinkley, Bishop of

Cloyne.

. Francois Arago.

Peter Barlow.

26. Sir William South.

27. William Prout.

Captain Henry Foster.

. George Biddell Airy.
2. Michael Faraday.

Baron Simeon Denis Poisson.

. Giovanni Plana.
5. William Snow Harris.

36. Jons Jacob Berzelins.

Francis Kiernan.

. Antoine C. Beequerel.
. John Frederic Daniell.
. Karl Friedrich Gauss.
. Michael Faraday.

Robert Brown.

COPLEY MEDAL—continued.

1840. Justus Liebig. 1856. Henry Milne-Edwards. 1876, Claude Bernard.
Jacques Charles Francois | 1857. Michel Hugéne Chevreul. 1877. James Dwight Dana.

Sturm. 1858. Sir Charles Lyell. 1878. Jean Baptiste Boussingault.
1841. George Simon Chm. 1859. Wilhelm Eduard Webcr. 1879. Rudolph J. #. Clansius.
1842. James MacCullagh. 1860. Robert Wilhelm Bunsen 1880. James Joseph Sylvester.
1843. Jean Baptiste Dumas. 1861. Louis Agassiz. 1881. Karl Adolph Wiirtz.
1844. Carlo Matteucci. 1862. Thomas Graham. 1882, Arthur Cayley.
1845. Theodor Schwann. 1863. Rey. Adam Sedgwick. 1883. Sir William Thomson.
1846. UrbainJeanJosephLeVerrier. | 1864. Charles Darwin. 1884, Carl Ludwig.
1847. Sir John Frederick William | 1865. Michel Chasles. 1885. August Kekulé.

Herschel. 1866. Julius Pliicker. 1886. Franz Ernst Neumann.
1848. John Couch Adams. 1867. Karl Ernst von Baer. 1887. Sir Joseph Dalton Hooker.
1849. Sir Roderick Impey Mur- | 1868. Sir Charles Wheatstone. 1888. Thomas Henry Huxley.

chison. 1869. Henri Victor Regnault. 1889. Rev. George Salmon.
1850. Peter Andreas Hansen. 1870. James Prescott Joule. 1890, Simon Newcomb.
1851. Richard Owen. 1871. Julius Robert Mayer. 1891. Stanislao Cannizzaro.
1852. Baron Alexander von Hum- | 1872. Friedrich Wohler. 1892. Rudolf Virchow.

boldt. 1873, Hermann Ludwig Ferdinand | 1893. Sir George Gabriel Stokes.
1853. Heinrich Wilhelm Dove. Helmholtz. 1894, Edward Frankland.
1854. Johannes Miller. 1874. Louis Pasteur. 1895. Carl Weierstrass
1855. Jean Bernard Leon Foucanlt. | 1875. August Wilhelm Hofmann.

RUMFORD MEDAL.

1800. Benjamin Count Romford. 1848. Henri Victor Regnault. 1872. Anders Jonas Angstrém.
1804. John Leslie. 1850. Francois Jean Dominique 1874. Joseph Norman Lockyer.
1806. William Murdoch. Arago. 1876. Pierre Jules César Janssen.
1810, Etienne Louis Malus. , 1852. George Gabriel Stokes. 1878. Alfred Cornu.
1814. William Charles Wells. 1854. Neil Arnott. 1880. William Huggins.
1816. Sir Humphry Davy. 1856. Louis Pasteur, 1882. William de W. Abney.
18i8. David Brewster. | 1858. Jules Jamin. 1884. Tobias Robertus Thalén.
1824. Augustin Jean Fresnel. | 1860. James Clerk Maxwell. 1886. Samuel Pierpont Langley.
1832, Jolin Frederic Daniell. | 1862. Gustav Robert Kirchhoff. 1888. Pietro Tacchini.
1834. Macedonio Melloni. | 1864. John Tyndall. 1890. Heinrich Hertz.
1838. James David Forbes. | 1866. Armand Hippolyte Louis | 1892. Nils C. Dunér.
1840, Jean Baptiste Biot. | Fizeau, 1894, James Dewar.
1842. Henry Fox Talbot. | 1868. Balfour Stewart.
1846. Michael Faraday. | 1870. Alfred Olivier Des Cloizeanx. |

. John Dalton.

ames Ivory.

. Sir Humphry Davy.

Friedrich Georg Wilhelm

Struve.

. Johann Friedrich Encke.

William Hyde Wollaston.

9. Charles Bell.

Eilhard Mitscherlich.

. David Brewster.

Antoine Jerome Balard.

. Auguste Pyrame De Can-

dolle.

Sir John Frederick William

Herschel.

4. John William Lubbock.

Charles Lyell.

. Michael Faraday.

Sir William Rowan Hamilton.

5. George Newport.

Sir John F. W. Herschel.

7. Rev. William Whevell.
. Thomas Graham.

Henry Fox Talbot.

9. James Ivory.

Dr. Martin Barry.

0. Sir John F. W. Herschel.

Charles Wheatstone.

. Robert Kane.

HKaton Hodgkinson.

2. William Bowman.

John Frederic Daniell.

. James David Forbes.

Charles Wheatstone.

. Thomas Andrews.

George Boole.

. George Biddell Airy.

Thomas Snow Bevk.

). Michael Faraday.

Richard Owen.

. George Fownes.

William Robert Grove.

8. Thomas Galloway.

Charles James Hargreaye.

. Colonel Edward Sabine.

Gideon A. Mantell-

50. Benjamin Collins Brodie.

Thomas Graham.

. John

ROYAL MEDAL.

. Earl of Rosse.

George Newport.

. James Prescott Joule.

Thomas Henry Huxley.

. Charles Darwin.
. August Wilhelm Hofmann.

Joseph Dalton Hooker.

. John Russell Hind.

John Obadiah Westwood.

. Sir John Richardson.

William Thomson.

. Edward Frankland.

John Lindley.

. Albany Hancock.

William Lassell.

. George Bentham.

Arthur Cayley.

. William Fairbairn.

Augustus Waller.

. William B. Carpenter.

James Joseph Sylvester.

. Rey. Thomas Romney Robin-

son.

Alexander William William- |

son.

. Rey. Miles J. Berkeley.

John Peter Gassiot.

4. Jacob Lockhart Clarke.

Warren De La Rue.

. Joseph Prestwich.

Archibald Smith.

. William Huggins.

Wiliiam Kitchen Parker.
Bennet Lawes

Joseph Henry Gilbert.
Sir William Logan.

and

. Alfred Russel Wallace.

Rev. George Salmon.

59. Sir Thomas Maclear.

Augustus Matthiessen.

70. William Hallowes Miller.

Thomas Davidson.

. John Stenhouse.

George Busk.

2. Thomas Anderson.

Henry John Carter.

3. George James Allman.

Henry Enfield Roscoe.

. Henry Clifton Sorby.
William Crawford Williamson.
. William Crookes.
Thomas Oldham.

. William Fronde.

Sir C. Wyviile Thomson.

. Frederick Augustus Abel.

Oswald Heer.
. John Allan Broun.
Albert C. L. G. Giinther.
. William Henry Perkin.
Andrew Crombie Ramsay,
. Joseph Lister.
Andrew Noble.
. Francis Maitland Balfour.
John Hewitt Jellett.

2. William Henry Flower.

Lord Rayleigh.

3. Thomas Archer Hirst.

J. S. Burdon Sanderson.
. George Howard Darwin.
Daniel Oliver.
. David Edward Hughes.
Edwin Ray Lankester.

>. Francis Galton.

Peter Guthrie Tait.
. Colonel Alexander
Clarke.
Henry Nottidge Moseley.

Ross

. Baron Ferdinandvon Mueller.

Osborne Reynolds.

. Walter Holbrook Gaskeli.

Thomas Edward Thorpe.

90. David Ferrier.

1895.

John Hopkinson.

91. Charles Lapworth.

Arthur William Ricker.

2. John Newport Langley.

Rey. Charles Pritchard.

3. Arthur Schuster.

Harry Marshall Ward.
. Victor Alexander Haden
Horslev.
Joseph John Thomson.
James Alfred Ewing.
John Murray.

DAVY MEDAL,

1877. Robert Wilhelm Bunsen.

Gustav Robert Kirchhoff.

878. Louis Paul Cailletet.

Raoul Pictet.

79. Paul Emile Lecoq de Boisbaudran.

80. Charles Friedel.

81. Adolf Baeyer.

$82. Dimitri Ivanovitch Mendcleeff.
Lothar Meyer.

1883. Marcellin Berthelot.

Julius Thomsen.

1884. Adolph Wilhelm Hermann Kolbe.

1885. Jean Servais Stas.
1886. Jean Charles Galissard de Marignac.
1887. John A. R. Newlands.
1888. William Crookes.
1889. William Henry Perkin.
1890. Emil Fischer.
1891. Victor Meyer.
1892, Francois Marie Raoult.
1893. J. H. van’t Hoff.

J. A. Le Bel.
1894. Per Theodor Cleve.
1895. William Ramsay.

DARWIN MEDAL.

1890. Alfred Russel Wallace.
1892. Sir Joseph Dalton Hooker.
1894, Thomas Henry Huxley.

HALRISON AND SONS, PRINTERS IN ORDINARY TO HER MAJESTY, ST. MARTIN'S LANE, LONDON,

PHILOSOPHICAL

PR eA Nes Ace lt O NS

OF THE

ROYAL, SOCLET Y
OF

LONDON.
(A.)

FOR THE YEAR MDCCCXCV.

VOL. 186.—PART I.

LONDON:

PRINTED BY HARRISON AND SONS, ST. MARTIN’S LANE, W.C.,

Printers in Ordinary to Her Mlajesw.

MDCCCXCV.

ADVERTISEMENT.

THE Committee appointed by the Royal Society to direct the publication of the
Philosophical Transactions take this opportunity to acquaint the public that it fully
appears, as well from the Council-books and Journals of the Society as from repeated
declarations which have been made in several former Transactions, that the printing of
them was always, from time to time, the single act of the respective Secretaries till
the Forty-seventh Volume; the Society, as a Body, never interesting themselves any
further in their publication than by occasionally recommending the revival of them to
some of their Secretaries, when, from the particular circumstances of their affairs, the
Transactions had happened for any length of time to be intermitted. And this seems
principally to have been done with a view to satisfy the public that their usual
meetings were then continued, for the improvement of knowledge and benefit of
mankind: the great ends of their first institution by the Royal Charters, and which
they have ever since steadily pursued.

But the Society being of late years greatly enlarged, and their communications more
numerous, it was thought advisable that a Committee of their members should be
appointed to reconsider the papers read before them, and select out of them such as
they should judge most proper for publication in the future Transactions ; which was
accordingly done upon the 26th of March, 1752. And the grounds of their choice are,
and will continue to be, the importance and singularity of the subjects, or the
advantageous manner of treating them; without pretending to answer for the
certainty of the facts, or propriety of the reasonings contained in the several papers
so published, which must still rest on the credit or judgment of their respective
authors.

It is likewise necessary on this occasion to remark, that it is an established rule of

the Society, to which they will always adhere, never to give their opinion, as a Body,

tye
upon any subject, either of Nature or Art, that comes before them. And therefore the
thanks, which are frequently proposed from the Chair, to be given to the authors of
such papers as are read at their accustomed meetings, or to the persons through whose
hands they received them, are to be considered in no other light than as a matter of
civility, in return for the respect shown to the Society by those communications. The
like also is to be said with regard to the several projects, inventions, and curiosities of
various kinds, which are often exhibited to the Society ; the authors whereof, or those
who exhibit them, frequently take the liberty to report, and even to certify in the
public newspapers, that they have met with the highest applause and approbation.
And therefore it is hoped that no regard will hereafter be paid to such reports and
puble notices; which in some instances have been too lightly credited, to the

dishonour of the Society.

—_—

1895.

List oF INSTITUTIONS ENTITLED TO RECEIVE THE PHILOSOPHICAL TRANSACTIONS OR
PROCEEDINGS OF THE RoyAL SocrEty.

Institutions marked A are entitled to receive Philosophical Transactions, Series A, and Proceedings.

22 ”

»

Series B, and Proceedings.
50 Series A and B, and Proceedings.

Proceedings only.

America (Central).
Mexico.

p- Sociedad Cientifica “ Antonio Alzate.”
America(North). (See Unirep Srarzs and Canapa.)
America (South).

Buenos Ayres.
AB. Museo Nacional.

Caracas.
B. University Library.
Cordova.
as. Academia Nacional de Ciencias.
Demerara.
p. Royal Agricultural and Commercial
Society, British Guiana.
La Plata.

B. Museo de La Plata.
Rio de Janeiro.
p. Observatorio.
Australia.
Adelaide.
p. Royal Society of South Australia.
Brisbane.
p. Royal Society of Queensland.
Melbourne.
p. Observatory.
p. Royal Society of Victoria.
Ap. University Library.
Sydney.
p. Australian Museum.
p. Geological Survey.
p. linnean Society of New South Wales.
4B. Royal Society of New South Wales.
ag. University Library.
Austria.
Agram.
p-. Jugoslavenska Akademija Znanosti i Um-
jetnosti.
p- Societas Historico-Naturalis Croatica.

MDCCCXCY.—A. b

Austria (continued).
Brinn.
AB. Naturforschender Verein.
Gratz.
AB. Naturwissenschaftlicher Verein fiir Steier-
mark.
Innsbruck.
AB. Das Ferdinandeum.
p. Naturwissenschaftlich
Verein.

Medicinischer

Prague.
AB. Konighche Bohmische Gesellschaft der
Wissenschaften.
Trieste.
B. Museo di Storia Naturale.
p. Societa Adriatica di Scienze Naturali.
Vienna.
p. Anthropologische Gesellschaft.
AB. Kaiserliche Akademie der Wissenschaften.
p. K.K. Geographische Gesellschaft.
AB. K.K. Geologische Reichsanstalt.

B. K.K. Naturhistorisches Hof-Museum.
B. . K.K. Zoologisch-Botanische Gesellschaft.
p. Oesterreichische Gesellschaft ftir Meteoro-
logie.
A. Von Kuffner’sche Sternwarte.
Belgium.
Brussels.

p. Académie Royale de Médecine.

AB. Académie Royale des Sciences.

b. Musée Royal d’Histoire Naturelle
Belgique.

p. Observatoire Royal.

p. Société Belge de Géologie, de Paléonto-
logie, et d’Hydrologie.

p. Société Malacologique de Belgique.

Ghent.
AB.

ae

University.

[

Belgium (continued).
Liége.
AB. Societé des Sciences.
p. Société Géologique de Belgique.
Louvain.
8. Laboratoire de Microscopie et de Biologie
Cellulaire
AB. Université.
Canada.
Hamilton.
p. Hamilton Association.
Montreal.
4B. McGill University.
p. Natural History Society.
Ottawa.
AB. Geological Survey of Canada.
AB. Royal Society of Canada.
Toronto.
p- Astronomical and Physical Society.
p. Canadian Institute.
AB. University.
Cape of Good Hope.
A. Observatory.
AB. South African Library.
Ceylon.
Colombo.
Bb. Museum.
China.
Shanghai.
p. China Branch of the Royal Asiatic Society.
Denmark.
Copenhagen.
aB. Kongelige Danske Videnskabernes Selskab.
Egypt.
Alexandria.
AB. Bibliotheque Municipale.
England and Wales.
Aberystwith.
AB. University College.
Bangor.
As. University College of North Wales.
Birmingham.
AB. Free Central Library.
as. Mason College.
p- Philosophical Society.
Bolton.
p. Public Library.
Bristol.
p- Merchant Venturers’ School.
AB. University College.
Cambridge.
AB. Philosophical Society.
p- Union Society.

|
England and Wales (continued).
Cooper’s Hill.
AB. Royal Indian Engineering College.
Dudley.
p. Dudley and Midland Geological
Scientific Society.

p- Philosophical Society.
4B. Yorkshire College.
Liverpool.
AB. Free Public Library.
p. literary and Philosophical Society.
A. Observatory.
AB. University College.
London.
AB. Admiralty.
p. Anthropological Institute.
AB. British Museum (Nat. Hist.).
AB. Chemical Society.

p-. “ Electrician,” Editor of the.

B. Entomological Society.

AB. Geological Society.

AB. Geological Survey of Great Britain.

p. Geologists’ Association.

AB. Guildhall Library.
Institution of Civil Engineers.
Institution of Electrical Engineers.

. Iron and Steel Institute.
B. King’s College.

3. Linnean Society.

AB. london Institution.

A

Pp

A.

A. Institution of Naval Architects.
pP

A

B

p. London Library.

\. Mathematical Society.

p- Meteorological Office.
Odontological Society.
Pharmaceutical Society.
Physical Society.

Quekett Microscopical Club.
Royal Agricultural Society.
Royal Asiatic Society.
Royal Astronomical Society.
Royal College of Physicians.
Royal College of Surgeons.

PRP RSS SEs

Hssex.
p. Hssex Field Club.
Falmouth.
p- Royal Cornwall Polytechnic Society.
Greenwich.
A. Royal Observatory.
Kew.
B. Royal Gardens.
Leeds.

A. City and Guilds of London Institute.

Institution of Mechanical Engineers.

and

[ vil

England and Wales (continued).
London (continued).

p. Royal Engineers (for Libraries abroad, six
copies).
AB. Royal Engineers. Head Quarters Library.
p. Royal Geographical Society.
p. Royal Horticultural Society.
p- Royal Institute of British Architects.
AB. Royal Institution of Great Britain.
B. Royal Medical and Chirurgical Society.
p. Royal Meteorological Society.
p. Royal Microscopical Society.
p. Royal Statistical Society.
4B. Royal United Service Institution.
AB. Society of Arts.
p. Society of Biblical Archeology.
p- Society of Chemical Industry (London
Section).
p. Standard Weights and Measures Depart-
ment.
as. The Queen’s Library.
4B. The War Office.
ap. University College.
p. Victoria Institute.
B. Zoological Society.
Manchester.
AB. Free Library.
as. Literary and Philosophical Society.
p- Geological Society.
AB. Owens College.
Netley.
p- Royal Victoria Hospital.
Newcastle.
aB. Free Library.
p. North of England Institute of Mining and
Mechanical Engineers.
p- Society of Chemical Industry (Newcastle
Section).
Norwich.
p. Norfolk and Norwich Literary Institution.
Nottingham.
ap. Free Public Library.
Oxford.
p. Ashmolean Society.
AB. Radcliffe Library.
A. Radcliffe Observatory.
Penzance.
p. Geological Society of Cornwall.
Plymouth.

Bg. Marine Biological Association.

p. Plymouth Institution.
Richmond.

4. “Kew” Observatory,

b2

]

Fngland and Wales (continued).
Salford.
p. Royal Museum and Library.
Stonyhurst.

p. The College.
Swansea.
AB. Royal Institution.

Woolwich.

AB. Royal Artillery Library.
Finland.
Helsingfors.
p. Societas pro Fauna et Flora Fennica.
AB. Société des Sciences.
France.
Bordeaux.
p. Académie des Sciences.
p. Faculté des Sciences.
p-. Société de Médecine et de Chirurgie.
p. Société des Sciences Physiques et
Naturelles.
Cherbourg.
p. Société des Sciences Naturelles.
Dijon.
p. Académie des Sciences.
Lille.
p. Faculté des Sciences.
Lyons.

An. Académiedes Sciences, Belles-Lettreset Arts.
AB. Université.

Marseilles.
p. Faculté des Sciences.
Montpellier.
ap. Académie des Sciences et Lettres.
B. Faculté de Médecine.
Nantes.
p. Société des Sciences Naturelles de l’Ouest
de la France.
Paris.
ap. Académie des Sciences de I’ Institut.
p. Association Frangaise pour l’Avancement
des Sciences.
p. Bureau des Longitudes.

A. Bureau International des Poids et Mesures.

Commission des Annales des Ponts et
Chaussées.

Conservatoire des Arts et Métiers.

p. Cosmos (M. t’ABpi VaLerre).

AB. Dépét de la Marine.

as. Ecole des Mines.

ab. Heole Normale Supérieure.

az. Ecole Polytechnique.

AB. Faculté des Sciences de la Sorbonne.
AB. Jardin des Plantes.

p. WUlectricien,

[viii

France (continued).
Paris (continued).
A. L’Observatoire.
p. Revue Scientifique (Mons. H. pp Varieny).
p. Société de Biologie.
4B. Société d’Encouragement pour |’Industrie
Nationale.
AB. Société de Géographie.
p. Société de Physique.
B. Société Entomologique.
AB. Société Géologique.
p. Société Mathématique.
p. Société Météorologique de France.
Toulouse. 3
An. Académie des Sciences.
A. Faculté des Sciences.

Germany.

Berlin.
A. Deutsche Chemische Gesellschaft.
A. Die Sternwarte.
p. Gesellschaft fiir Erdkunde.
AB. Konighche Preussische Akademie der
Wissenschaften.
A. Physikalische Gesellschaft.
Bonn.
AB. Universitat.
Bremen.
p. Naturwissenschaftlicher Verein.
Breslau.
p. ‘Schlesische Gesellschaft fiir Vaterlindische
Kaltur,
Brunswick.
p. Verein fiir Naturwissenschaft.
Carlsruhe. See Karlsruhe.
Charlottenburg.
A. Physikalisch-Technische Reichsanstalt.
Danzig.
AB. Naturforschende Gesellschaft.
Dresden.
p. Verein fiir Erdkunde.
Emden.
p. Naturforschende Gesellschaft.
Hrlangen.
AB. Physikalisch-Medicinische Societit.
Frankfurt-am-Main.
AB. Senckenbergische Naturforschende Gesell-
schaft.
wv. Zoologische Gesellschaft.
Frankfurt-am-Oder.
p. Naturwissenschaftlicher Verein.
Freiburg-im-Breisgau.
AB. Universitat.
Giessen.
AB, Gvrossherzogliche Universitit.

|

Germany (continued).

Gorlitz.
p. Naturforschende Gesellschaft.
Gottingen.
as. K6nigliche Gesellschaft der Wissenschaften.
Halle.
Ap. Kaiserliche Leopoldino - Carolinische
Deutsche Akademie der Naturforscher.
p. Naturwissenschattlicher Verein fiir Sach-
sen und Thiiringen.
Hamburg.
p. Naturhistorisches Museum.
ap. Naturwissenschaftlicher Verein.
Heidelberg.
p. Naturhistorisch-Medizinischer Verein
AB. Universitat.

Jena.
Ap. Medicinisch-Naturwissenschaftliche Gesell-
schaft.
Karlsruhe.

A. Grossherzogliche Sternwarte.

p- Technische Hochschule.
Kiel.
p. Naturwissenschaftlicher Verein ve

Schleswig-Holstein.
A. Sternwarte.
AB. Universitit.
Konigsbere.
ab. Konigliche Physikalisch - Okonomische
Gesellschaft.
Leipsic.
p. Annalen der Physik und Chemie.
4. Astronomische Gesellschaft.
aB. Kénigliche Siichsische Gesellschaft der
Wissenschaften.
Magdeburg.
p. Naturwissenschaftlicher Verein.
Marburg.
AB. Universitat.
Munich.
AB. Konigliche Bayerische Akademie der
Wissenschaften.
p. Zeitschrift fiir Biologie.
Miinster.
AB. Ko6nigliche Theologische und Philo-
sophische Akademie.
Potsdam.
A. Astrophysikalisches Obseryatorium.
Rostock.
4B. Universitat.
Strasburg.
ap. Universitit.
Tibingen.
as. Universitat.

Germany (continued).
Wiirzbure.
as. Physikalisch-Medicinische Gesellschaft.
Greece.
Athens.
4. National Observatory.
Holland. (See NeTHERLANDS.)
Hungary.
Buda-pest.
p. Ko6nigl. Ungarische Geologische Anstalt.
ap. A Magyar Tudés Tarsaség. Die Ungarische
Akademie der Wissenschaften.
Hermannstadt.
p. Siebenbiirgischer Verein fiir die Natur-
wissenschaften.
Klanusenburg.
ap. Az Erdélyi Muzeum. Das Siebenbiirgische
Museum.
Schemnitz.
p. KK. Ungarische Berg- und Forst-Akademie.
India.
Bombay.
AB. Elphinstone College.
p. Royal Asiatic Society (Bombay Branch).
Caleutta.
4B. Asiatic Society of Bengal.
4B. Geological Museum.
p. Great Trigonometrical Survey of India.
4B. Indian Museum.
p- The Meteorological Reporter to the
Government of India.
Madras.
B. Central Museum.
A. Observatory.
Roorkee.
p. Roorkee College.
Treland.
Armagh.
a. Observatory.
Belfast.
AB. Queen’s College.
Cork.
p- Philosophical Society.
AB. Queen’s College.
Dublin.
a. Observatory.
Ag. National Library of Ireland.
zB. Royal College of Surgeons in Ireland.
Aap. Royal Dublin Society.
4B. Royal Irish Academy.
Galway.
4B. Queen’s College.

be 3]

Italy.

Acireale.

p. Accademia di Scienze, Lettere ed Arti.
Bologna.

AB. Accademia delle Scienze dell’ Istituto.
Catania.

AB. Accademia Gioenia di Scienze Naturali.
Florence.

p-. Biblioteca Nazionale Centrale.

AB. Museo Botanico.

p. Reale Istituto di Studi Superiori.
Genoa.

p. Societa Ligustica di Scienze Naturali e

Geogratfiche.

Milan.

AB. Reale Istituto Lombardo di Scienze,

Lettere ed Arti.

AB. Societa Italiana di Scienze Naturali.
Modena.

p. le Stazioni Sperimentali Agrarie Italiane.
Naples.

p. Societa di Naturalisti.
AB. Societé Reale, Accademia delle Scienze.
B. Stazione Zoologica (Dr. Doury).

Padua.
p. University.
Palermo.
A. Circolo Matematico.
AB. Consiglio di Perfezionamento (Societa di
Scienze Naturali ed Economiche).
a. Reale Osservatorio.

p. UU Nuovo Cimento.
p. Societa Toscana di Scienze Naturali.

p. Accademia Pontificia de’ Nuovi Lincei.

p. Rassegna delle Scienze Geologiche in Italia.

A. Reale Ufficio Centrale di Meteorologia e di
Geodinamica, Collegio Romano.

AB. Reale Accademia dei Lincei.

p. R. Comitato Geologico d’ Italia.

A. Specola Vaticana.

4b. Societa Italiana delle Scienze.

p. Reale Accademia dei Fisiocritici.

p. Uaboratorio di Fisiologia.
ap. Reale Accademia delle Scienze.
Venice.
p. Ateneo Veneto.
ab. Reale Istituto Veneto di Scienze, Lettere
ed Arti.

Java.

Mauritius.

Netherlands.

New Brunswick.

New Zealand.

Norway.

Nova Scotia.

axe

Japan,
Tokio.
AB. Imperial University.
p. Asiatic Society of Japan.

Buitenzorg.

p. Jardin Botanique.
Luxembourg.
Luxembourg.

p. Société des Sciences Naturelles.
Malta.
p. Public Library.

p. Royal Society of Arts and Sciences.

Amsterdam.
AB. Koninklijke Akademie van Wetenschappen.
p. KK. Zoologisch Genootschap ‘Natura Artis
Magistra.’

Delft.

p. eole Polytechnique.

Haarlem.

ab. Hollandsche Maatschappij der Weten-

schappen.

p. Musée Teyler.
Leyden.

AB. University.
Rotterdam.

AB. Bataafsch
vindelijke Wijsbegeerte.
Utrecht.
AB. Provinciaal Genootschap van Kunsten en
Weteuschappen.

Gencstschap der Proefonder-

St. John.
p. Natural History Society.

Wellington.
AB. New Zealand Institute.

Bergen.
AB. Bergenske Museum.
Christiania.
aB. Kongelige Norske Frederiks Universitet.
Tromsoe.
p. Museum.
Trondhjem.
AB. Kongelige Nors'te Videnskabers Selskab.

Halifax.
p. Nova Scotian Institute of Science
Windsor.

p. Wing’s College Library.

Portugal.
Coimbra.
AB, Universidade.
Lisbon.
as. Academia Real das Sciencias.
p. Seccio dos Trabalhos Geologicos de Portugal.
Oporto.
p. Annaes de Sciencias Naturaes.
Russia. =
Dorpat.
AB. Université.
Irkutsk.
p. Société Impériale Russe de Géographie
(Section de la Sibérie Orientale).
Kazan. 2
AB. Imperatorsky Kazansky Universitet.
Kharkoff.
p. Section Médicale de la Société des Sciences
Expérimentales, Université de Kharkow.
Kieff.
p. Société des Naturalistes.
Moscow.
AB. Le Musée Public.
B. Société Impériale des Naturalistes.
Odessa.
p. Société des Naturalistes de la Nouvelle-
Russie.
Pulkowa.
A. Nikolai Haupt-Sternwarte.
St. Petersburg.
AB. Académie Impériale des Sciences.
B. Archives des Sciences Biologiques.
Ab. Comité Géologique.
p. Compass Observatory.
A. Observatoire Physique Central.
Scotland.
Aberdeen.
AB. University.
Edinburgh.

p. Geological Society.
p- Royal College of Physicians (Research
Laboratory).

p- Royal Medical Society.
A. Royal Observatory.
p. Royal Physical Society.
p- Royal Scottish Society of Arts.
AB. Royal Society.
Glasgow.
Ak. Mitchell Free Library.
p. Natoral History Society.
p. Philosophical Society.
Servia.
Belgrade.
p-. Académie Royale de Serbie.

[
Sicily.
Spain.
Cadiz.
A. Instituto y Observatorio de Marina de San
Fernando.
Madrid.
p- Comision del Mapa Geoldgico de Espana.
AB. Real Academia de Ciencias.
Sweden.

(See Iraty.)

Gottenburg.

AB. Kong]. Vetenskaps och Vitterhets Samhalle.
Lund.

4B. Universitet.
Stockholm.

4A. Acta Mathematica.

AB. Kongliga Svenska Vetenskaps-Akademie.
AB. Sveriges Geologiska Undersdkning.
Upsala.
AB. Universitet.
Switzerland.
Basel.
p- Naturforschende Gesellschaft.
Bern.
AB. Allg. Schweizerische Gesellschaft.

p. Naturforschende Gesellschaft.
Geneva.

AB. Société de Physique et d’Histoire Naturelle.

4B. Institut National Genevois.
Lausanne.

p- Société Vaudoise des Sciences Naturelles.
Neuchatel.

p- Société des Sciences Naturelles.
Zirich.

AB. Das Schweizerische Polytechnikum.

p. Naturforschende Gesellschaft.

p. Sternwarte.

Tasmania.

Hobart.

p-. Royal Society of Tasmania.

United States.

Albany.

AB. New York State Library.
Annapolis.

AB. Naval Academy.
Austin.

p. Texas Academy of Sciences.
Baltimore.

ag. Johns Hopkins University.
Berkeley.

p. University of California.

XI

|

United States (continued).

Boston.
AB. American Academy of Sciences.
b. Boston Society of Natural History.
A. Technological Institute.

Brooklyn.

AB, Brooklyn Library.
Cambridge.

ab. Harvard University.

B. Museum of Comparative Zoology.
Chapel Hill (N.C.).

p. Hlisha Mitchell Scientific Society.
Charleston.

p. Elliott Society of Science and Art of South

Carolina.

Chicago.

AB. Academy of Sciences.

p. Journal of Comparative Neurology.
Davenport (Iowa).

p. Academy of Natural Sciences.
Ithaca (N.Y.).

p. Physical Review (Cornell University).
Madison.

p. Wisconsin Academy of Sciences.
Mount Hamilton (California).

A. Lick Observatory.

New Haven (Conn.).
AB. American Journal of Science.
AB. Connecticut Academy of Arts and Sciences.

New York.
p. American Geographical Society.
p. American Museum of Natural History.
p. New York Academy of Sciences.
p. New York Medical Journal.
p. School of Mines, Columbia College.

Philadelphia.
aB.- Academy of Natural Sciences.
AB. American Philosophical Society.
p. Franklin Institute.
p. Wagner Free Institute of Science.
Rochester (N.Y.).
p. Acaderzy of Science.
St. Louis.
p. Academy of Science.
Salem (Mass.).
p. American Association for the Advance-
ment of Science.

AB. Hssex Institute.

San Francisco.
As. California Academy of Sciences.

United States (continued).

Washington.
As. Patent Office.
AB. Smithsonian Institution.
AB. United States Coast Survey.
B. United States Commission of Fish and
Fisheries.
AB. United States Geological Survey.

lr xu

]

United States (continued).

Washington (continued).
AB. United States Naval Observatory.
p. United States Department of Agriculture.
A. United, States Department of Agriculture

(Weather Bureau).

West Point (N.Y.)

as. United States Military Academy.

CONTENTS.
(A)

VOL. 186.—PART I.

I. On the Newtonian Constant of Gravitation. By C. V. Boys, A.R.S.M, F.RS.. .
Assistant Professor of Physics, Royal College of Science, South Ken-
SOIC LOT Mer a er te cosa Wide Gale Me aa, Pg iol ieny SV eee page 1

Il. On the Photographic Spectrum of the Great Nebula in Orion. By J. NoRMAN
OGRA ER Ot AD Sse ey ta celia fl Ra, a SO dBc oie irene anny Pee E SS

Ill. Propagation of Magnetization of Iron as affected by the Electric Currents im
the Iron. By J. HorKinson, F.R.S., and H. WILSON. .... . . . 98

IV. On the Dynamical Theory of Inconypressible Viscous Fluids and the Determination
of the Criterion. By Osporne Reynowps, V.A., LL.D., F.RS., Professor of
Engineering in Owens College, Manchester . . . . ..... ~. 128

V. On a Method of Determining the Thermal Conductwity of Metals, with
Applications to Copper, Silver, Gold, and Platinum. By James H. Gray,
M.A., B.Sc., late “1851 Exhibition” Scholar, Glasgow University. Commu-
ALCON COADUPUOTOL SWORE VINEE SHiiSs)) re oe ess) i ee vee ee ce ae OD

VL. Argon, a New Constituent of the Atmosphere. By Lord Rayueicu, Sec. B.S.,
DUET OESSOT. NV MGHEAM SEUAMISAY, EheS.. <5 0 2 8 ee LOY,
MDCCUXCV.—A. c

exces]
VIL. On the Spectra of Argon. By Witutam Crookes, F.R.S., de. . . page 243

VII. The Inquefaction and Solidification of Argon. By Dr. K. OtszEwsx1, Pro-
fessor of Chemistry in the University of Cracow. Communicated by Professor
WiinietaM RAMSAY, oh ReS. Se a ee con | eee

IX. The Latent Heat of Evaporation of Water. By E. H. Grirritrus, I.A.,
HeGe Sussex ee Cambridge. Communicated by R. T. GLAZEBROOK,

X. Contributions to the Mathematical Theory of Evolution.—Il. Skew Variation im
Homogeneous Material. By Karu Pearson, University College, London.
Communicated by Professor HENRICI, HohaS. 9). 22) ee

XI. A Determination of the Specific Heat of Water in Terms of the International
Electric Units. By Artuur Scauster, F.R.S., Langworthy Professor of
Physics at the Owens College, Manchester, and Witit1am Gannon, J.A.,
Exhibition (1851) Scholar, Queen’s College, Galway . . . . . . . 415

XII. The Oscillations of a Rotating Ellipsoidal Shell containing Fluid. By S. 8.
Hoven, B.A., St. John’s Rees Cambridge. Communicated by Sir RoBEert
jam, wee . . k Mr ee ese gio | ED)

XIII. On the Velocities of the Ions. By W.C. Dampier Wuetuam, M.A., Fellow of
Trinity College, Cambridge. Communicated by Professor J. J. THomson,
PRIS. Ss a ye. ile ate, cw lomea i ae es

XIV. On the Singular Solutions of Simultaneous Ordinary Differential Equations
and the Theory of Congruencies. By A. C. Dixon, M.A., Fellow of Trinity
College, Cambridge, Professor of Mathematics in Queen’s College, Galway.
Communicated by J. W. L. GuaisHer, S6D., VRS... . . . . . . 523

XV. On the Ratio of the Specific Heats of Some Compound Gases. By J. W.
Carstick, M.A., D.Sc., Fellow of Trinity College, Cambridge. Communicated
by Professor J. J. THomson; HRS. ~ 24. x oy pan

XVI. Iron and Steel at Welding Temperatures. By T. Wricutson, M.P., Memb.
Inst. CE. Communicated by Professor Roperts-Austen, C.B., PRS. 593 _

Index to Part I.

LIST OF ILLUSTRATIONS.

Plates l and 2.—Professor C. V. Boys on the Newtonian Constant of Gravitation.
Plate 3.—Mr. Witiram Crookes on the Spectra of Argon.
Plates 4 to 6.—Mr. E. H. Grirriras on the Latent Heat of Evaporation of Water.

Plates 7 to 16.—Mr. K. Pearson on the Mathematical Theory of Evolution.—II.
Skew Variation in Homogeneous Material.

Plate 17.—Mr. T. Wricutson on Iron and Steel at Welding Temperatures.

PHILOSOPHICAL TRANSACTIONS.

I. On the Newtonian Constant of Gravitation.

By C. V. Boys, A.RSIL, FRS., Assistant Professor of Physics, Royal College of
Science, South Kensington.

Received May 31,—Read June 7,—Revised October 18, 1894.

[PLATEs 1, 2.]

TABLE OF CONTENTS.

PAGE.
Part I. (pp. 1 to 37).
FEST HUTTE AIG ear Se ion ok hc hsct yous = Ge ea Ye WNT us etna. ss eR nla Nate aca J
TNK@ GTA PARES oe oh Reenteraena cir rhea i aa ac ae hn aah A os oh fa ed neha 8
hesaboratorygan dhaccessOries: ver-teg masts towne eed Aveta Came ene Peay vila PNM ce eae tee MN SGUR tae Belt
Ni oparceiscale he nest tas ms: jot aes sy geet pstileed nah ideen (ure cits ave Fie EAU Eas eat eNOre as ae Ad AL
hheoverheadapulliess-seu caine iesabictes oo Pore erLtteace Gabe mei as Ace we oot ete earl.
sh otsteelstaperan del tsga CCOSSOlICS ii seaese ie )inr sachs Toile tel that qian Pienaar ara ac Meare eee
eRHeOPLiCaECOM Passe yn -UUomer en lao [mote cs yee ia aAP AE eee een Mace erat) se hace ariel
iiversmallpolassiscaletecmense ca ee cee TP ce MN eka Le tame c gt nr te oe as O()
Theclock. . . bs ie hese) an Lice ici che Lani ba kot Ae Raa cal gr ete SN ese eigen oetd
The large balls se ee stipports Pic diets Obey GH Gea Gy SO anc Uke Baa Te atch ol he ea cement ets st e45)
Rhejsmallaballstoreylinderse me uaewunme-g aire Caern Meer go lam tases hake ead, ete ee pp oo,
die |seaiin Tiyeamare Cheb ies panera bas! 6 5) oe og 5M toe ps Mellig) eo melee co a all
Conclusiongotarby lars many melt emai. Mrareti.t cere cedute treretabedeoea co! op Nova atl Payal cee re EEE OY
Part II. (pp. 37 to 50).
Parr III. (pp. 51 to 71).
bre denlecionsancs periods mergrata cs Ae een nih se ets he es ie aunjoll
PREF CCOMEL Eye OLaLIGap PAL auusmen ait eile: is) (Boise yn Mae Fae BL ove een lla earo ©
The dynamics of the moving system . . Bo Eis tot NS DD AA LRAT ort oe Bis | ep Ae recreates OS)
The combination of the preceding three esate Bec lch Ge Mein Carlen ea ace | B.Se ae rte ee ga aL
COnchisione meme MT el amr Pee eon ket Gn Seu chag sib ene be Seay joe Roars veer a sue Oe)

MDCCCXCV.—A. B d.3,90.

9 PROFESSOR GC. V. BOYS ON THE

Parr I,
Preliminary.
In a paper on the CavENDISH experiment, published in the ‘ Proc. Roy Soc., vol. 46,
p- 253, I showed how the famous experiment of CAVENDISH could be transformed in
several particulars, so that greatly increased delicacy and accuracy would be obtainable.

The experiment is-so well known that there is no occasion to describe the apparatus
which CAVENDISH employed, or the subsequent work of Reicu,t Barty,{ or Cornu
and Bariie.§ It is sufficient to state that, owing to the extremely small value of the
Newtonian constant of gravitation, all these experimenters made use of balls as large
as they conveniently could, so as to increase the force of attraction as much as
possible, and of a lever as long as they could, so as to increase the effect of the force
in producing torsion. However, Cornv realized that if he could keep the period the
same by the use of a sufficiently fine torsion wire, and reduce the dimensions of the
whole apparatus, the angle of deflection would not be reduced but would remain the
same. Cornu also introduced refinements which have made the behaviour of his
apparatus far more consistent than that of any which had preceded it.

Soon after I had made and found the value of quartz fibres for producing a very
small and constant torsion, I thought that it might be possible to apply them to the
CAVENDISH apparatus with advantage, which opinion I found was also held by
Professor TynpAuLL. Before employing them for this purpose I examined the theory
of the apparatus with a view to using them in the most suitable manner.

The sensibility of this kind of apparatus is, if the period is maintained always the
same, independent of its linear dimensions ; for in two similar instruments, in which
all the dimensions of one are n times the corresponding dimensions of the other, the
moments of inertia of the beams and their appendages are as n° : 1, and, therefore, if the
period is to be unchanged, the torsional couples must be as 7? : 1 also. The attracting
masses, both fixed and movable, are as 1°: 1, and their distances apart asm: 1; there-
fore, the attractions are as n°/n”, or as n*: 1, and these, acting on arms n times as long
in one as in the other, produce moments as “> : 1; that is, in the same proportion as
the torsional rigidities, and so the angles of deflection are the same in the two cases.

If, however, the length of the beam only is changed, and the attracting masses are
moved until they are opposite to and a fixed distance from the ends of the beam, then
the moments of inertia will be altered in the ratio 2* : 1, while the corresponding
moments will only change in the ratio n : 1, and thus there is an advantage in
reducing the length of the beam until one of two things happens, either it is difficult
to find a sufficiently fine torsion thread that will safely carry the beam and produce the
required period—and this, no doubt, has prevented the use of a beam less than that

* ¢ Phil. Trans.,’ 1798, p. 469.

+ ‘Comptes Rendus,’ 1837, p. 697.

t ‘Phil. Mag.,’ vol. 21, 1842, p. 111.

§ ‘Comptes Rendus,’ vol. 76, p. 954; vol. 86, pp. 571, 699, 1001.

NEWTONIAN CONSTANT OF GRAVITATION. 3

half a metre in length—or else, when the length becomes nearly equal to the diameter
of the attracting balls, they then act with such an increasing effect on the suspended
balls at the other end of the beam, that the balance of effect begins to fall short of that
which would be due to the reduced dimensions if the opposite ball did not interfere.

I showed, in the paper already referred to, that when the attracting balls have been
brought as near to the equatorial plane, or plane perpendicular. to the length of the
beam, as they are to the plane of the beam, so that the line joining them makes an
angle of 45° with the beam, that is that the azimuth is 45°, the ultimate sensi-
bility is still further increased by shortening the beam to half the length that would
bring the ends opposite the attracting balls. After that the sensibility very slowly
begins to fall.

Since, with such small apparatus as the quartz fibre seemed to make practicable, it
is easy to provide attracting masses which are very large in proportion to the length
of the beam, while with the usual long beam relatively small masses must be made
use of, it is clear that much greater deflections can be produced with small than with
large apparatus. For instance, to obtain the same effect in the same time in an
instrument with a 6-foot beam that I was able to realize in my preliminary apparatus,
in which the beam was 2 inch in length, as seen from above, with attracting balls
2 inches in diameter, it would be necessary to provide and deal with a pair of balls
each 25 feet in diameter, and weighing 730 tons, instead of about 1 lb. apiece.
There is the further advantage in small apparatus that if, for any reason, the greatest
possible effect is desired, attracting balls of gold would not be entirely unattainable.

The use of attracting bails which are themselves very large compared with the
beam length makes it convenient to hang the beam in a cylindrical tube, instead of in
the long box almost universally employed hitherto. Several advantages follow from
this. In the first place, if the beam is hung centrally, neither the gravitational
attraction of the tube nor any minute difference of potential between the tube and the
beam and its accessories, produce any effect. In the second place, the attracting balls
may be carried round outside the tube through a complete circle, and yet be placed
but little further from the attracted balls than would be necessary if no intervening
tube existed. For this purpose they are conveniently supported by a common
metallic structure, symmetrical in form, about the axis of the tube, and able to rotate
about this axis also. If, following the usual arrangement, all four balls are on one
level, there are obviously two planes, one containing and one normal to the beam, in
which the centres of the attracting balls may be placed so as to produce no deflection.
At some intermediate position the deflection will be a maximum, The use of this
position has the obvious advantage that, besides the fact that this gives the greatest
effect, the accuracy with which the angle of azimuth is measured is of little conse-
quence, the geometrical measurements of real importance being the distance between
the centres of the large balls, the corresponding distance between the centres of the
sinall balls, and the angle of deflection. This is all the more important since it would
be extremely difficult to make a really accurate determination of the azimuth,

B 2

4 PROFESSOR C. V. BOYS ON THE

whereas the other three quantities can be measured, as will appear later, with the
highest degree of precision.

It will be evident that, as the size of the attracting balls is increased with the
object of increasing the deflection, their action on the opposite suspended balls increases
in a very high ratio, so that very soon a practical limit is reached, beyond which any
increase of size produces an insignificant effect. For instance, if the distance between
the centres of the attracting balls is five times the length of the beam, and they are
set at the angle (58° 20’) at which their action is a maximum, the counteracting
couple due to the far ball is § of that due to the near one, so that the resultant couple
is only & of that which would be produced if the attraction on the remote end of the
beam could be annulled. This, in effect, I practically accomplished by arranging the
two sides of the apparatus at very different levels. In this way, if only the exact
position of the balls can be determined, or rather their co-ordinates can be ascertained
with degrees of accuracy in proportion to their importance, then the arrangement is
eminently suitable for the purpose of finding the gravitation constant.

The preliminary apparatus that I made on this principle in 1889 worked so well, .
even under the unfavourable conditions met with at South Kensington, that I felt
satisfied that an instrument built on the same lines, but in which the necessary
geometrical measurements could be made, would enable me to make a more accurate
measure of the Newtonian constant than had been considered possible hitherto. I
even felt satisfied that it could be determined with an accuracy of 1 in 10,000; and
this extreme degree of precision I now feel certain may be attained by a skilled
experimentalist, if the very small modifications suggested by my recent work, which
are described at the end of this paper, are adopted, and if, above all, the experimen-
talist,, whoever he may be, has time and place at his command, and is not driven by
necessity to steal as much time for observation from his holidays and nights as his
physical strength will allow.

In the design of any apparatus, it is necessary to have some definite idea as to the
degree of accuracy which is to be aimed at, so that trouble may not be taken in
attaining an absurd degree of precision in one part, while some other part is glaringly
in defect. The aim which I made, and which my preliminary experiments showed
to be reasonable, was one of 1 in 10,000 in the result; for this purpose the large
masses would have to be determined

to 1 in 10,000;
times) ,, Las Z0s0008
some lengths ,, 1 ,, 20,000 about ;
other * Bole se TOMOKO) |.
1 ,, 10,000.

I gathered from conversation with some physicists of note, whose judgment and
experience I fully appreciated, that there was some doubt whether I was doing right
in persisting in making small apparatus where absolute determinations were the
object, for though I had clearly enough shown that so far as sensibility and constancy

an angle ,,

NEWTONIAN CONSTANT OF GRAVITATION. 5

of deflection and period were concerned an advantage could_so be obtained, it did not
at all follow that I should be able to determine the geometry of small apparatus with
sufficient accuracy. Of course, as the apparatus is made smaller, this difficulty
necessarily increases.

Tf in the apparatus upon which I have finally decided the angular deflections and
squares of the periods can be determined with greater proportionate accuracy than
the masses or lengths, or lengths squared, as the case may be, then I have gone too far,
and the apparatus is too small, but if, as I expect to satisfactorily prove in this paper,
my geometry and weighings (of course, the latter) are well in excess of the
deflections and squares of the periods in point of accuracy, then I maintain that I am
justified in having acted up to my principles, even though I did so in opposition to
the views which I heard expressed.

There is one point referred to (p. 258), but not sufficiently in detail, in my paper
already quoted which I should like to develope, more especially as Professor Poyntinc*
has noticed it, and has, I think, agreed with my conclusion. At the same time I owe
to him the discovery of a mistake which I made which led me to attribute too high an
importance to the advantage of smallness from this point of view. What follows is
the result of a discussion, which I took the opportunity of entering upon while
travelling recently with Professor Poyntinc. The point is, that the disturbances
due to convection are likely to be relatively of less importance in small than in large
apparatus, even though the period is maintained the same. As convection disturb-
ances are those which are the last and the most difficult to avoid, and as I feel sure
that they set the limit to the accuracy that is obtainable in this experiment, and that
discrepancies attributed to silk, or even to quartz fibres, and to other causes, are in
many physical investigations simply due to convection, I think that too much
attention cannot be given to this part of the subject.

Let there be two pieces of apparatus, precisely similar in all respects, but with the
linear dimensions in one 7 times those in the other, then when the pieces of
apparatus are set up, they are subject under the best conditions to infinitesimal
variations of temperature from the outside of two kinds; in the first, the surrounding
space may not be uniform in temperature, it may be hotter on one side than on the
other; in the other, the temperature, whether uniform or not, may slowly change
from day to day.

In the first case the instruments may be considered as being placed in a region
which would, but for their existence, possess a constant but very small temperature
gradient. If an instrument be placed in such a region, the temperature gradient in
the instrument will be also constant in certain cases, and will depend simply on the
conductivity for heat of the material of which it is made and of the medium in which
it is placed, but it will be independent of the linear dimensions. Further, whatever
form a pair of similar instruments may have, the gradients at corresponding points in

* ©Phil. Trans.,’ 1892, vol. 182, p. 601, and “‘The Mean Density of the Earth,” p. 107,

6 PROFESSOR C. V. BOYS ON THE

each will be independent of the linear dimensions, and so the temperature differences
of corresponding pairs of points or of the two sides will be proportional to n. In con-
sequence of this difference of temperature the included air will be warmer on one side
than on the other and will circulate. The linear velocity of circulation will depend
upon the difference of pressure between the ends of the upcast and downeast sides
divided by the resistance due to viscosity, 7.e., in such cases as we are concerned with,
where the pressures and velocities are infinitesimal, and practically all the energy is
expended in overcoming viscosity and none in imparting energy of motion to the gas.

The difference of pressure varies as the height multiplied by the difference of tem-
perature, or as 7? : 1. The effect of viscosity is proportional to the length of the
channel, and inversely as its area; it varies, therefore, as n~! : 1. The velocity of
circulation will vary as 1*/n~1, or as n? : 1. In order to ascertain what disturbing
effect this movement may have upon the suspended part of the apparatus, we may
either consider that the force depends upon the product of the area into the velocity
gradient or rate of shear of the surrounding air, 2.e., that it is proportional to n? x n°,
or 7‘, in which case, since the force is to be multiplied by an arm also n times as long
in order to obtain the couple, this becomes n* ; or without considering the velocity at
all we may consider the suspension as part of the boundary of the gas receiving its
share of the drag which is felt by the surrounding tube. The proportion must be the
same in the two cases. The force causing the drag is proportional to the difference in
temperature of the air columns multiplied by their area, or to n*, and, therefore, the
drag on the suspension varies as 7* and the couple produced as n°, as before. From
this it would appear that no gain or loss results from a diminution of size. It must,
however, be remembered, that, as apparatus is made larger, the three-fold increase in
velocity in the air-current may well bring it up to such a value that its square can no
longer be considered inappreciable. When the velocity is sufficient for the effect of
impact to be felt, then the couple will follow a law depending upon a higher power
of n than the fifth which, with increase of velocity, will approach the eighth power of
the linear dimensions.

I do not anticipate with my design, which with its double tube and protecting
screens is eminently favourable for the attainment of a uniform temperature im the
inside, that the ai velocity will ever approach that in which the square becomes
appreciable, so that in a suitable underground observing room I should not expect any
loss of definiteness to follow a moderate increase of size ; nevertheless, I should feel
doubtful as to the result if the dimensions were increased inordinately. Practically,
however, smallness has a very great advantage, owing to the length of time which
must elapse between the carrying out of any operation in which the apparatus is
handled or otherwise warmed by manipulation, and its acquiring such a steady state
again as to be fit for the observer to make the delicate observations of the movements
of the suspended system. I have even considered three days to be necessary for my
small apparatus to be ready for observation of deflection and period after making the

NEWTONIAN CONSTANT OF GRAVITATION. 7

micrometric observation. This, in fact, corresponds, but not exactly, with the second
case mentioned above, where a gradual change of temperature is going on in the
surrounding space ; those parts of the apparatus that are massive will lag behind in
temperature more than the lighter and thinner parts, and, as was pointed out by
CAVENDISH, this is especially the case in apparatus for measuring the Newtonian
constant of gravitation. The large lead balls are sure to be hotter or cooler than the
light rectangular box, and, when hotter, by warming the side of the box near to
them they set up a circulation, which, in the apparatus of CAVENDISH, produced an
appearance of attraction.

Tf it is supposed that after all has acquired a uniform temperature a slight change
occurs in the surrounding space, then the asymmetrical store of heat will, in the
case of a large apparatus, be n> times as great as in the other. As before, the
conductivity will be n times as great, so that an asymmetrical distribution of
temperature will be 7 times as great, and will Jast 1 times as long in the large as in
the small apparatus.

Before I come to describe the apparatus which forms the subject of the present
paper, I wish to explain why I have employed what may appear objectionable, viz.,
mixed units. I applied to Mr. Cuanny, at the Standards Office, for his opinion, as
to the limit of accuracy with which he could verify certain lengths and masses. The
lengths upon which the accuracy of the whole research would depend were to be of
the order of 1 inch and 6 inches. If I could, as he considered certain, have them
determined more accurately in relation to the standard 1-inch than I could in
relation to the centimetre. it would be preferable to have the main dimensions of
the apparatus set out in terms of the inch, and for construction in England there
were practical advantages in adopting the inch system. On the other hand, the
cathetometer that I used (Cambridge Scientific Instrument Co.’s), and the screw
micrometer (Exiior), both of which were required to make measures of only
secondary importance, were divided in centimetres. I have therefore had to make
use of both kinds of measures, but have retained the inch as my standard. With
respect to the masses, no difficulty could arise in obtaining the necessary accuracy,
whether pounds or grammes were used. Having gramme weights I was led to
make all the weighings in grammes, except where, owing to an insufficiency, I
had to make up with a standard 7 Ib. and 4 lb. weight belonging to the South
Kensington Museum. These were determined in grammes, and expressed as such.
Circumstances have therefore compelled me to carry out my experiments on the
inch gramme second system, and this I have done, finally converting the values
for G so found into the C.G.S. system, by multiplying by the number of cubic
centimetres in a cubic inch. (2°53995)? = 16°3861.

As the suspended masses take up slightly different positions according as they are
attracted by the large balls in one or the other direction, I was most careful in the
design to arrange that the apparatus, with the exception of these balls, should be one

8 PROFESSOR C. VY. BOYS ON THE

figure of revolution about the suspending fibre as an axis. With the hope of obtainmg
very perfectly conducting and uniform cylinders, both for the outer case and for the
central tube, I ascertained what sizes of Elmore tube would be obtainable, and thus
determined the actual and final dimensions of the apparatus. When this was too
far advanced for change to be possible, the Elmore Company informed me that they
could not supply the sizes previously settled, and so I had to be content with a piece
of thick triblet-drawn brazed copper tube for the centre, and a thick brass casting
for the surrounding case. The experiments show that no appreciable disturbance has
arisen owing to any want of perfection in the tube. The casting was turned inside and
out without being moved from the face plate, and, except in conductivity, is as perfect
as pure copper. In order to keep the gravitational symmetry round the axis as perfect
as possible, I had holes drilled in the massive base round the levelling screws, so as to
remove as much metal as they added. The important dimensions on which I finally
decided were :— .

Distance from centre to centre of large balls 77 plan, 6 inches or 4 inches.

Distance from centre to centre of small balls a plan, 1 inch, about.

Diameter of large balls, 44 inches or 24 inches.

Diameter of small balls, °2 inch and ‘25 inch.

Difference of level between upper and lower pairs, 6 inches.

With these settled the rest of the design of the apparatus shown in figs. 1-15
followed naturally enough. I think it most convenient first to describe the apparatus
in moderate detail, without going into the reasons why I decided upon each particular,
and afterwards to show how the design accomplishes all that is needed for an accurate
determination of G, the Newtonian constant of gravitation.

The Apparatus (Plate 1).

Fig. 1 is a vertical section through the centre of the apparatus, the window alone
being in elevation ; fig. 2 is a sectional plan through aa. Taking the structure first,
B is a massive brass base, turned on both sides, carried by three levelling screws with
lock nuts. C is the outer brass cylindrical casing screwed to the base B and accu-
lately turned as already mentioned. Lisa turned brass lid mechanically fitting C,
on which it can be made to turn by the action of the train of wheels WWW. ‘The
edge of the flange is divided in degrees, and can be read to 75° upon the vernier V,
fig. 3. Two tubular pillars PP are fitted into holes diametrically opposite to one
another and 6 inches or 4 inches apart, according to the size of ball that is to be
used. The heads of these pillars are shown half size in figs. 4, 5, 6, where it will
be seen that at angles of 120° there are three radial V’s forming a geometrical clamp
with either ball support. Also that on just raising the latter and giving it a rotation
of 60° it ean be let down through the tubular pillar. As seen, the large balls hang
from these geometrical clamps by wires, but into these particulars and into the details

NEWTONIAN CONSTANT OF GRAVITATION. 9

connected with the construction of the balls I shall enter later. The central tube T
is held accurately in its place by a cylindrical fitting and the hollow screw 8. This
tube, up to the window just above the lid, is made of thick copper; at the window
level it is united by the window casting to the upper tube of the same size, which is
made of brass, and this carries at its upper end the torsion head surmounted by the
bell jar J with a central stop-cock. The torsion head admits of a variation of level
of about 2 inches and of horizontal adjustment by means of three screws. The
window casting forming the centre of the tube does not touch the lid, there being a
space of about 35 of an inch between them. The equality of this all round is
an excellent test of the accuracy of this part of the construction. The window is
shown half size in figs. 8, 9, and 10. Fig. 8 is a front view, the upper part being in
section, fig. 9 is a side view, and fig. 10 a section through aa. The thick cylindrical
casting is cut through front and back so as to form two flat square faces FF 2 inches
in the side each, and over these 2 inches the casting is cut right through, forming
a square chamber in which the beam mirror hangs, and certain operations can be
carried on. Four milled heads h,, , are employed in making the transfer of the
smaller balls to and from the beam mirror, of which an enlarged view is shown in
fig. 7. This operation is performed as follows: the two heads h, are fixed to
the same cross axle, and when turned through a right angle cause two arms
with V notches at their ends to pick up the beam (fig. 7) by its upper cross
arms. In this way the beam can be raised or lowered a little or let down so
as to hang from its torsion fibre. The small balls hang by quartz fibres from the
hooks and eyes seen in fig. 7. When not on the beam these hang by their eyes from
the points projecting from the cranked ends of the pins operated by the heads h, hg,
which can be turned or pushed in or drawn out. By combining the movement of
the heads /, and h, one of the hooks and eyes can be transferred to the V at the end
of the upper arm of the beam mirror resting there by its hook. In the same way
the other one is transferred. To prevent risk of the tipping of the beam and
fracture of the torsion fibre during this operation, a weight is first hung on to the
lower central hook of the beam and removed when the double operation is complete.
The ends of the mirror have very fine V grooves ground in them, so that the quartz
fibres hanging from the hooks may lie in these grooves and so be held definitely in
position, both with respect to their distance apart and circumferentially with
respect to the mirror. A cylindrical counter-weight K, fig. 7, of known very small
moment of inertia, but of exactly the same weight-as the small balls with their hooks
and fibres, can be hung upon the central hook of the beam, when the balls are
removed to the side hooks, so that the fibre may be stretched to the same extent
and therefore have the same torsional rigidity when the periods are being taken with
or without the small pair of balls.

A series of windows are provided to fit upon and make an air-tight joint with the
plane-faces FF. Two are mere squares of plate-glass of the exact size needed. These

MDCCCXCY.—A. c

10 PROFESSOR C. V. BOYS ON THE

are used to protect the freely hanging mirror from draughts when observations are
made upon it with the cathetometer. The window, fig. 11, is made of biass, electro-
gilt, with a small aperture just large enough to allow the telescope T, figs. 18, 19,
and all parts of the scale §, figs. 18, 21, to be seen from all parts of the mirror. The
outer face of this window is covered with a plate of glass optically worked by H1temr,
held in place by soft wax. The top and bottom sectors and the faces F F are smeared
with vaseline to make an air-tight joint when the window is in position. The
window, fig. 12, is made of brass, electro-gilt ; it is similarly fixed in position behind
the mirror. A brass tube, lightly filled with cotton-wool, screws into this window on
one side. The window shown in vertical section, fig. 13 and in plan, fig. 14, is made
of brass with a flat tubular opening with rounded ends. This enters the rectangular

chamber and rests against the faces F F, which have been cut away at their lower »

part sufficiently for this purpose. The inner end of this tube is covered with a
naturally cleaved thin film of mica, which enables the two quartz fibres hanging from
the freely suspended mirror to be seen by two high-power microscopes whose noses
penetrate into the flat tube without allowing them to be blown about by draughts.
The use of mica for this purpose is essential. Mr. CunyncHame had previously
shown me that the definition of a good telescope, which is absolutely destroyed by
window glass held im front of it and impaired by any but perfect optically worked
glass, is not affected by a leaf of mica, even though it may be bent or be apparently
irregular. In the same way, the apparent position of anything seen by a microscope
is altered if a piece of ordinary cover glass is placed between the two at some distance
from the object, besides which the definition suffers. A thin leaf of mica in no way
affects the definition or the apparent position, and so the distance apart of the fibres
measured by the microscopes, as will be described later, is the true distance, which it
never would be if cover glass were employed. This distance must be measured with
the mirror freely hanging so that it may be the same as it is when the deflections, etc.,
are being observed.

Resting on the base B, fig. 1, are four india-rubber discs I R, with large central
holes, their object being to form a soft cushion for the lead balls MM to rest upon
when not suspended or to fall upon in case of accident.

In the same way I have provided a safety catch and recovering device in case the
small balls should fall down the central tube. When the mirror is suspended and
has been adjusted with its torsion fibre axial, the loss of time that would ensue if
the little balls could only be recovered by moving the central tube is so great that
some contrivance of the kind is necessary. At first I merely had some cotton-wool
at the bottom of the tube, and fished for the little balls with an india-rubber tube
let. down through one window opening. On sucking air through the end with the
mouth, the balls could generally be picked up and drawn out attached to the lower
end of the pipe. My present plan is less precarious. W is a piece of wood loosely
fitting the tube. On this there is half an inch or so of cotton-wool on which is a dise

+

NEWTONIAN CONSTANT OF GRAVITATION. 11

of wash-leather just fitting the tube. A piece of thread long enough to reach beyond
the window is fastened at one end to the piece of wood and at the other end to a
small fragment of iron wire. The thread and wire rest upon the wash-leather, and
to make sure of this a second cylinder of wood is let down to press all in place. In
case of accident to the little balls, a magnetized tuning-fork is let down the tubes by
a piece of string, and the iron wire pulled up. It is then easy, by pulling the thread,
to bring the wash-leather to the window level and so to pick out the little balls with
forceps, i

Fig. 15 is a vertical section of the mnermost of the series of screens employed to
protect the apparatus from variations of temperature. I could not at first believe that
these would be required, but each additional protection of the kind has certainly
improved the constancy of behaviour of the apparatus, and I have now no doubt as to
the necessity for their use. ¢, is a brass tube with inner and outer ledges split into
two halves, so as to fit on to the upper part of the window casting shown in chain
lines ; f, is a plain brass tube reaching nearly to the top of the central tube, and ¢; is
a third brass tube, with an internal ledge resting on ¢,. This is large enough to
clear the milled heads h,, h,. An opening is made in it large enough to allow the
telescope T and all parts of the scale S to be seen from all parts of the mirror. There
is also a smal] hole in the back, through which the tube of the window, fig. 12, can
be screwed. The screen tube ¢, is just clear of the lid and the window tube.

To protect the whole instrument from variations in temperature it is completely
surrounded by the octagon house, of which a horizontal section is shown in fig. 22.
It is double-walled, and is made in two halves of 23-inch pine boards, separated by a
space of 1 inch. This is filled with cotton-wool. The top is flat, double, and packed
with cotton-wool in the same way. The two halves slide together upon the table on
which the instrument is placed, and meet, completely enclosing it, with the exception
of a small hole in the centre of the top, through which a cord, the use of which will
be described later, can pass ; of a narrow slit in the front, through which the scale
and telescope may be seen from the mirror; and of two small apertures through
one of which the vernier V may be seen by the aid of the small telescope ¢ (figs. 18,
19), the other admitting of the driving wheel D and air tube. The connecting wire
between D and the wheelwork above lies in the narrow space between the inner and
outer boards and the two styles which separate them.

By way of illustrating the state of steadiness to which I have reduced the air in
the central tube, I may give the result of a calculation made in the case of Experi-
ment 8. In that experiment the points of rest would have been disturbed by one
unit if the air in the tube had been moving round at the rate of one turn in six weeks,
z.€., at such a rate as to blow past the balls at a rate of 1 inch in 133 days. This
follows immediately from the torsional rigidity, decrement, period, and angular value
of one division. No uncertainty so great as this appears in the mean deflections
obtained during the night.

12 PROFESSOR C. V. BOYS ON THE

The Laboratory and Accessories (Plate 2).

The apparatus is set up in the vaults under the Clarendon Laboratory at Oxford, to
fit which, in fact, it was specially designed. I cannot sufficiently express my obligation
to Professor Ciirron for giving up to me entirely for four years this very perfect
observing room, for not only was I able to make my observations under speciaily
favourable conditions, but I have had the advantage of having at hand the resources of
his splendidly equipped laboratories, and of being allowed to make any use of them
that. I desired. I feel that Professor Ciirron’s kindness in the matter is the greater
as I have no claim upon him whatever, and I can only hope that in so far as my work
carried out in his rooms may represent progress in practical physics, he may feel
justified in haying sacrificed to this end his best observing quarters.

The vault is a double one, of which the southern half is shown in plan im fig. 18.
This is separated from the northern half by two piers. The entrance is by a door at
the east end of the northern half. The two tables, A,, Aj, which Professor CLirron
had built for the purpose of the experiment in the positions shown, are of his standard
pattern. The top, made of one slab of slate, rests on a large block of freestone, and
this is supported by three walls of brick set in cement, forming an H. ‘The instrument
surrounded by the octagon house is placed upon the table A,. On the table A, is
arranged a large astronomical telescope T, by Cooke, of York, by means of which the
scale is read by reflection from the mirror. The great focal length and the perfection of
the object glass are necessary to obtain sufficient magnifying power to be able to read
with certainty to =}5 inch on the scale; the large diameter of 4 inches has the
advantage of giving a large field of view, which is almost essential in taking rapid
transits. Moreover, telescopes of the same perfection of construction and length are
not immediately obtainable of smaller diameter. This telescope is supported by two
cast-iron standards, each with its own travelling V, of my own construction, which
give absolute steadiness, being geometrically designed. In this way a considerable
range of height can be obtained in case it is wanted. The small telescope ¢, for
reading the vernier V, by which the angular position of the lid and of the large balls
M M is determined, also stands on the table A,. Besides the telescopes, a pulley-
wheel p, rests upon the table, and a driving-wheel d is clamped to it; p, is pulled
by a stretching weight, so as to keep the blind cord b passing round the other wheels
P2, Ps and fastened to the go-cart g in a state of tension. The cart is a beautifully
executed specimen of part of a “natural philosophy set” of the last century, and was
lent me by Mr.G.S. Newrs. It runs on the wooden framework, which is wedged into
the recess at the east end of the room, between a pair of rails made of angle brass. It
carries an albo-carbon lamp, so that the flame can be brought behind any division of
the great scale 8, which may be seen in the telescope T by reflection from the mirror.
The flame is turned down very low to avoid heating the room unnecessarily. I

NEWTONIAN CONSTANT OF GRAVITATION. 13

generally set it so that the flame is about 4 inch wide and $ inch high. The driving-
wheel D is made with two heavy projections not shown in the figure, to give it con-
siderable moment of inertia, and with the handle at a distance of an inch about from
the axis. Any motion given to it by hand is therefore less likely to be subject to
jerks than it would be if unweighted. A very light cord rests loosely round this
pulley, is supported by an arm of wood projecting from the other end of the table, is
supported again on the edge of the other table, and then lightly passes round the
little wheel D, figs. 1 and 2. This rests upon the table, and is kept from moving
about by a weighted foot. Two pins fastened into the wheel D engage in a hole and
slot in the cross-piece y at the bottom of the hanging wire b. Thus when D is turned
the motion is communicated to the wheel-work WWW through the light and loose
cord, the wheel D, and the cross-arm and wire. The only kind of force between the
wheel D and the wire is by the construction a couple, and this, owing to the high
ratio of gearing in the wheel-work WWW, need be only very small to give motion to
the lid L. The friction due to the great weight of the balls M M, and of the lid, is
largely reduced by hooking to the two rods R R screwed into the lid guys joined to a
cross-bar above the bell-jar, which there hangs from a single line passing round the
centre one of five wheels secured to the arch, the edge of this being exactly above the
axis of the instrument. The line then passes over a second wheel close to the west
wall of the vault, and carries two weights each exactly equal to one of the balls, and
an extra weight to partly balance the weight of the lid. When the handle of the
wheel d is turned the lid slowly and almost insensibly creeps round, and no tremor
appreciable with ordinary apparatus is communicated to the suspended mirror.
Owing to the extreme sensitiveness of the apparatus, and the very great magnifying
power, a high period tremor is set up in the mirror, about equal in amount to that
caused by ordinary traftic in St. Giles’, about a quarter of a mile away. This dies
away very rapidly, and I am unable to trace any anomaly to this cause. The corner
of the vault, in which the instrument is placed, is screened off from such small
variations in temperature as my presence and the small gas flame produce, by
two double partitions of felt, f, fi, fpf. Furthermore, the vault itself is protected
from variations in the temperature of the air, in the long underground passage by
which it is approached, by two felt curtains some distance apart.

Slits and holes, no larger than are necessary, are made in the partitions f, f, to
allow the scale and telescope T to be seen from the mirror, the vernier V to be seen
from the telescope ¢ and the light string to pass through. These partitions are
temporarily lifted out of the way when a certain beam /,, shown in position in fig. 19
but not in fig. 18, is being used. The two beams J,, /, have their upper edges planed
true, and are so supported by levelling screws that their upper edges form one level
straight edge. These are employed when the distance from the scale to the mirror is
being determined in the manner to be described under the heading “The Steel Tape
and Accessories.” The beam /, I leave in position permanently, but as 7, would be in
the way, it is only put up when required.

14 PROFESSOR C. V. BOYS ON THE

The Large Scale.

The large scale is etched on a piece of plate-glass 9 feet long, 6 inches wide, and
half an inch thick. The divisions are 50ths of an inch, and there are 4800 of them.
I made many experiments to find the most suitable kind of scale and thickness of line
to suit the mirror which I had to use. I shall return to this point when I explain
the advantages that I have gained by the use of the curious form of beam mirror. It
is sufficient te state now that the divisions are black upon a clear ground, and that
the thickness of the lines is greater than at first anyone would be likely to think
suitable, being about 35 of an inch. The method by which the scale is held rigidly
aud definitely in place but without strain, is illustrated by the isometrical projection
in fig. 23, which shows one end only. Z Z are a pair of gun-metal castings screwed
to the wood frame which is securely wedged into the recess at the east end of the
vault. wis a brass rod passing through a hole in each casting and able to be
clamped by a screw at each end. v is a casting with a cylindrical piece turned at
each end and exactly the same length between shoulders as wis. This rests at each
end upon a levelling screw, and can be clamped by pinching screws. At the other
end of the scale, 9 feet away, there is an identical construction. Two plates of glass,
the back one of which is a dummy, the front one only being divided, rest upon the
cylindrical projections of v, being definitely held in position by the V notch shown,
which of course is only at one end. The glass plates rest also against the shoulders
and against the ends of w uw and are kept in contact by the action of a bent piece of
brass at each end which lightly presses them towards one another. The glass plates
are therefore geometrically clamped, each resting on seven points, the one in excess
of six being introduced to counteract the one degree of freedom which the flexure of
so long a plate introduces. The middle of the front plate is silvered at the back up
to near the line of divisions, which is 15 inch from and parallel to the upper edge.
The levelling screws enable me to bring the upper edge and therefore the line of
divisions truly level, and this is finally tested by observation with the telescope and
swinging mirror. The rods ~ and v are then gently worked in or out as needful
until an observer with his eye at the window of the apparatus in the place of the
mirror sees the window reflected from the clear glass on the line of divisions. The
silvering of the middle of the scale is not absolutely necessary, but it enables one
more quickly to recognize the position of objects placed against the lower part of the
apparatus and so acts as a finder. When the scale is thus adjusted and has been
placed with its divisions on a level with the mirror, a division not far from the middle
will be the point at which a perpendicular dropped from the centre of the instrument
will cut the scale. The eight pinching screws are then clamped and this division is
recorded when its position has been more accurately determined by the use of a small
telescope in the place of the eye. The division 2260 was the perpendicular reading

NEWTONIAN CONSTANT OF GRAVITATION. 115}.

in all the experiments made up to the present. The dummy was provided partly to
absorb radiation from the flame and so to protect the working scale from heating,
but mainly so that I should have a glass plate ready to divide myself without loss of
time in case of accident to the working scale. This happily has not occurred.

I calibrated this scale by reference to an American steel scale divided into 50ths
of an inch, the uniformity of which I had previously tested. This steel scale became for
the purpose of the angular measurements the standard to which everything was
referred. For this purpose its absolute value is of no consequence ; all that matters
is its uniformity. A long board was supported so that its upper surface was every-
where level. Sheet lead strips were rolled until they were just thicker than the steel
scale and a double row were laid upon the level board. The glass scale was made to
rest upon these with its face downwards and the steel scale was slipped underneath,
so that the glass and steel divisions should be superposed. An erecting eyepiece was
placed on a stand above the glass and was used as a reading microscope. Every tenth
division was observed, and the 480 corrections were entered in a book, and were
also plotted out on an enlarged scale, so that an error of 3$9 inch should be repre-
sented by 39 inch. From the irregular curve drawn through all the points the
calibration error of every scale reading was afterwards ascertained. In order to
determine the circular error, the true distance in scale divisions between the mirror
and the scale was measured according to the plan to be described on p. 17. A. large
number of values of the circular correction were calculated from the expansion
for tan~' « and tabulated in terms of scale divisions. It was necessary to include

the term + = as at the ends of the scale this amounted to half a division, while at

1800 divisions on either side of the perpendicular reading it was one-tenth of a
division. The perpendicular reading 22,600 being invariable, these corrections were
plotted on the same sheet as the calibration errors, thus the two corrections could
be taken out simultaneously for every reading which was thus converted into the
reading that would have been obtained if every division subtended the same angle at
the mirror. In this way the time and labour that are ordinarily required in finding
the angles corresponding to scale divisions and in correcting for calibration are
reduced to a few seconds for each, and error is almost impossible.

The Overhead Pullies.

The overhead wheels are eight in number, and are all of the same size. Five are
over the instrument, and three close to the west wall. As already stated the edge
of the middle one, which has a round groove in it, is exactly over the centre of the
apparatus. Those on either side have flat-bottomed grooves, and they can be placed
either 6 or 4 inches apart, according as 44 or 24-inch balls are to be used. Outside
these, and the same distance apart as the screwed pillars R Rin the lid, are two round

-16 PROFESSOR C. V. BOYS ON THE

grooved wheels. The central wheel of the set near the west wall is round grooved,
and the other two, which can be set either 6 or 4 inches apart, have flat-bottomed
grooves. The purposes which these wheels serve are numerous and important. In
the first place the middle ones are employed to reduce the friction of the lid, as has
already been explained. In one of the cathetometer operations the lead balls and the
tops of their supporting pieces have to be observed in order to find the levels of their
centres when they are hanging out of sight inside the apparatus. At the same time
the lid must be raised, and held out of the way; but it cannot conveniently be
removed altogether. To accomplish this, steel bands are passed over the flat-grooved
pullies, and are each of them pinned to the ball holder at one end and hooked to an
exactly equal counter-weight at the other. The balls can then be raised, and will
remain hanging at any level at which they may be left. Two cords are hooked on to
the eyes of the pillars R R of the lid, and after passing round the outermost pullies
above, converge, and then, becoming single, pass over the central pulley next the
west wali. There, a weight exactly equal to the lid, serves to counterbalance it, so
that it will remain suspended in a horizontal position at any level. The height is se
chosen that one of the ball holders is just above the pillar on its side, while the other
is just below the lid on the other. The balls are then at the same level, and their
upper portions can be seen just above the edge of the casting C. The balls under
these conditions hang quite freely, neither touching the instrument nor being deflected
hy contact between their wires or steel bands with the lid. The steel is necessary to
give detiniteness to the positions of the lead balls during the cathetometer measures
as if they were to hang from cord the twisting and uncertain and variable stretching
would make accurate measurement impossible. The central overhead wheel alone is
employed in placing the small balls in position. I used at first, after fixing them to
their own fibres and hooks, and measuring the distances when hanging from the point
of the hooks to the tops and bottoms of the balls, to get them in through the window,
supporting the hook by a bent pin held in one hand and passing the fibre over a bent
pin held in the other. The process was one of great delicacy and difficulty, but it
answered with gold balls ‘2 mch in diameter. It was, however, next to impossible
with balls of double the weight, as the fibre would not, under such a strain, bend
round a pin, a polished steel rod, or anything that [ could think of. I had therefore
to adopt the plan with the overhead wheel, which has never failed. A pin, with the
point bent at right angles to form a horizontal hook, is tied to a piece of sewing silk,
and allowed to hang from the central pulley. A weight equal to the ball is tied to
the other end. The pin-hook is inserted in the eye of one of the hooks and eyes
from which the gold ball is suspended, and pulled up till the ball is over the tube.
It is then let down until the eye is opposite the window, when its hook is made to
rest upon the point of a large pin held in one hand ; by this means it is transferred
to the side hook where it is left hanging by its eye, and ready to be placed upon the
arm of the mirror when that is in position.

NEWTONIAN CONSTANT OF GRAVITATION. 17

The Steel Tape and its Accessories.

In order to make an accurate determination of the optical distance between the
reflecting surface of the mirror and the foot of the perpendicular upon the scale, I
have prepared a steel tape to lie upon the beams L, and L, already described, and
two sliders, one carrying an erecting eyepiece or low power microscope, and the other
a sliding brass rod.

The steel tape is one of ordinary construction, half an inch wide, and divided on
one side in millims. and on the other in inches and eighths. As the lines on this, as
is necessary with etched tapes, are thick and raised above the general surface, I
engraved fine lines on the divisions—2 inch; 7 ft. 4 in.; 14 ft. 6 in.; 21 ft. 8 in. ;
and 21 ft. 9in. After removing the lead slips which had supported the glass scale
while it was being calibrated, I laid this scale face downwards on the steel tape,
setting 0 of the glass scale upon the first engraved line at 2 inch. The reading in scale
divisions of the fine line at 7 ft. 4 in. was then observed to be 4302°5. The tape was
drawn back until 0 of the glass scale was over 7 ft. 4 in., and the reading taken for
14 ft. 6 in.; this was 4302°85. The readings for 21 ft. 8 in. and 21 ft. 9 in., taken
in the same manner, were 4302°5 and 4352°5. The temperature was 19°75 C. The
calibration correction for the division 4302 of the glass scale is 3°0. Hence the
distance in corrected scale divisions from the engraved lines at 2 inch and 21 ft. 8 in.
at 19°75 C. is 12898°85. The glass scale was calibrated in terms of the steel
standard at 14°°5 C. ; it had, therefore, relatively contracted at the higher tempera-
ture. Taking -000002 as the differential coefficient of expansion, the distance
between the engraved line becomes 12898°98 in terms of the divisions of the
standard steel scale at any temperature. The sliders have bases made of plate glass,
on each of which is an engraved cross line. One carries on two V’s the low power
microscope, and this, after the tape is placed in position, is arranged with its cross-
line over the engraved line on the 2 inch division. The microscope is then made to
slide in its V’s until a small cross engraved at the centre of the back of the freely
suspended mirror is seen through the front window sharply in focus. The microscope
is then clamped to its V’s, and the slides moved out of position and again set several
times, the relative position of the engraved lines being noted. If these are systemati-
cally on one side, the microscope is shifted in its V’s until repeated settings bring the
engraved lines together. At the other end of the tape a corresponding slider is
_ placed with its engraved cross-line over one of the engraved lines at 21 ft. 8 in. or
21 ft. 9 in., and the brass rod 1s slid forward until it just touches the scale at the foot
of the perpendicular from the mirror. The two sliders are then placed upon the
original steel scale, from which the glass scale was calibrated, and moved until the
fine lines on the end of the brass rod are seen sharply in focus. The distance between
the engraved lines on the plate-glass bases, so determined, added to the distance
between the engraved lines at 2 inch and 21 ft. 8 in. or 9 in., as the case may be, is

MDCCCXCV.—-A. D

18 PROFESSOR C. V. BOYS ON THE

the true optical distance from the reflecting surface of the mirror to the foot of the
perpendicular upon the scale. This includes the small correction for the reduction in
distance owing to the refractive power of the glass composing the mirror and front
window. The divisions on the scale are, of course, placed on the side facing the
instrument, so that no refractive correction is needed for the scale.

The Optical Compass.

In order to make the horizontal measures of the distances between the wires from
which MM hang, and the quartz fibres which carry mm, measures which have to be
made with the greatest possible accuracy, I had to design a special instrument which
was suggested to me by Professor CLIFToNn’s optical compass. That is an arrangement
by which two microscopes can be made to slide parallel to one another. After being
simultaneously focussed on the two marks whose distance asunder is required, the
frame to which they are clamped is rotated so as to bring them relatively unchanged
in position to view a scale divided by lines microscopically fine. In this way the distance
is directly transferred to a scale in terms of which it is known. In my case the chief
difficulty was to keep the whole apparatus confined within the horizontal limit of 14
inches, which was all I had liked to allow myself in the design of the apparatus itself.
Into this space I had to get (1) a rotating slide to move on the lid round the axis of
the apparatus ; (2) a focussing slide to move to and from the plane of the wires and
fibres ; (3) a pair of traversing slides, each to carry one microscope capable of being
separated by a fine adjustment and with a motion parallel to the planes of the fibres
and wires. It was essential, moreover, that the slides should be very rigid, and that
the focussing slide in its traverse should remain upon the same supports to avoid
difference in flexure in case there should be any. The geometrical principle was of
course followed, each moving piece resting on five independent small surfaces, and free
from mechanical constraint. This instrument is shown in figs. 24 to 29. To avoid
confusion, the rotating and focussing slides, with scale and micrometer screw only, are
shown in figs. 24, 25, 26, in full lines upon the lid in chain lines, and the focussing and
traversing slides in figs. 27, 28,29. The rotating slide R rests upon the lid by
means of two curved V’s, v,v,, resting in a circular V groove upon the lid, and by
the flat surface f bridging the V groove at the back. It can, therefore, rotate upon
the ld without shake, but no other motion is possible. This piece is made very stiff
by the raised rib x round the triangular part, and by the overhanging ledge which
extends over its whole width. The rotating slide also carries a micrometer screw 8
of 100 threads to the inch, with a head divided into 100 parts, and two parallelizing
screws, 8,S,. On the flat surface before 8,S8,, a glass microscopically divided scale
stands upon two little glass feet. Full particulars of this will be given after the
description of the optical compass. It merely rests against the parallelizing screws
and can be moved bodily to the right by the micrometer screw. No slide of any sort

NEWTONIAN CONSTANT OF GRAVITATION. 19

is provided, this simple construction, though perhaps less convenient, being far more
perfect than any possible kind of slide.

The focussing slide F rests upon R by means of the two V’s, v,v, which fit into
a straight V groove in R, and by means of the flat surface fi, which rests upon
a planed surface parallel to the v groove. This focussing slide is stiffened by
longitudinal ribs above and below the general level, one on one edge, and the other on
the other edge. It also carries a focussing screw 8, of 50 threads to the inch
roughly divided on the head. This merely pushes against the tail rib of R, causing the
slide F to retreat from the centre of the apparatus. It can be moved the other way by
hand, or by a gentle forward pressure on the screw head when it is being turned back-
wards. Asit is necessary to be able to give a fine focussing movement to this slide in two
separate positions, about one inch apart, a focussing block b of the required length is
pivotted on R, so that it may either remain out of use as shown in the figures, or may
be brought under the focussing screw after the focussing slide has been withdrawn.
A turn or two isall that is necessary then for the purpose of focussing in either
position.

Two traversing slides T,, T, each rest upon the focussing slide by five small
surfaces, of which four in each case are due to the long projecting V’s v, on the front
edge, of which the middle parts are scraped so as not to bear upon the longitudinal
V groove in the traversing slide.

The fifth point in each is formed by a small friction wheel w, which lies in a
recess in the traversing slide, and runs upon a planed surface on T parallel to its
V groove. ‘The reason that I introduced a wheel here is, that while a very small
vertical uncertainty is of no consequence, I was thus able to cause the whole of the
frictional resistance to traversing to lie in the V itself, which is the more necessary as
the distance between the ends of the V is necessarily less than the distance perpen-
dicular to it. This is taken advantage of further, for I have arranged that the force
that draws the two traversing slides together is produced by a long, very small helical
spring of steel lying in a hole drilled in the V’s themselves, thus being in the line of
friction and producing no tendency in either to depart from its geometrical bearings.
For the same reasou I have made the fine adjusting screw which separates them act
in the same line. This consists of a fine steel screw §,, fitting rather loosely in its
very short nut, carried by T, at one end, and with a fine polished conical point at the
other, which rests between a little V carried by T, and a vertical surface on T,. The
screw and cone piece, therefore, are free from constraint, but simply push the
traversing slides apart in the same line where the friction and the opposition of the
spring act. Thus, when the screw is turned forwards, the slides simply separate to a
minute extent, but have no tendency to lose their parallelism. Each traversing slide
is furnished with three grooves cut away so as to support a microscope lying in any
of them at each end only over small surfaces at 45° on either side, thus allowing it
two movements, one of rotation, and one fore and aft. The latter is prevented by

Dp 2

20 PROFESSOR C. V. BOYS ON THE

the use of focussing collars C, C, which slide stiffly on the microscopes and are so
adjusted that when the two microscopes are alternately placed in the same groove
and pushed up to their focussing collars they will each be in focus upon the same
object. The positions of the grooves are such that the microscopes, when in their
symmetrical positions, can be brought upon points distant from one another by 1, 4,
or 6 inches, with a stnall margin on either side of a few hundredths allowed by the
screw cone. Each microscope is furnished with a cross-wire and an eyepiece divided
scale, one or other of which can be used according to the position of the positive eye-
piece. If the microscopes are laid in grooves that do not correspond with one another,
they may also be focussed upon points 23, 34,.and 5 inches apart. If the two
traversing slides are made to exchange places, for which purpose the screw cone has
an extra nut and bearings provided, then distances of 2, 3, and 44 inches can be
measured also, should any of them be required.

Beyond stating now that the optical compass does a great deal more in the investi-
gation than merely measure horizontal distances between vertical wires or fibres, and
that the geometrical and rigid construction makes it possible to work to the full limit
which optical definition imposes, I shall not at present explain the details and the
order of the operations carried out by its aid. They will come more conveniently
under the description of the experiment itself (Operation 9, p. 40).

The Small Glass Scale.

This was made for the optical compass by Zerss. A strip of plate glass 64 x 1 x 4
inch was divided by lines microscopically fine as follows. <A line was ruled at every
inch from 0 to 6,and at 2°50 and at 3°50 inches. In addition to these, five lines,
too Of an inch apart, were ruled on either side of the divisions 1:00, 2°50,
3°00, 3°50, 5°00, and 6:00. The five on either side of the zero were by inadvertence
omitted, and the zero line was, by some obscure accident, ruled at ‘04 instead of at
its true place. This, however, was of no consequence, as the 6-inch distance was
measured by reference to the divisions ‘04 and 6°03, 6°04, or 6°05. The 4-inch
distance (not yet wanted, however), by reference to 1:00 and 5:00, and one or two
contiguous divisions, and the small distance which was to have been 1 inch about,
but which is in reality almost exactly ‘9 inch by reference to 2°55 and 3°45. When
I was in Cardiff at the meeting of the British Association, Professor VirIAMU JONES
allowed me to measure the absolute distances between these divisions and a few on
either side upon his measuring machine. This machine is one of WHITWORTH’s ten-
thousandth machines, but of more than usual stability, and with a bed long enough
to take in bars three feet long. It is provided with a set of these bars increasing by
inches from 1 to 12 inches, and with a 2-foot and a 3-foot bar. The glass scale was
attached to the upper surface of the tail headstock by being simply pressed down
edgeways upon two wafers of soft wax, and it was pressed endways against a third

NEWTONIAN CONSTANT OF GRAVITATION. 21

on the index. Safety fingers of wire were also attached to the headstock, but not in
contact with the scale, so as to prevent it from falling, if it should by accident get
displaced. One of the microscopes of the optical compass was allowed to rest in
brass V’s bolted to a solid iron casting, which rested on the same slate-topped pier
as the machine. The microscope was moved in its V’s until one end of the scale was
in focus; the tail headstock was then traversed on the bed of the machine until the
other end was opposite the microscope. The scale was then moved until this end was
in focus, but the process, being only carried out by the fingers, was difficult to
perform, as besides fixing the scale parallel to the bed as tested by the focus of the
microscope, it was necessary also to see that it remained parallel in the vertical plane,
and to adjust this by pressing out or adding to the soft wax wafers by which the
scale was lightly held. At first this quadruple adjustment, in which the setting of
one right generally put the other three out, seemed as if it would require for its
successful accomplishment some mechanical contrivance more under control than the
fingers. However, by a happy accident, I succeeded in soon getting the scale so that
IT could detect no want of parallelism either way with the fairly powerful microscope
that I was using. The actual distances were determined along a line about 95 of an
inch below the upper ends of the short divisions.

The distances which it was necessary to know with the greatest accuracy, were
those from 0 to 6, from 1 to 5, and from 24 to 34. These were determined as follows.
The loose headstock was traversed on the bed, and clamped when the division at one
end of the distance to be measured was on the cross-wire of the microscope. <A bar
was then put in, the feeling piece put in its place, and the micrometer head turned
until the feeling piece was just prevented from slipping, when the reading was taken,
The headstock was unclamped, moved, and the process repeated until two or three
readings had been taken. The bar was then removed, the loose headstock moved
until the division at the other end was on the cross-wire, and a new bar of suitable
length put in, and the micrometer turned until the feeling piece was again just held.
When the three readings had been taken in the second position, the headstock was
set back to the first position, the first bar placed in position again, and three new
readings taken ; then in the same way three more were taken in the second position.
The microscope was not touched at all during the process.

In connection with these measures, the following important details may be referred
to. I found great difficulty in setting the loose headstock by means of the high-
p-tched leading screw, especially as the wheel was almost out of reach, and in seeing
the cross-wire in the eyepiece projected upon any division of the scale so as to bisect
that division exactly. These difficulties were practically removed by placing the
microscope so that its cross-wire was slightly inclined to the vertical in which
direction the divisions are ruled, and by setting the ruled lines symmetrically between
a pair of microscopically fine specks of dust upon the cross-wire which, with the
particular inclination then, just lay on either edge of the line. The width of the line

22 PROFESSOR C. V. BOYS ON THE

itself was found to be gogo inch. In this way there was no doubt as to the setting
of the cross-wire accurately to a tenth of the thickness of the line. I was not,
however, always able, owing to the circumstances to which I have already referred, to
leave the headstock set and clamped so accurately in position, that I could detect no
want of symmetry in the microscope. Ina few cases I left it with a + or — error
of one-tenth of a division as estimated by the eye, which error I entered in the note-
book at the time, and before I knew what the reading of the Whitworth machine
would be. These were taken by Mr. Harrison, the very skilful assistant in the
Physical Laboratory at Cardiff, and he did not know what correction I had entered,
or indeed, if I had entered any correction. His reading was then entered into the
book also. In this way I hoped to avoid that spurious appearance of accuracy that
is apt to result from knowing during a process of adjustment when the last setting
has been reproduced. The temperature, of course, was frequently taken, but it only
rose half a degree during the day, and to avoid as far as possible differences in
temperature in the apparatus, the bars that were used were kept during the measure-
ments upon the bed of the machine. As an exampie, I give the figures of the middle
inch exactly as they were entered. The whole numbers represent yodgoths, and the

decimals ypponths of an inch.

Division on | PB: Reading and Reading and Reading and
av used. Bn sem ,
Scale. | correction. | correction. correction.
| 315°

21 | 9-inch Be 3149 315-0
33 8-inch 3133 313°4 313-4
24 9-inch 3144 3144 3146
32 | 8-inch { She aes lie 22028 Aes

Temperature 16° ‘9 C.

The distance between 24 and 33 on the scale found by taking the simple mean of
the above figures and subtracting, is 99983 inch, or allowing for the gradual change,
due probably to temperature variation, which seems to have been going on at this part
of the day (about 1 p.m.) more particularly, the distance is 99986.

A determination, made early in the afternoon, of the same distance by direct com-
parison with the l-inch bar, the 8-inch bar remaining in the machine, gave as the
length of the middle inch of the scale 99979. Since the bars are not guaranteed to
be nearer to the truth than zodo 9th of an inch, the agreement between the 1-inch
bar and the difference between the 8- and the 9-inch bars is better than might have
been expected. Meanwhile, I may consider for the present that the true length of
the middle inch is known with an accuracy of 1 in 10,000 at least, I have taken it .
to be equal to 99980.

NEWTONIAN CONSTANT OF GRAVITATION. 28

The interval 1:00 to 5°00 was compared with the difference between an 11-inch and
a 7-inch Whitworth standard bar. Assuming the difference to be 4 inches, this
interval was found to be 3°99970 inches. In the same manner the interval between
zero (really 0°4) and 6:00 was found by comparison with the difference between a
12-inch and 6-inch Whitworth standard bar to be 5°95996 inches.

The distance from 6°00 to each of the divisions up to. 6°05 was measured in the
Whitworth machine, and also by means of the micrometer screw of the optical
compass. The value of the screw was found in terms of the middle inch of the scale,
which had been measured most carefully upon the Whitworth machine. The screw
measures were found short by ‘145 per cent. Allowing for this the distances were
found to be :—

Corresponding totals
Between | By serew corrected.| Total from 6:00. measured in
Whitworth machine.

6-00 and 601 010145 010145 OLOLS

601 ., 6-02 “010105 020250 02019
| 6-02 ., 6:03 009815 030065 03002
6-03 ., 6:04 009915 039980 03995
| 6-04.

» 6:05 010095 050075 05012

Adding the measures of the intervals -04 to 6°00, and 6:00 to 6:04, the sum is
5°99994 or 5°99991 according to the value taken for the smaller interval. Mr. CHANEY
allowed me to measure the distance from ‘04 to 6°04, at the Standards Office, by com-
parison with the intervals 24 to 30 and 30 to 36 in the standard yard measure. The
two measures did not differ by an amount that could be detected and the result was
found to be 5°99995 at the temperature 59°7 F. There was no question, therefore,
that the 6-inch distance was known correctly to one part in 100,000.

The distances from 2°50 to 2°55 and from 3°45 to 3°50 were measured by the micro-
meter screw of the optical compass, and their sum was found to be (employing the
corrected value of the screw) ‘100125, so that the distance between the divisions 2°55
and 3°45, which are those actually used in all the measures of the horizontal distances
between the fibres, is 89967. There can be little doubt that this is correct to one part
in 10,000 and, as a small error in the working length of the beam produces an error of
about the same magnitude in the result, the value of G is not likely to be affected
seriously by uncertainty in the value of this inch. I did not attempt to determine
this inch at the Standards Office, as I found that, owing to the coarseness of the lines
on the standard bars and the imperfect optical means, so small a distance could not be
measured with a high degree of proportionate accuracy. Should the rest of the ex-
periment ever be carried out with such perfection that a possible doubt of one in 10,000
on this measure becomes of importance (and I see no reason why it should not), then
I should have to rely upon a measurement made at the International Bureau at

94 PROFESSOR CG. V. BOYS ON THE

Sevres, but up to the present I am quite content with that made upon the Whitworth
machine.

The Clock.

The clock, the position of which is indicated in fig. 18, is a Frodsham regulator,
which was lent to me by the late Professor PrrrcHarD, who took a great interest in
the experiment. The present owner has kindly allowed me to retain it until the
work is finished. The clock is placed so that it can be seen from the observing stool
at the telescope, and is illuminated when necessary by a small incandescent lamp.
It is employed to mark time upon a smoked drum, upon which also are marks made
by the action of a key at the telescope. I finally determined to employ the chrono-
graphic method after seeing Professor Cornu’s apparatus. To the lower end of the
pendulum I screwed a platinum wire flattened and filed to a rounded edge at its
end, the edge being in the plane of oscillation. This passes through a horizontal
line of mercury, standing up by its capillarity above a transverse groove in a piece of
wood. The end of the groove opens into a large well filled with mercury, so as to
retain the purity and the level. The wood on either side of the groove is cut away
to an edge, so that mercury dust carried over by the platinum cannot accumulate
and give trouble. The wood is so placed that when the pendulum is moving through
a small swing of a quarter of an inch only, the time marker actuated by the contact
ticks regularly. With the full excursion the alternate marked seconds are then
indistinguishable in length. I soldered two platinum wires to the second hand and
brought an insulated elastic platinum point over the seconds dial and under the
minute hand, so that the second hand should make contact twice a minute. I so
bent the wires that at the minute contact should be made again immediately after
the pendulum had broken contact, and retained till the end of the first second, while
at the half-minute it was made again after the thirtieth second and immediately
broken. The minutes and the half-minutes were in this way clearly and differently
marked (fig. C, p. 48), and it was thus unnecessary to count more than 15 seconds on
the charts. The time markers and the drum to carry the smoked paper were made
by the Cambridge Scientific Instrument Company, and are of their well-known
pattern. I took out the long heavy wires of the time markers, which, I understand,
are made to the order of the physiologists, and replaced them by very small and
light styles of copper foil tapering to a point. The two are arranged close together
so that the tracing points are not more than 7}, of an inch apart. The sheets of
paper, 12 X 19 inches, are most readily smoked when stretched on the drum by
pouring a little benzine into the india-rubber pipe which supplies a fishtail burner.
The very smoky gas flame which results rapidly produces a deep and uniform coat of
soot. The sheets when finished are passed through a bath of very dilute shellac varnish,
the strength being such that the smoke does not rub off, but may have numbers, &c.,
readily scratched upon it with a pointed style. The drum is driven through worm

NEWTONIAN CONSTANT OF GRAVITATION. 25

gearing by a P 1 electric motor, by Curtriss, of Leeds, the current being supplied by
a couple of E.P.S. cells. Mr. F. J. Suir has kindly allowed me to charge them
when required at his laboratory. The same cells are connected up to the two
time-marking circuits, and to a small electric lamp placed in the octagon house
to illuminate the vernier and divisions close by. This is lighted by raising, and so
making the upper contact of the key, which on depression is employed to make the
signal marks from the telescope. Owing to the self-indication of the small electro-
magnet of the time marker, a considerable spark would be formed at the mercury
break in the clock, to the destruction of the contact, if it were not for two electrolytic
cells in series, charged with battery acid and with platinum electrodes, which are
employed as a bridge across the clock break. This sets up an electromotive force of
polarization which prevents any current from-passing when the contact is kept
broken, but its resistance is so small that the high electromotive force set up at the
break is able readily to fall through them, thus practically abolishing the spark.
I found this greatly superior in every way to a non-inductive resistance. There
is one point connected with this break which I believe to be worth recording. To
ensure good contact J amalgamated the platinum point with sodium amaleam, but
immediately found that the contact lasted longer, and was more irregular than
before. However, I left the point amalgamated for a fortnight, during which it gave
more trouble by drawing the mercury out of the trough. I then unamalgamated it
by holding it over a candle flame, until I concluded that the mercury was all gone.
I did not make it very hot. Since that time the contact has never failed, which it
occasionally used to do before. I attribute the improvement to an atomic roughening
produced by the penetration of the mercury. Before the point was unamalgamated,
the pendulum, as I afterwards discovered, made a second contact with a pool of
mercury drawn out of the trough and electrically insulated, which contact mechani-
cally disturbed its period. For this reason Experiment 4 is incomplete, as its time
observations are untrustworthy. I took, however, the rigidity of the fibre from
Experiment 5, and so completed the calculation.

The Large Balls and their Supports.

One of the difficulties in the preparation of apparatus for measuring the mutual
gravitation of comparatively small bodies is met with in making the large balls.
CAVENDISH employed large balls of cast lead 1 foot in diameter. Professor PoyntTine
made the balls in his apparatus of an alloy of lead and antimony, for the sake of the
extra hardness, which would make it easier to turn them accurately to form and would
render them less liable to subsequent deformation. Though special precautions were
taken to avoid cavities, and to obtain homogeneity, the large one was found to
act differently in different directions, and he localized a cavity by observations
in this way. Afterwards he found the centre of gravity was to one side of the

MDCCUXCV.—A. EB

26 PROFESSOR C. V. BOYS ON THE

centre by an amount corresponding very nearly with that which he had deduced
from his gravitational observations. I do not feel satisfied myself that this affords any
proof of the existence ofan actual cavity, asa gradual variation of density, such as might
easily occur in an alloy, might have produced the same effect in each case. For this
reason, when a much higher degree of accuracy is being sought for, I consider that alloys
are fatal to success. Professor Cornu has without any doubt avoided any uncertainty
as to cavities or uniformity of density, or probably truth of form, by employing
mercury aspirated from one pair of spherical hollow cast-iron moulds to another pair
so placed as to reverse the attraction. By this means it seems to me everything may be
known with more than abundant accuracy, except the actual position of the centres of
the spheres, or what comes to the same thing, their actual distances from the centres
of the attracted masses. As I explained in my first paper, in my arrangement, the
difficult geometrical measurements are almost all made of secondary importance. A
small uncertainty in the levels is, as in previous arrangements, of secondary importance,
as in this sense they are at a position of maximum effect. A small uncertainty of the
angle of azimuth does not matter, for this also is at a position of maximum effect.
If there is a small eccentricity of position of the gold with respect to the lead balls,
either in the plane of the lead balls, or across that plane, again the effect is infini-
tesimal, for the departure is from a minimum of effect in the first case, and a maximum
in the second. The only measures of serious importance, on the accuracy of which
the result directly depends, is the distance 7m plan from the centre of one lead ball to
the centre of the other, and the corresponding distance in the case of the gold balls.
In the first there must not be an uncertainty of 3959 of an inch, or in the second
of zotoo Of an inch. I do not think it would be possible on Professor CorNnv’s plan
to obtain a knowledge of the positions of the centres of the mercury spheres, especially
when one is six inches above the other, with anything like this degree of accuracy,
and therefore, though with the large apparatus he used, and the proportionally
lower degree of accuracy that was sufficient, the plan is most excellent, and answers
perfectly, it would not be suitable in the present case. There is a second objection
depending upon the magnetic quality of the iron moulds. For though to ordinary
tests the beam and gold balls are not affected by magnetism, I have felt that in
measurements of forces of such supreme delicacy it is safest to avoid introducing
magnetic materials, lest any systematic disturbance should be introduced. I have
however, satisfied myself by experiment since putting up the apparatus, that a
magnetic force much greater than that due to the earth produces no effect.

The plan that I have adopted seems to me to be free from the objections that I
have urged, to be easily carried out, and to be specially adapted to the purpose of
exact measurement of the distance in plan from the centre of one ball to the centre of
the other.

Mr. Munro, who has special experience in accurate spherical work, made the cast-
iron mould shown in figs. 16 and 17. The internal hemispheres are turned out so

NEWTONIAN CONSTANT OF GRAVITATION. 27

truly that the steel disc used as a template would audibly rattle when placed in
either alone, but could not be got in at all when a single strip of cigarette paper was
inserted on one side only. The two halves can be screwed together by means of six
steel bolts as shown. A 4-inch hole is bored in the centre of one hemisphere and
one of 3-inch in the centre of the other. Into the latter an accurately fitting steel
plunger was inserted, and when pressed down to the head, was turned at the inner
end, so as to complete the sphere. A small hole is drilled on the equator, enlarged
almost immediately to a greater size. Into this a brass plug can be pushed. Before
being used, the mould is warmed, and the internal surface smoked with a gas flame.
Into the 1-inch hole the brass ball-holder e is inserted. A number of these were made
by Mr. Conesrook, of the utmost possible accuracy of the form shown, this being a
4-inch sphere, surmounted by a + X 4-inch cylinder with a shoulder of ; inch, of
such a depth that when pressed home the $-inch sphere should be tangential to the
41-inch sphere. Though these ball-holders were made to measure only, their weights
were closely alike, being 10°70 grams for each before cutting the slot and drilling the
eross hole, and 10°28 afterwards. Since the whole effect of the gravitation of these
ball-holders and of the 44-inch lead balls, all in their ultimate positions, is 7 yp in
excess of what it would be on the supposition that the whole mass is concentrated at
the centres of the lead balls, any doubt as to the amount of the correction, which
cannot be so much as one part in a hundred, leaves an uncertainty in the result of
about one part in a million, and is of no consequence. I should state here that this
correction includes the very smali pieces of brass fastened to the lower end of the
wires, which with their pins were made to occupy the same volume as the material
removed in the slot and cross hole. The brass ball-holder, before being inserted
in the smoked mould, was tinned on the spherical surface, and then wiped to remove
superfluous metal. The mould was then put together, and the steel bolts, after being
well rubbed with blacklead, screwed up as tightly as possible. The mould was then
slowly heated over a Fletcher gas burner, until a piece of lead lying upon it began to
melt. The brass plug was then inserted in the side hole, and pure skimmed lead
was gently poured in through the neck from an earthen pot until it was full. The
mould was then lifted on to a cold block of iron, but a large blow-pipe was kept
playing on the top of it, the effect of which was that the metal slowly solidified from
below upwards. The progress coald be followed by inserting a fine carbon rod, or
more evidently by watching the contraction of the metal in the neck. It was
necessary to add lead from time to time to keep the neck full, and in the case of the
41-inch ball the amount required would have filled about 3 inches of the neck had
it been so long. In this way perfectly sound castings, free from vacuous cavities,
which always form when the metal solidifies on the surface first, are easily obtained ;
but to make the metal free from pores, and to close up any such cavities should they
by any possibility exist, the moulds were placed in the hydraulic press immediately
the metal in the neck had become solid, and after removing the brass plug, the steel
E 2

28 PROFESSOR C. V. BOYS ON THE

plunger was forced down upon its shoulder. The solid metal was thus under great
pressure made to flow, and a quantity of wire was forced out of the small side hole.
Under these circumstances cavities are impossible, and since pure metal was employed,
variations of density were out of the question. It may be worth mentioning here
that of all metals in commerce, lead may be obtained of a greater degree of purity
than any other. As soon as the pressing had been completed, the mould was
removed, and allowed to cool. On being opened the lead ball was found perfect in
form, and, so far as it is possible to judge, perfect in every respect, or at any rate so
perfect that any departure from such a state cannot produce a disturbance in its
gravitative power which is comparable with the limits of accuracy with which the
attractions can be observed. I have made four balls of the 44-inch size, numbered 1,
2, 3, and 4, but I have at present used only numbers 1 and 2. Besides these I have
made four of the smaller size of 24 inches in a mould of the same construction and
numbered them numbers 6, 7, 8, and 9. To avoid risk of injury, the balls are kept
in pairs in four well-made mahogany boxes, with two velvet-lined hemispherical
hollows, in each half of each of the boxes. I have made lifters also to raise them by
their brass lugs.

I weighed these balls on August 18, 1891, on the large Oertling balance in the
South Kensington Museum. Through the kindness of Mr. Coanry I was able to
find the true value of all the weights employed, by comparison with the standards
at the Standards Office. The weights of the two lead balls made use of, with their
included brass ball-holders are, taking due account of the corrections :—

NOME eRe. eee LO oman.
Qe Nae ear Gait oie ela Om LG tears

37

The lead balls are suspended from the geometrical clamps at the tops of the lid
pillars by phosphor-bronze wires, which I drew myself down to the smallest size that
I considered safe. This was found by measure to be ‘0232 inch in diameter. As it
had to carry 16°33 lbs., the stress would be one of between 15 and 16 tons to the
square inch only, or about one-third of what I had found the wire able to carry. I
could not silver-solder the wire into the upper and lower connecting pieces, as the
strength was destroyed by annealing, and I found that soft solder allowed it slowly
to creep out even when it was soldered into a hole which it nicely fitted, and 4 inch
long. I overcame this minor difficulty by dipping the ends of the wires into copper
solution and thickening them by electro-depositing copper until they were just too
large to enter the enlarged holes prepared for them. I then drew them through holes
in a draw plate down to the right size. They were then sweated into their places,
and the end of the wire at the upper end bent over at the bottom of the slot where it.
just protruded, hammered down and again sweated ; while at the lower end a small
transverse hole was drilled on each side so as just to touch the side of the wire, and
pins driven in, and the whole sweated together. This was done on September 2nd,

NEWTONIAN CONSTANT OF GRAVITATION. 29

1892, and though the wires have carried the balls ever since, they have not broken,
stretched, or drawn out. The wire, as it left the draw plate, was free from kinks,
and was not allowed to be bent afterwards. As it is stretched so severely, I have
assumed that the centre of gravity of the suspended ball is vertically below the axis
of the wire, measured at a point nearly 2 inches below its point of support. The
actual horizontal distance between the axes of the wires at this level can be deter-
mined with the optical compass, with an accuracy of yo,000 inch; and therefore I
maintain that this, the most important of the geometrical determinations, is known
with abundant accuracy.

The Small Balls or Cylinders.

Owing to the small size of the attracted masses, I was able to make them of pure
gold, a metal which possesses all the advantages of lead, besides increased density
and freedom from oxidation or corrosion. As the inside of the central tube of copper
in which the gold balls move is polished and electro-gilt, and as they move about an
axis which coincides with the axis of this tube, any attractions or disturbances due to
difference of electrical potential after contact must be of the smallest order possible.
The method of making the gold balls is somewhat similar to that followed in the case
of the lead balls, the difference in procedure depending upon the nature of the metal
and the reduced size. Mr. CoLeBroox made for me pairs of hardened steel bars, with
ends ground out and polished to true spherical surfaces, each of them just under a
hemisphere in extent of surface. These were made in pairs for spheres of diameter,
2, °25,and 3 inch. The quantity of gold necessary for making a ball, plus a small
excess for waste, was placed in a hollow in a piece of Bath brick or of prepared char-
coal, and heated with an oxy-hydrogen jet with just enough oxygen to melt the gold
until it had run down to a clean button. When this was allowed to cool by itself,
the surface was drawn in by the contracting centre, and a cavity and dimple were
formed. When, however, the flame was gradually withdrawn, or reduced in size, so
that the metal solidified from below upwards, a solid button with a perfectly smooth
surface was easily obtainable. The button so formed was placed in one of the hemi-
spherical moulds, held in a vice, and covered with the other, which was then given a
smart blow with a hammer. The gold was thus compressed to an almost spherical
form with an equatorial rib. On being turned over through a right angle, the rib
was compressed into the gold, leaving a projecting head on each side, and these were
finally compressed into the gold after a further twist through a right angle. The
gold was then annealed, and beaten in the moulds with gradually reduced blows,
being turned between each blow. When the ball was made practically perfect, it was
weighed, and brought down by a very fine file to within 1 milligram. of the ultimate
weight. It was then annealed and gently beaten again with rapid light blows, being
turned between each, until a highly polished perfect sphere was the result. Rubbing
with wash-leather and a little rouge brought it to the required weight, when it was

30 PROFESSOR C. V. BOYS ON THE

finally gently beaten in the mould. These balls were made in pairs, identical in
weight, so far as I could determine with the balance. The smallest weighed
1:'2983 grams each. The point of a fine needle, held in a special tool in which the
ball was placed, was forced a short way into the gold, and removed, after which the
ball was replaced in the dies and compressed again, which process forced down the
very small elevation round the little hole, and left a much smaller hole than could be
made direct. In order to fasten these balls to their respective fibres, a pin was
dipped in shellac varnish and rapidly passed across the end of the fibre. After one
or two trials, a semi-microscopie bead of varnish, formed by capillarity, was left just
above the end of the fibre. This was then placed in the little hole in the ball, and
the latter was placed in a conical hole in a brass blank, which had been warmed in
the flame of a spirit lamp. Under the influence of the warmth the little bead slid
down, and instantly flashed into vapour as it touched the gold ball. If necessary, a
small quantity more varnish could be applied upon the point of a very fine needle.
The ball thus attached formed the lower part of a perfect Borda pendulum, there
being nothing visible outside the spherical surface. So perfect is this mode of support
that when a gold ball is hung up by its fibre, and set in torsional vibration, the image
ot the window seen reflected on the spherical surface was not seen to move or quiver
when examined by a strong lens. The upper end of the fibre was fastened with
shellac to the tail of the hook and eye, seen in fig. 7, the length of course being
adjusted so that the gold and lead ball would hang at the same level.

There is no question that this is the most perfect method of holding the gold balls,
but when I came to the larger size of -25 inch, weighing 2°6501 grams, the risk
of fracture due to an accidental roll of the ball was increased, and in one case, after
a week spent in making all the preliminary measurements, one of the balls drew off,
owing to imperfectly dried varnish, and it and its companion and the mirror were all
precipitated down the central tube and the torsion fibre was lost. To reduce the
risk, I therefore arranged another process which is practically as good and is much
safer. A piece of No. 40 copper wire, 3 inch long, weighing *00084 gram, was
inserted into the hole, and soldered in its place with a scarcely visible amount of
solder, the wire and solder weighing exactly 001 eram. A calculation of the total
attraction of ball and wire, on the supposition that the wire as well as the ball acts
upon the centre of the lead ball as if it were concentrated at the centre of the gold
ball, shows the error to be only ssgae of the whole, it is therefore of no consequence.
To the side of this wire the quartz fibre was easily fastened with shellac varnish, the
amount of shellac used being 0001 gram, or even less. I have not made any balls
of the largest size, but in the one experiment in which larger masses were employed,
have made instead cylinders of gold, 4 inch in diameter and ‘2587 inch long. These
were prepared in a similar manner. Mr. CoLeBRooK made for me a hardened steel
cylindrical mould, the inside being lapped out to size and polished. The end was
made plane and truly perpendicular to the cylindrical hollow. A polished steel plane

NEWTONIAN CONSTANT OF GRAVITATION. 31

was kept pressed against this face by screw pressure, and a steel plunger, accurately
fitting the mould, with a polished plane perpendicular end completed the tool. The
required quantity of gold, plus a small quantity for excess, was melted into a button
as before, and placed into the mould. The plunger was beaten with a heavy hammer,
under the blows of which the solid gold flowed as freely as the lead in the other case,
penetrating the fissure between the cylinder and the bottom slab. A second plunger,
made of brass, with au exactly central, fine needle point, was then pressed with light
blows upon the gold to make a central hole, into which to solder a supporting wire,
as in the case of the gold balls. Mr. Epser, of the Royal College of Science, was
kind enough to calculate for me, by means of spherical harmonics, the very small
difference between the attraction of the cylinder upon a point at the centre of the
lead ball, and that which would be exerted if the whole of the mass of the cylinder
were concentrated at its centre. The correction is for a greater variation of distance
and of inclination from the equatorial plane than can have been met with —:00030
of the whole, and this correction is accordingly applied in the one experiment (9) in
which the cylinders were employed.

I have not at present referred to the attractions between the suspending wires and
the gold balls, and between the suspending quartz fibres and the lead balls. The
attractions of the fibres and wires for one another are, of course, infinitesimal to the
second degree. Calculation shows that in experiments 4 to 8 and 10 to 12, the
attraction of the lead balls for the fibres is to their attraction for the gold balls as
lis to 204,500, and in the same direction, while the attraction of the gold balls
for the wires is to their attraction for the lead balls as 1 is to 115,000, and in the
opposite direction. The reversal of the direction is surprising, but it is due to the
fact that the most effective part of the fibres is absent in the case of the wires, owing
to the large diameter of the lead balls, and, therefore, the action of the long wire on
the upper gold ball, which is on the other side, is the preponderating influence. The
difference of these two corrections is sgsyo9 of the main effect, and in the opposite
direction. I should add, that though the absolute masses of the small balls are known
with an accuracy of 1 in 10,000, this is in no way necessary. So long as they are
practically alike, it does not matter whether their mass is known or not, as it is
ultimately eliminated. I have, however, introduced into the numerical work the
actual masses in order to obtain the constants of the fibres and of the mirror, and the
viscosity of the air absolutely.

The Beam Mirror and its Attachments.

One of the most important parts of the whole apparatus, and certainly the most
difficult to arrive at in perfection, is the combination of beam and mirror which shall
support the gold balls definitely in position, and shall, in its capacity as mirror, make
it possible to determine their position with the greatest possible accuracy. In my

32 PROFESSOR C. V. BOYS ON THE

paper on the radio-micrometer,* I dwelt on the importance of the proper propor-
tioning of the mirror to the rest of the suspended body. Then I only considered its
moment of inertia and weight. In the present case these remain important, and
there is besides the resistance to motion due to the viscosity of the air, which unfor-
tunately is of the most serious moment. If the usual round mirror is employed, the
definition, as is well known, is directly proportional to its diameter—that is, if its
figure is perfect. The advantage of a large mirror is somewhat counterbalanced by
its weight, which tends to break the fibre, so that lighter balls or a coarser fibre are
necessary ; by its moment of inertia, which increases the already prolonged period ;
and by the resistance which it meets with in moving through a viscous atmosphere.
As it is important to keep the mirror or mirror and balls swinging as long as possible,
in order to determine their periods accurately, a high decrement is most objectionable.
By making the mirror in the form of a long bar, I have succeeded in partly reconciling
the incompatible conditions, for not only may the weight and moment of inertia be
reduced to less than half of that which would be due to a disc of the same diameter,
but the definition is decidedly better, as I have proved by experiment, and as is
shown by optical theory. I should have said that the definition in a direction
parallel to the length of the har is better, that at right angles being obviously not so
good. For the purpose of reading the divisions of a horizontal scale, vertical definition
is of consequence only in so far as it is sufficient for the purpose of reading the figures
attached. These I had made large with this object. I have already stated that the
scale is formed by black lines on a luminous ground. By this means I am able to
obtain a degree of reading power which might seem beyond that which a mirror of the
size used ought to give. The mirror will form a spurious image of a luminous point
of an oblong form, the long dimensions being vertical, and bearing the same relation
to the short as the length of the mirror, which is horizontal, bears to its breadth,
which is vertical. If the mirror could be made indefinitely long, the image would shrink
to a vertical line, and horizontal definition would be perfect. Owing to the limited
length of the mirror (‘9 inch, about) the width of the spurious image subtends an
angle of about 5”, and this is the limiting separating power in the horizontal direction.
Now, if the scale were made by very fine white or luminous lines upon a dark ground,
each line would be seen as a band with shaded edges 5” wide; but, as the angular
distance which I have been able to employ from one division to the next is only 14”,
the lines would have appeared half as broad as the spaces. If the lines on the real
scale were of sensible thickness, then the proportion of apparent line to space would
have been higher. If, on the other hand, the ground is luminous, the lines are dark
and are made rather coarse ; the effect of the spreading of the light is to pare off the
dark edges, and leave the appearance of a finer line, which, though it is not sharp, is
symmetrical, and, as a recurring phenomenon, allows of definite observation to one-
tenth of a division, ¢.c., in the actual case to 1:4”. This corresponds to a movement
* © Phil. Trans.,’ Jan., 1889.

NEWTONIAN CONSTANT. OF GRAVITATION. 33

of the mirror of °7”, and of the balls of zsglpqq inch. To this degree of accuracy
there is no difficulty in observing; in fact, I might have made the divisions smaller,
and still have been able to read to tenths. Of course this perfection is only possible
with a very perfect mirror, and for this I applied to Mr. Hincer, who took special
pains in preparing several as thin as he dare. Of these, one only, when tested while
still round with the large astronomical telescope upon an artificial star, was perfect
in its definition, and formed the spurious disc and diffraction rings equally in all
directions. ‘This mirror was the one employed in all the experiments up to date. A
second one was nearly as good. One made of quartz showed the diffraction rings
strongly in three directions only, 120° apart. In making the test I was careful to
notice in which direction the two images, one due to the front surface and the other
to the silvered back surface, were separated, owing to the inevitable want of perfect
parallelism between the faces. I then cut them in such a direction that the displace-
ment should be vertical, so as to avoid the confusion caused by the superposition of
the dim reflection of the scale upon the image under observation. The two good
mirrors I slit with a fine steel disc and diamond dust, so as to leave a central bar
4 inch wide. This gives abundant light, and defines well enough to enable the
figures tobe read. I found by the use of screens that a bar $ inch wide, though it gave
enough light, so destroyed the vertical definition that the figures could not be read,
and the long and short lines were not so clearly distinguished. I then, with a very
sharp-edged brass dise and washed emery, ground in the thickness of each mirror at
each end a vertical V, seen in the plan (fig. 7). The bottom was so fine and sharp
that a quartz fibre 7,455 inch in diameter would rest definitely in its place. The
mirror was cemented with three spots of shellac varnish to the gilt copper support O.
This was so formed that the balls could hang by their eye-hooks from the notches at the
end of the arms, with the fibres resting in the vertical V grooves of the mirror. The
beam mirror was carried by a quartz fibre, fastened to the point of O by shellac in all
experiments up to No. 3, and soldered to an intermediate tag in the later ones. The
details of the soldering process are given in the ‘ Phil. Mag.’ for May, 1894. From the
lower central hook of the beam mirror the silver counterweight K may be suspended
when the gold balls are removed. This was turned by Mr. CoLEBrook out of pure
silver, which I had prepared by casting and hammering. It is truly cylindrical, and,
with the triangular wire hook to which it is soldered, weighs exactly the same as the
corresponding pair of balls with their fibres and hooks. Its diameter was measured
in several places with a screw micrometer. The weight of the cylinder, of the little
hook, and of the solder used were separately determined, and the very small radius of
gyration of the hook esiimated from its dimensions and form. The period of the mirror
was observed (a) with the balls on, (b) with the counterweight on, and (c) alone. From
(a) and (b) the unknown moment of inertia of the beam could be determined, and
from a, b, and c the effect of the stretching upon the rigidity of the fibre could be
ascertained. The suppositions made are rather numerous, and are best discussed here,

MDCCCXCV. —A, F

34 PROFESSOR C. V. BOYS ON THE

In the first place it is supposed that the mirror does not change its axis when
swung alone or with the balls or counterweight suspended, for, if it does, its unknown
moment of inertia will not be a constant, as assumed. Secondly it is supposed that
when the gold balls are suspended from the beam mirror, they are rigidly connected
with it, or that the mobility of suspension or torsion is so minute as to be equivalent
to a rigid suspension. Thirdly, that the counterweight, when suspended from the
beam mirror, is rigidly connected with it, and that it rotates about its geometrical
axis. Jt is obvious that however carefully the parts have been made, the suppositions
cannot be rigidly true. It is necessary, therefore, to find what order of error is intro-
duced by any possible or observed want of perfection.

It is evident that the axis of rotation of the mirror must always pass through the
point at which the quartz fibre leaves it, and that, when it is unloaded, its axis passes
through its centre of gravity. As the construction is intended to be symmetrical
with respect to this axis, and is so, as far as observation enables one to judge, and as
such an axis is an axis of maximum or minimum moment of inertia, the uncertainty
in the moment of inertia, due to a small angular displacement, is proportional to the
square of the angle, and is altogether beyond the region of experimental certainty.
When, however, the balls or counterweight are placed in position, if the construction
is not truly symmetrical, the beam mirror will now rotate about an axis which does
not pass through its centre of gravity. In an experiment made for the purpose, this
displacement, when the larger balls were suspended, was found to be ‘0068 inch, an
amount considerably larger than I had expected. In this case the moment of
inertia, added to the whole combination on this account, is, weight of beam
X 0063? = 844 X 0063 = 0000335 inch® gram. The corresponding increase, when
the counterweight was added, was 844 X 0012? = :0000012 mch* gram. Applying
these small differences to the observations of Experiment 12, if I may so far antici-
pate, the torsional rigidity of the suspending fibre is changed from ‘0012577 to
001257736, so that if this had been overlooked, the error introduced would have
been 1 in 35,000. It was not, as a matter of fact, observed until after the conclusion
of Experiment 12, and then I placed one of the microscopes so as to see the edge of
the lower hook of the beam, and measured the unexpectedly large deviations in the
plane of the mirror; those perpendicular to the plane I had always known to be
practically inappreciable by the very small change in the position of the observing
telescope needed to again see the scale reflected centrally. This insensible correction
which tends to make G seem greater, can only be applied to Experiments 10, 11, and
12, as the fibre met with an accident after Experiment 9, and was re-fastened to the
beam, As it cannot be applied to the others, and is far smaller than the uncertainty
of the experiment, it is not taken account of in the table.

The rigid attachment of the gold balls to the mirror might seem to be purely
imaginary, seeing that they hang from fibres 5 and 11 inches long, and so can lag
behind when the mirror is subject to angular acceleration, that they must fly out

NEWTONIAN CONSTANT OF GRAVITATION. 35

owing to their centrifugal force when this acceleration has given rise to an angular
velocity, and must be pulled by the gravitation of the lead balls so as to be further
apart than supposed. Moreover, since each ball can rotate separately on its own fibre
with a period of its own of as much as 6°720 and 9°055 seconds in Experiments 4 to 8
and 10 to 12, they must, in their rotation about their own axes, lag behind the
rotation of the mirror when it is being accelerated. The magnitude of these several
errors is infinitesimal, or greatly below the limiting accuracy aimed at, and, in all
cases, may be calculated and allowed for if necessary. Thus, in Experiment 8, the
lower ball in the extreme case of an amplitude of 10,000 divisions, or 100,000 units
(I make +5 division the unit, to avoid decimals), is at the middle of the swing thrown
out by centrifugal force sso inch, and the upper one about half as much. The
linear acceleration on the balls, due to the action of the torsion fibre, is the same as
that due to a pendulum nearly six miles long, or, more exactly, 364,335 inches, so
that the actual acceleration produced by the fibre in the case of the lower ball is
about 1 in 33,000 more than is supposed, and, on. the upper ball, about 1 in 70,000.
The amount by which the lower ball is pulled outwards by the gravitation of the lead
ball next to it, even when that is in its neutral position, where its actual attraction is
a maximum, is less than a ten-millionth of an inch. The rotational mobility of the
gold balls, however, in Experiments 4 to 8 and 10 to 12, was more than I had
intended, and, as I felt that it was important to know precisely what effect this
would have upon the result, I referred the problem to Professor GREENHILL, who very
kindly explained to me exactly how to evaluate it, and, with Professor Mincuin, went
through the great labour of obtaining and solving the resulting cubic equation. The
rigidity of the fibre, in this the worst case, should “be diminished by less than
1 im 7850. An increase in the thickness of the two suspending fibres of a few
ten-thousandths of an inch, such as I made use of in Experiment 9, would reduce
this to the order of 1 in 100,000, or even less, and the complex calculation of this
correction would no longer be necessary.

Finally, it is assumed that the counterweight, when it has replaced the gold ball,
is also rigidly connected with the mirror and acts axially. With respect to the
rigidity of the attachment, it is unnecessary to do more than state that the friction on
the suspending hook must be many thousand times greater than the greatest couple
ever developed by the torsion fibre, and that, with regard to its axiality, the same
remarks that were made with respect to the beam mirror apply with even greater
force. There is only one point about which, in consequence of the microscopic
examination after Experiment 12, I am not altogether satisfied. It seemed as if the
hook suspension was not quite pendularly free so that the counterweight could rest
hanging from the beam mirror at a very small angle to its natural position of verti-
cality. This was not observable on the counterweight itself, but only by microscopic
examination of the beam. Though the beam hook rarely varied in position by so
much as ‘001 inch, I was able, by using great care in trying to make it rest in

F 2

36 PROFESSOR C. V. BOYS ON THE

extreme positions, to introduce an uncertainty of position nearly four times as great.
I cannot think that any serious discrepancy can have resulted from this, as the
uncertainty of moment of inertia would be only a very small fraction of that found in
the case of the beam mirror when the balls were suspended. This fault, such as it is,
however, I intend to remove in my next experiments, from which I hope, also, to
almost entirely exclude the small eccentricities already referred to. For this purpose
I may either file the hook rather wider, or, as I think preferable, hang the counter-
weight by a loop of silk, which will in no way constrain its hanging, but which will
be rigid with respect to torsion, I wish, also, to make use of a slightly-silvered
torsion fibre, so as to reduce the effect of electrical disturbances if they should be set
up by the movements of the air. The square of the corrected period, with the
counterweight on, diftered more in Experiments 5 and 8 than it should have done,
being 1702°35 in Experiment 5, and 1698°73 in Experiment 8. In order to see to
what extent this discrepancy may have affected the result, I have calculated the
rigidity of the torsion fibre in these two cases with the observations of this quantity
reversed, that 1s, 1698°73 instead of 1702°35, and vice versd. The effect upon the
result is 1 part in 10,600, so that if all the error is in one observation only, the other
one is on this account alone less than yg$o9 in error. As any sticking of the counter-
weight would tend to increase the moment of inertia, and hence the period, I am
inclined to look with greater favour on the smaller observation, but the difference, in
any case, is considerably less than the actual differences found in the final results.

In connection with the beam mirror, it is convenient here to describe the means
provided for keeping it under control from the telescope without entering the shielded
corner of the vault.

Below the apparatus, figs. 1 and 2, may be seen a tube terminating in a bent glass
pipe which enters the hollow screw s. This is joined to a narrow piece of composition
piping, which is carried across the interval between the two tables by the wooden bar
which serves to protect the light driving cord, and, at the eyepiece of the telescope T,
terminates in a mouthpiece. Where observations of deflection and period are being
made, air may be drawn through the tube causing a very gentle indraught through
the tube of the window, fig. 12. This acting on one end of the mirror produces upon
it a couple which may be employed to bring it to rest or to get up a swing of large
amplitude. The extreme precision and delicacy of this process is best explained by
considering an electrical analogue. The window tube, fig. 12, acts as a moderate
resistance, the open space between the glass tube and the large hole in the screw as
a short circuit or very low resistance, and the long tube across the room as a high
resistance again. The electromotive force is the suction of the mouth. Owing to
the high resistance of the long tube, but a feeble effect is felt at the glass end, and
this is practically entirely satisfied by the low resistance leak. The available electro-
motive force acting upon the resistance of the window tube is therefore very small,
and in consequence the current acting on the needle is similarly minute. So delicate

NEWTONIAN CONSTANT OF GRAVITATION. 37

is this that it is quite easy by pinching the tube properly with the fingers to bring
the movements of the mirror, when the counterweight but not the balls are suspended,
down to one unit, corresponding to 7539900 Inch movement of the gold balls if they

were in their place.
Conclusion of Part I.

The apparatus and optical compass were made by the Cambridge Scientific
Instrument Company. I cannot lose this opportunity of expressing my great
indebtedness to Mr. Pyx, who, in the absence of Mr. Darwin through illness,
entered into every detail with the greatest care and faithfully carried out all the
directions as to modes of construction upon which, after consultation with him, I
finally decided.

As already mentioned, Mr. CoteBrook constructed the special tools and the very
numerous extraneous apparatus. He also made all the special windows. Mr. Munro
made the tools for compressing the lead balls, and being his work they are of course
accurate in the highest degree. Mr. Stantey undertook the large scale, but though
the execution of the etching is excellent, the accuracy is not good. This, however,
matters little, for the errors are eliminated by the calibration.

The actual work of making the gold balls, the lead balls, the finish of the beam
mitror, the quartz fibre work, the gilding and polishing of the inside of the central
tube, and a great deal of the general fittings I did myself, either alone or with the
help of Mr. CoapmAN and Mr. Cotesrook of the Physical Laboratory.

The apparatus, which belongs to the Science Collection of the South Kensington
Museum, will, I hope, on the completion of the experiments, be set up in a special
place in the Museum so that it may be seen in action by anyone interested. I intend
to leave also permanently in the Museum a series of photographs of the apparatus as
it appears 77 situ when each one of the operations is being carried out. Besides this,
the note books and all the calculations will be left there permanently so that
reference may be made to them in case any point is insutliciently explained.

Parr II.
The Mode of Procedure.

The actual method of carrying out the experiment, though in the main obvious to any
one who has read the first part of this paper, is nevertheless in some particulars by no
means evident. As, moreover, a careful explanation of the several operations and
the purposes which they serve will make the mere numerical details of the actual
experiments, which form the third part of the paper, more intelligible, I shall describe
them in order, under distinguishing numbers.

The operations, as described, are fourteen in number, but they are of very different

38 PROFESSOR C. V. BOYS ON THE

importance, and the time required for carrying them out differs also very much.
Some few need only to be performed on the first putting together of the apparatus.

Operation 1.

After placing the instrument in the selected spot, with its centre tube vertically
below the edge of the central overhead pulley, it is to be levelled accurately by
placing a spirit level on the lid, and adjusting the Jevelling screws, until the bubble
occupies the same position in the tube when the lid, carrying with it the level,
is slowly made to revolve. Fix also the scale and large telescope in position.
Operation 2.

Hang up the lead balls by their wires and upper supporting pieces, pinning the latter
to the thickened lower ends of the two steel bands. These are carried over the
flat-rimmed pullies, and carry at their other ends counter-weights, so that the balls will
remain suspended at any level. If the central tube is not in position the three readings,
a, b, and ¢, fig. A, are made with the cathetometer, and thus the true distance from
a to the centre of the lead ball, when the wire is stretched by the weight of the latter,
is known. If, after one experiment, it is desired to make this measure, but not to
move the central tube, since it is impossible to remove the lead balls completely, they

Fig. A.

must be left suspended at such a height that the 6 of each is visible, This can be
accomplished without taking away the lid and lid pillars, since they can be left
suspended by their counterweight at such a height that the a cf the (ultimately)
upper ball is below the lid, while the @ of the (ultimately) lower ball is above its lid
pillar. Since all hang freely without touching one another, the a’s and 6’s can
be determined, and on adding the known radius of the lead balls, the distances ah
are known.

Operation 3.

Hang the gold balls by their eye hooks upon a pin driven into any temporary stand.
Measure with the cathetometer the three positions d, ce, and f of each, fig. B. From

NEWTONIAN CONSTANT OF GRAVITATION. 39

these the distances dg can be determined when the fibres are stretched by the weight
of the balls. Also find their individual torsion periods by the method of coincidences,

Fig, B.

poy

|

Beene,

oS
watching them with the cathetometer telescope, and listening to the clock. This latter
is needed for the purpose of calculating the very small correction (p. 35) which should
be evanescent. The cathetometer measures can be made with an accuracy of two or

three-hundredths of a millim., and this, as will appear when the figures are
examined, is more than abundantly accurate.

Operation 4.

Put the lead balls in the apparatus, fix the central tube in place, with its front
window facing the scale, let the gold balls down the central tube, and hang them on
the side hooks, place the lid in position ; having marked one side of the lead balls in
some distinguishing manner (a very small spot of shellac varnish is what I used),
suspend them with these marks pointing in some definite direction, e.g., inwards ;
let down the mirror by its torsion fibre, and adjust the torsion head so that it hangs
approximately centrally, and at a convenient height.

Operation 5.

Find, as already described, the division at which a perpendicular from the axis of
the tube falls upon the scale. Twist round the central tube, if necessary, until the
window reflects a light placed behind this division into the large telescope.

Operation 6.

Find the optical distance in terms of the corrected scale division from the silvered
surface of the mirror to the foot of the perpendicular upon the scale, and thus find
the angular measure corresponding to any observed deflection.

The details of this process are sufficiently described under the heading The Steel
Tape and its Accessories (p. 17).

Operation 7.

Make cathetometer readings of a, a and d, d. Subtract from these the corre-

40 PROFESSOR C. V. BOYS ON THE

sponding quantities found in operations 2 and 3, ah and dg, and thus find the levels
of the centres of the gold and of the lead balls. If the gold balls are on the whole
high or low, lower or raise the torsion rod the necessary amount and re-measure
a, a and d, d,

Operation 8.

If tbe mirror rests so that the foot of the perpendicular is about the position of
rest as seen by reflection in the telescope, when the lead balls are, so far as it is
possible to judge, in the same plane as the gold balls, all is ready for the next
operation ; otherwise it will be necessary to turn the support of the torsion rod, which
will not raise or lower it, until observation at the telescope shows that this is the case.
The mirror will then be symmetrically placed with respect to the window.

Operation 9.

This is a long operation carried out with the optical compass, the object being to
find the horizontal distances between the axes of the wires and between the axes of
the fibres, to centre the torsion fibre with respect to the axis of the instrument, and
to find the corresponding readings of the vernier of the lid and of the glass scale
seen by reflection in the telescope when the plane of the wires and fibres is
identical. Owing to the great length of this operation, the description of it is
divided into sections.

Section a.—Remove the two pillars RR from the lid, and the first spur-wheel of
the driving train W, which is made to simply lift off. Put the optical compass in its
place on the lid so that the line of traverse is apparently parallel to the line joining
the wires.

Focus the positive eye-piece of each microscope upon its cross-wire or scale, and
then shift the focussing collars ¢ of each, so that when the microscopes change
places in the same groove and are pressed up to their collars, they are each in focus
on the same object.

Section b.—Using one microscope in any one groove of one of the traversing slides
T, or T,, focus alternately on the edges of the two wires, using the focussing screw
S; to move both the same way, and turning the base of the optical compass upon the
lid to move them opposite ways. When both are found in exact focus the line of
traverse is parallel to the plane joining the axes of the wires.

Section c.—Measure this distance. To do this the two traversing slides are placed
together, and the fine steel spring passed through the hole in their V’s. The spring
is then stretched and prevented from contracting by a pin passed through it at one
end. The two slides T,, T, then are pulled together by the spring, but are separated
more or less by the adjusting screw cone S,. The two microscopes are laid in the
outer grooves (or the middle pair in case a 4-inch distance has to be measured), and
the slides moved until each is directed upon one side of the corresponding wire. The

NEWTONIAN CONSTANT OF GRAVITATION. 44

final exact adjustments are easy of execution, for the focussing screw §, supplies a
slow fore and aft motion, while the corresponding slow lateral movement is given by
the screw cone S, In order to allow one only of the traversing slides to move, the
fingers of one hand are made to rest upon the slide which is to be kept still, and thus
its friction on the base increased, the other one then only moves. When both
microscopes are focussed upon (say) the right or apparent left sides of the wires, and
their eross-wires are directed upon them also, the focussing slide is withdrawn about an
inch, and the focussing block ) put into its place. The slide is then pushed forward
until the focussing screw rests against the focussing block. The small glass scale is
then placed so as to rest against the two parallelizing screws S, §,, and against the
micrometer screw S,, and §,S, are moved until the scale is in focus in both microscopes
at the same time. S, is then turned until the intended zero of the scale 04 is on
the cross-wire of the left microscope and its head is read : it is then turned forward a
fraction of a turn until a division at the other end of the scale 6°03 or 6:04 is on the
cross-wire at that end. The amount of movement indicated by the head of the screw
S,, added to the tabulated distance from ‘04 to 6°03 or 6:04, is the distance from the
right side of one wire to the right side of the other. If the eye-piece micrometer is
used instead of the cross-wire, then ‘04 is brought in the central division of the left-
hand microscope, and the micrometer readings of the divisions 6:03 and 6:04, or 6°04
and 6°05, are taken in the right microscope. Knowing the tabulated length of either
of these divisions and the number of eye-piece divisions corresponding to it, the
amount to be added to the tabulated distance between ‘04 and the lower of the two
observed, is readily found. The distance between the left sides of the wires is found
in the same way, and the mean of the two is taken for the distance between their axes.
The thicknesses of the wires are also found by subtracting the readings of the apparent
right from the readings of the apparent left sides, remembering that there are two
whole turns of the screw. After each operation the focussing block is moved round,
and the focussing slide moved up so as to bring the wires into view. If they are not
exactly on the cross-wire as before, the measure is rejected and a new one taken, but
this is rarely the case.

The example taken from Experiment 8 does not show the confirmatory observations
made with the eye-piece micrometer, for at that time the micrometer scales had not
been made. As [I still rely upon the screw measure of the fractions and only take
the eye-piece micrometer readings to satisfy myself that the screw observations have
been correctly worked, this example will serve as well as a later one.

MDCCCXCV.—A. G

42 PROFESSOR C. V. BOYS ON THE

Measures of Wires with Optical Compass.

| |
Side. | Wire. Scale. | Head. | Correction.
| |
Atppanentorich ties Rach tess oy eae 6:03 641
- guy! | ett ceaaewical ae 04 (+4) 029
| | + 000025
eS left Right (605+2). .)| 603 | 955
90 ff somo Pulte eg lg 6 20 04 (+4) 357
|
Thickness.
Apparent left side. | Apparent right side. 7
| Left. Right.
6:03955 | 603641 "02357 02955
05357 | 05029 “00029 00641
598598 | 598612 02828) \)./)) 02374
5'98612
Mean . . 5°98605 centre to centre. |
+ :000025 correction. |
5°986075 corrected value. |

The (+ 4) after ‘04 indicates that when the right microscope was exactly on the
division 6°03, the left one was, by eye estimation, at 044, or yo of a division above
04. Since also the screw-head reading has passed 1000, or a complete turn, and has
risen in the two cases to 029 and 357, °05 is the quantity that must be written in
the subtraction below to find the distances from side to side of the wires.

(6:05 + 2) means that 6°05 was the division seen when the scale was put in its
former place and that two whole turns of the screw were needed to bring 6°03 into
view again. It was because there was only one division at the supposed zero ‘04,
that the scale had to be pushed forward so as to bring 6:03 into view again, and
‘04 and 6:03 were used to measure the apparent left (but really right) sides of the
wires.

Section d.—Place the two microscopes in the centre pair of grooves and bring
them both in succession to focus on the same wire, adjust the focussing collars, if
necessary, so that when pushed up to their collars they are each in exact focus.
Having the proper back window, figs. 13, 14, in position, withdraw the microscope
and move the traversing slides till the microscope will be able to slide forward and
view the fibres. Push both up to their collars and move laterally until the
fibres are found. If, as is probable, they ave out of focus, ascertain by moving either
microscope by hand in its grooves whether the error of focus is in the same direction
for both. If it is not, slowly turn the lid, using a lever bearing upon the pin of the
first wheel of the train and entering the nearest tooth on the edge of the lid. This

NEWTONIAN CONSTANT OF GRAVITATION. 43

does not affect the parallelism of the line of traverse with the plane of the wires, for
the optical compass is carried round with the lid. When the fibres seem about
equally out of focus and in the same direction, bring them towards or away from the
microscopes, as may be necessary, by the adjusting screws of the torsion head.
However carefully this may be done, the suspended beam and gold balls are sure to
be set swinging slightly as a pendulum. This is easily overcome by resting a wax
taper or very flexible piece of wood against the central tube, and while watching the
motion in the microscope bearing very lightly upon it in time with the oscillations.

If a torsional swing has begun, there is nothing to be done except to wait until the
amplitude is reduced to a very small amount. It is impossible to obtain real quiet in
this sense, as owing to gravitation the observer’s body and the gold balls will attract
one another unequally. After one or two trials the two fibres wili be found
simultaneously in focus, at any rate, if not continuously owing to the small torsional
oscillations, yet between the elongations at successive half periods. I prefer to leave
the apparatus at this stage and to return after an hour, when the mirror is more
quiet, to verify the accuracy of focus. If this is correct since the focussing screw
has not been touched, the plane of the fibres coincides with the plane of the wires.
If more than u very small focussing correction is made, Operation 8 will have to be
repeated afterwards.

Section e.—Read the great scale in the telescope and take the vernier reading of
the lid. Then, since the wires and fibres are in the same plane, the lid reading and
corresponding scale reading are known for one position, and, since the angular value
of a scale division is known, also for all positions.

Section ~—Measure the distance between the fibres and their thicknesses, using
exactly the same procedure as described under Section c. I may mention here that
as the beam mirror is only ‘9 instead of 1 inch as intended, the traversing slides as
made would not come near enough together for both fibres to be seen at the same
time. I therefore made use of the traversing slides in their other position, @.e., with
T, to the right of T, instead of to the left, after having had the right side of T,
reduced by slot drilling so as to allow the now inner grooves to come } inch nearer to
one another. The change from one position to the other is made in a moment.

b>

G

44 PROFESSOR C. VY. BOYS ON THE

EXAMPLE. — Measures of Fibres with Optical Compass.

Edge. | Fibre. Seale. | Head. Correction.
Apparent right. . | Iie 6 3 3:45 439 |
3 Syaieceysea Wekbl way + 255 (+ 7 078
| —:00033
66 KR poo) Iaeanth 3°45 545
ss aD erga | Weft . .|) 2:55 (+4 7) 180
Thickness.
Apparent left edge. | Apparent right edge.
| Left. Right.
3°45545 | 3745439 180 545
2:56180 2°56078 | 078 439
‘89365 ‘89361 | — -00102 ‘00106
89361
|
Mean. . *89363 centre to centre.
— ‘00033 correction. |
*89330 corrected value.

Section g.—Set one microscope to see one fibre and the other in the proper groove
in the traversing slide to see one wire. Measure, as in Section c, the distance from
one edge of one fibre to one edge of one wire. Then move the traversing slide so
as to measure the corresponding interval on the other side. Knowing the two
intervals, the thicknesses of the wires and of the fibres, and the distance between the
axes of the wires (2 R), and between the axes of the fibres (2 7), it is at once known
to what extent the pair of fibres are eccentric with respect to the pair of wires.
Without touching the back adjusting screw of the torsion head, screw the other two
until one of the fibres has moved the right amount as measured by the eyepiece
micrometer. Ifa movement of more than a few thousandths of an inch is necessary,
it is best to re-measure the right and left intervals, and again adjust. When this is
done the two fibres are in the same plane as the wires and exactly half-way between
them. :

If now the construction were perfect the torsion fibre would be in the axis of the
instrument, and the lead balls would move centrally round it, but if either the two
radii of movement of the gold balls 7,7 or the two radii of movement of the lead
balls R, R differ from one another, or if the two lead balls hang from points which

NEWTONIAN CONSTANT OF GRAVITATION. 45

are not diametrically opposed to one another, then the lead balls will not rotate about
the torsion fibre as an axis. If, however, the optical compass is removed and the lid
is turned round 180°, and the measurement repeated, then half the movement
necessary to bring the fibres into focus as measured by the head of the focussing
screw is the diametrical inaccuracy of the lead balls, and half the inequality of the
right and left intervals is their eccentricity with respect to their mechanical axis
measured in their own plane. The torsion head may now be moved half of each of
these amounts separately, and then the vertical line half way between the pair of
fibres, which by construction is necessarily the same as the torsion fibre within less
than yo'09 inch, is also in the mechanical axis about which the lead balls actually
turn.

Exampues.—Plane of Fibres and Wires.

Focus for wires, ‘05 on focussing screw.
eee LCS eca

23 23

Therefore the fibres are behind (away from microscope) the wires by 5p = 004 inch,

Eccentricity of Pair of Fibires.—After setting the pair of microscopes to one
interval and sliding to the other, the left appears in the eye-piece to be smaller than
the right by about 007 inch.

By measurement it is found to be ‘00792 less,-or the pair of quartz fibres are
00396 out of centre.

The necessary observations are :—

5°98607 Centre to centre, wires.
°89330 Centre to centre, fibres.
02314 Thickness right wire.

6°90251
00102 Thickness left fibre.
2)6-90149
3°45074 Mean of right and left intervals.
345470 Right edge left fibre to right side right wire.

‘00396 Excess of right interval above mean.
00792 Right interval greater than left.
Operation 10.
Prepare for observations of deflection and period. Remove the optical compass

and replace the windows by fig. 12 at the back and fig. 11 in front. Place the
tubular screens, fig. 15, in position, Screw in the pillars R, R, and arrange the guys, &e.

46 PROFESSOR C. V. BOYS ON THE

and counterweight so as to reduce the weight of the lids and balls and therefore their
friction to a small amount. Place the first of the train of wheels W in place. See
that the string operating the driving gear is in place, and that the india-rubber tube
under the apparatus is connected to the composition tube going to the telescope.
Place the two halves of the octagon house in position, and fill up the open gap where
it overhangs the table at the back with a duster. See that the little electric lamp
inside the house is properly placed to illuminate the vernier. Remove all superfluous
apparatus from the table. Place the felt screen in position, and, when all is proved
to be in working order, leave, if possible, for three days to acquire a uniform
temperature.

“The angle through which the lead balls must be turned in order to produce the
maximum deflection I had found in a preliminary calculation, completed before the
apparatus was made, in which 2 R was made 6 inches, 27 1 inch, and the difference
of levels 6 inches, to be 61° 15’, and the effect of an error of 15’ at this position to be
1 part in 280,000. With the actual apparatus, in which 27 is less than 1 inch, I
found by experiment the angle of greatest effect to be 65°, which is that adopted.
Knowing the vernier reading corresponding to the observed scale reading when there
is no deflection observable with the optical compass, 7.e., when the lead and gold balls
are in the same plane, or in the neutral position, and taking this provisionally as a
position of no deflection, move the lid in one direction through an angle of 65° by
turning the handle of the wheel d by the telescope round 115 times. ‘The exact
setting of the lid is finally accomplished by lighting the electric lamp in the octagon
house, and observing the vernier with the small telescope t. Three or more elonga-
tions of the apparently moving scale are now read in the large telescope, and then the
wheel d is turned 125 times back, and, when the mirror is approaching its position of
rest, the remaining 105 turns are given to the handle, which leaves the balls 65° on
the other side of the neutral point, and the mirror oscillating through 50 divisions of
the scale, or even less. The vernier reading must be correctly set by the use of the
electric lamp, little telescope, and handle d, as before. Three or more elongations are
again taken. The elongations are corrected, and from the corrected elongations the
positions of rest, when the lead balls are in their + and in their — positions, are
calculated. If the supposed neutral position had been accurately found, its scale
reading would be exactly half way between the + and — position of rest. If, as is
probable, it is not quite accurate, then, since the variation of the position of rest
of the mirror is hardly observable when the lid is moved even so much as 1° from its
position of maximum effect, while such an uncertainty of position is not possible in
the provisional setting, all that has to be done is to bring the lid into such a position
that the mirror is at rest exactly half way between its extreme + and — positions
already observed. It is not sufficient to move the lead balls through an angle
corresponding to the error, because, though at the neutral position the smallest
variation produces the greatest effect upon the gold balls, they do not follow it abso-

NEWTONIAN CONSTANT OF GRAVITATION. 47

lutely. I always take two observations with the telescope of the position of rest of
the gold balls when the vernier readings differ by about 2° at the neutral position,
and thus, knowing how many scale-divisions deflection are produced at this position
by a movement of the lead balls of 1°, I am able at once to find the vernier reading of
the true neutral position (N). Then, when the vernier reading is made N + 65° or
N — 65°. the deflections in the + and — directions are found to be the same within
i per cent., from which it is evident that the + and — positions have been set
truly, with a superabundant degree of accuracy. This preliminary determination I
generally make the night before the deflections and periods are determined, which in
Oxford is best done on Sunday night between midnight and 6 a.m. The daytime, of
course, is out of the question, owing to the rattling traffic on the stones in St. Giles’,
about a quarter of a mile away; and all nights except Sunday night the railway
people are engaged making up trains and shunting, which is more continuous and
disturbing to the steadiness of the ground than a passing train. Hven these come
through at intervals on a Sunday night, and this limits the accuracy with which the
periods can be observed. All having been prepared for the Sunday night during the
previous week, the room is shut up all day, and at midnight or a little later the
actual observations of deflection and period are begun.

For a long night’s work without accidents, I am able to take two or three sets of
observations alternately at each of the + and — positions, with one at the neutral
position ; one period at each of the + and — positions, lasting about 45 minutes, and
occasionally one at the neutral position, lasting about 15 minutes, and finally two or
three sets alternately at each of the + and — positions, followed rarely by one, or
even two, periods of 30 to 45 minutes. For each set of observations at the + and
— position, I observe six consecutive elongations, and sometimes eight if I am
disturbed by the trains. I do not begin them until the apparatus has quieted down
from any very small tremor which the rotation of the lid may have set up.

In observing the period, the point of rest is known from previous observation,
A conspicuous pointer tapering to a point, which can be inserted into any division,
or if between can be read to a tenth of a division, is placed at the point of rest.
Air is gently drawn from the mouthpiece for a quarter period and then stopped.
According to the speed at which the pointer flashes past I determine whether or not
to draw air again. If I do, I begin about a quarter period after the transit, and
continue until the next transit, or a quarter period longer still, according to the
velocity of the transit. It is most important not to begin or leave off drawing the
air suddenly, lest a quick period movement, of which there are five independent of
one another, should be set up in the mirror. I begin very gently, gradually increase
and gradually leave off, the result of which is a beautifully steady motion of the
mobile system, extending far beyond the limits of the scale. I then start the
drum and make a dozen marks with the key in rapid succession, to indicate the
beginning of an observation. At each transit, the key is pressed suddenly and then

PROFESSOR C. VY. BOYS ON THi

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aS Se Jee eye at sys pe cs [res Nal
ee TESS i+ aa; J

ee ES ee eet

Hi [ie Yeas (eee fy eee

‘

SSeS Se ae pia

I)
| EE Ee AE

SLE ENS Tesh

stood

TEENY

eee NS ee et aH ae
Lywir V

NEWTONIAN CONSTANT OF GRAVITATION. 49

held down for one second, which produces a “transit mark,” the purpose of which is
to indicate that the previous dash was made at a transit of the pointer. Immediately
afterwards I note in the book an arrow showing the direction of motion. Every
transit is thus marked during the first stage, which lasts 10 or 15 minutes. In order
to know the actual time of any of the minute marks, I hold the key down once ata
minute for six seconds and thus produce “time mark.” This also is noted in its
proper place in the book with the time. To still further make sure of the place in
the book which corresponds to any place on the smoked drum, I occasionally make
a “castle mark,” that is, hold the key down during alternate seconds four or five
times, and note that also in the book. The proper sequence of time marks, castle
marks, and transit marks, is sufficient to make it evident afterwards to which arrow
in the book any particular transit mark belongs. During this stage it is net possible
to take the elongations as they are off the scale. I then leave the apparatus to itself
for about 20 minutes after first stopping the drum. On my return | start the drum,
secure another time mark, and every transit, as before, with a castle mark soinewhere
for distinction, but now the elongations being observable I note them in the book at
the same time. Following the practice of Professor Cornu, but on an extended
scale, I take the transits of the chief divisions at first of every 1000 divisions, then
of every 100, and after a time of every 10. These are distinguished on the drum by
four rapidly repeated dashes after a 1000, three after a 500, two after a 100, one after
a 50, and none aftera 10. I cannot take single divisions as they pass by so rapidly.
I have not used these marks except in rare instances, but they are available for
reduction in case time for the very tedious calculation could be found. Fig. C is
a full size reproduction of a portion of the sheet of October Ist, 1893, after L had gone
over it and scratched in the actual times. The different classes of marks are all to be
seen. I do not, as a rule, find it possible to put in arrows while writing elongations,
and marking transits of divisions as well as of the pointer. Their existence 1s
understood between elongations. In addition, I generally place a letter or word
to distinguish good observations of transits from bad, thus: — ov atl,
or — 04 late. I do not think the v.g. observations can be more than ‘01 second
in error, or the g. more than ‘02 or ‘03 second. Those unmarked might be perhaps
as much as ‘1 second, though they may also be good, but those marked bad would
probably be more. If it were not for the high period tremor set up by the trains,
which prevent good observations when the amplitude is less than about 40 divisions,
I should expect to obtain a higher degree of accuracy in the periods than are actually
obtainable. I sometimes take observations of deflection and period on more than one
night.

Operation 11.
Transfer the gold balls to the side hooks, and leave for a day, if possible, to quiet.
Find the deflection, if any, produced upon the mirror alone, by moving the lid and
MDCCCXCV.—A. H

50 PROFESSOR C. V. BOYS ON THE

lead balls from the + to the — positions. Find also with large amplitude, the exact
period with and without the counterweight, using the drum and following all the
details given in operation 10. At this stage it is convenient to set up the
cathetometer and measure the stretching of the torsion fibres by observation on the
bottom hook of the mirror. This is not necessary for the purpose of finding G, but
it is of interest as bearing upon the elastic properties of quartz fibres.

Operation 12.

Turn the lid round to the neutral position. Place the steel bands on the flat-
rimmed pullies. Pin to the ball holders, and hang on at the other end the
counterweight. Raise the balls about $ inch, turn them individually through 60° and
let the geometrical clamps down through the triangular orifices of the lid pillars,
until the balls rest on the india-rubber rings on the base. Raise the lid, leaving it
balanced in the air by its counterpoise, and after removing the two counterweights
and the holding pins, take away the steel bands. Let down the lid again. Partly
balance it as before. Put screens and octagon house in position as before, and after
a day or two take deflections, if any, when the lid and lid pillars are moved between
the + and — positions. Three sets of six elongations at least should be taken at
each position.

Operation 13.

Re-suspend the gold balls in the same position as before, and find the deflection of
the mirror, if any produced, by moving the lid and lid pillars from the + to the
— positions.

Operation 14.

Take the focussing collar off one microscope of the optical compass, and slide it on
to the nose end of the other, so as to raise it high enough to see the side of the
bottom hook of the beam mirror. Remove the front Jens of the object-glass, which
reduces the magnifying power to rather less than one-half. Set the optical compass
so that the vertical tangent to the curve of the lower hook is on the zero of the
micrometer scale in the eye-piece, that is when the mirror alone is freely suspended.
Hang on the counter-weight and take the scale reading. Hang on the gold balls
instead of the counter-weight and take the scale reading again. The object of this
is to find to what extent, if any, the axis of rotation of the beam changes when the |
balls or the counterweight are suspended (see p. 84).

NEWTONIAN CONSTANT OF GRAVITATION. 51

Part III.

The calculation of the results from the figures obtained by observation is divided
into four sections:—(1.) The deflections and periods; (2.) The geometry of the
apparatus; (3.) The dynamics of the moving system; and (4.) The combination of
these resulting in the determination of G, the Newtonian constant of gravitation,
and indirectly of A, the mean density of the earth. In the preparation of this part
I have been greatly helped by Mr. 8. G. Srartte, of the Royal College of Science,
who has carried out the laborious numerical calculations.

_ 1. The Deflections and Periods.

The treatment of the figures obtained during the observations of deflection will be
best explained by an example. I give two consecutive sets, one the worst obtained
the whole night, and the other a particularly good one, but others obtained that
night were practically as good.

Sept. 17, 1893.

| |
A = 150°-9. 13h. Om. | 15°15 C.
{
| 24907 —94 | 24893
le ANG 390 24493
| 24193 —26 | 24167 | 835
| | 598 | 396 24.493
94789 | —24 24.765 e394 |
| | 499 271°5 244935
| 24202 | -26 | 24066 | ‘838
* | | 418 | 226 24.492
24709*+ —25 24684 | | 848 |
| oro aa senae| 192°3 (24491-7)
| 243554 | 255 | 949095 | | ‘842
298-5 | ————e
24.6544 —26 2.1628 | 24.492-9 |
A =20°9, | 13h. 15m. 15°15 C. . |
| |
19888 76) = | Tess |
| 1702 926-4 20795°4
21591 20 21571 | 8873 |
1425 | 7753 20795-7
20165 ~19 | 20146 | 9379 |
194 | 649:5 20795:5
21359 —19 21340 2384 | |
1001 | 5445 | 207955
20358 = 20339 8382 | | |
839 |__|
21197 —19 21178 20795°5

* A short period oscillation or tremor, set up probably by a passing train,
+ A pendular oscillation, set up probably by a passing train,
BH 2

92 PROFESSOR C. V. BOYS ON THE

A represents the lid reading differing from 85:9, the neutral position, by the
azimuth 65° of the lead balls. The actual time of the beginning of a set is next
marked and then the temperature of a thermometer set up close to the apparatus.
This is illuminated and read by the same means that are provided for reading the lid
vernier.

The first column of figures are observed elongations expressed in tenths of scale-
divisions. The second column contains the scale corrections, in which are included

+ postion

2449

2080

- position

both the calibration and the circular errors. The third column are the corrected
elongations, the fourth the differences of these or amplitudes, the fifth the ratio of
these or the decrements, in the sixth are the quotients of each amplitude by 1 + the
following decrement. The last column contains the algebraical sums of the corre-
sponding numbers in the third and sixth columns. They represent the points of
rest during the course of the oscillation. Each series gives a mean point of rest of
which a dozen or more may be obtained in one night. I prefer to arrange all the
individual points of rest as well as the mean points in their proper places in a
diagram, of which abscissee represent the hour and the ordinates the points of rest,
but on a very large vertical scale. The one of these for the evening’s work chosen
for illustration is shown in fig. D, from which it will be seen that a gap of 368 inches
has been cut out to save room. ‘The series of mean points of rest are shown in the
following table :—

NEWTONIAN CONSTANT OF GRAVITATION. 53

Position.
Time.
Neutral. Positive. | Negative.
|
heen: |
12 3Y 22649-9
| 12° 46 20797°3
13 0 244.92°9
13 15 | 20795°5
13 30 24491°3
| 3 7133 20795:1
(ee clseesz 244925
| Oscillation of large amplitude for period.
ey 2 | 20793°7
15 15 | 24.4.92°2
iby AL yn) | | 20795°2
15 42 | 244.90-2

The deflections P are obtained by taking these in groups of consecutive threes, to
allow as far as possible for steady creeping of the zero. It will be seen that in the
present instances there is nothing very definite that can be attributed to this.

The four deflections obtained in this way before the time interval are—

3696°5

3696°6

3696°0

3690°8
The two after are—

(3697°7)

369670.

As the mean point of rest 20793°7 was taken immediately after the oscillations of
large amplitude produced by the air draught and was definitely slightly disturbed,
I have not included the resulting deflection 3697°7 in the series from which the true
deflection on that particular night was determined. The agreement is exceedingly
close, so that the mean of the five values P = 3696°4 may be taken with considerable
confidence.

The observations on this night were rather more consistent than usual, owing, as I
believe, to the very unusual quiet noticed at the time.

I only took one observation of period on this night, recorded as follows :—

54 PROFESSOR C. V. BOYS ON THE

A =150°9, Pointer at 24520 Drew air once.
= O7

24493 No time correction worth making,

Times of Transit.

hey am s.
14 20 36°34 —> g., time mark, 14h. 21m.
22 3el: se:

23 49-7 4-02 —-» -02 early.
25 26:58 —-06 ~<— -06 late.

27 = 301 —> v.g. Castle mark.
28 39°68 pa

Interval.
Al 32:7 <—— Time mark, 14h. 42m. Castle mark.
43 9:42 — v.g.

Amplitudes. Points of rest.

(44 46-1) <— Pendular oscillation.

26915 — 26 7} 2 244.91:2
46 22°87 4406 &

22505 —22 | All bad with ane 24488
47 59-42 \ pendular dis- 3690 = =

26199 — 26 | turbance S| 24486°6
(49 36-1) Bad transit 3101 5 8

23106 — 24 J a
51 12°48 2601 —

25698 — 25 Castle mark.
52 49°35 T'ransit.

If the pointer had been found to have been definitely out of place, but, of course,
by a small amount, I should have corrected the observed times of transit by a series
of alternate + and — quantities, calculated from the amplitude, period, and error of
position. In the present case, owing to disturbance, the point of rest showed an
uncertainty of nearly half a division, and I could not be sure from these observations
that the pointer was not placed that much in error. On the other hand, after
subtracting the time of each transit from that above, the series of observed half
periods show a small, fairly regular, increasing and alternating second difference,
which is in itself a sign that the pointer was very slightly on one side of the true
position of rest. If no account is taken of this, the half period deduced from the
first and last observation is found to be

96°650 seconds ;
from the first observation marked g to the last marked g it is

96°649 seconds ;

NEWTONIAN CONSTANT OF GRAVITATION. 55

and if the times of transit are corrected by one quarter of their second ditierence, so
as to approximate to the times of transit of the point of rest, the half period over the
whole series becomes

96°645 seconds.

The object of examining so many transits is not so much with the idea of applying
methods of least squares or of otherwise equalising errors, but mainly to see that the
oscillation is going on regularly and that no sudden disturbance has arisen which, if
it were undetected at the time, might become lost and yet leave the result in error
by an observable amount. I find that in the present instance I did not try to improve
upon the obseryations by arithmetical manipulation, and that 96°650 was taken as
the observed half-period. Two small quantities had to be subtracted from this, one a
correction of — ‘0034 due to a gaining rate of two seconds a day of the clock, and one
of — ‘1508 on account of the damping effect of atmospheric resistance. The true
whole period for no damping then becomes 192:992 seconds, and its square 37245°9 is
the quantity which is finally made use of in the dynamical calculation. It is recorded
as T;”, the square of the time with the balls on. In a similar manner T,” is found
when the counterweight is on, and To” when the mirror alone is swinging.

Under this heading the deflections produced in Operations 11, 12, 13 must be con-
sidered. The deflection in Operation 10 is due to four possible attractions :-—

(1.) Lead balls, &e., on gold balls.

(2.) Lid and permanent fixtures, &c., on gold balls.
(3.) Lead balls, &c., on beam mirror.

(4.) Lid and permanent fixtures, &c., on beam mirror.

The deflection, if any, of Operation 11, is due to (3) and (4) above. Similarly the
deflection produced by Operation 12 is due to (4) alone, and of Operation 13 to (2)
and (4). Knowing, therefore (1) + (2) + (3) + (4); (3) + (4); (4); and (2) + (4);
(1), (2), (3) and (4) are separately determined. ;

I have on two occasions since Experiment 3 was completed (which was of a semi-
provisional nature) carried out the deflection observations of Operation 11. On
September 1, 1893, 1°5 units or ‘15 division was obtained. There was a very slight
+ creep. On September 11, with no creep and very consistent behaviour, °5 unit or
‘05 division was obtained, Ido not know whether I should take ‘5 or 1 unit. The
difference is beyond what can be observed with any certainty.

I find that the lid was turned 180° between the two experiments, but this could not
make any difference. I have taken 1 unit as the deflection in Experiments 4 to 12,
and have calculated what it should be in Experiment 3.

Most careful observations on September 2 and 3, 1893, fuiled to show any deflec-

56 PROFESSOR C. V. BOYS ON THE

tion under Operations 12 and 13; certainly not 1, and not, apparently, +1 unit.
From this it will be evident that since

(3) + (4)=1,
(4) =0,
(2) + (4) =0,

(2) = 0, (8) =1, and (4) =0. Therefore 1 unit must be subtracted from the
observed deflection of Operation 10 in all experiments after No. 3. It is for this
reason that the numbers under P in Table I., p. 63, differ very slightly from the
observed deflections.

2. The Geometry of the Apparatus.

In this part of the calculation I find the exact relative positions of the several
oravitating bodies, from which the couple twisting the fibre may be found in terms of
G. Thus, the couple = QG. As before, the process followed will be most readily

explained by giving an example.

NEWTONIAN CONSTANT OF GRAVITATION. j7

EXPERIMENT 8.

@ = 65° — 22’ = 64° 38'

Re => R, = 2°99304
iii = 446650
log 7 = 1:6499673

p= Rsin 0 = 2704465
6=R8 cos 0 = 1:282247

sin 64° 38’ = 9035847
cos 64° 38! = 4284095

b—r =) :83559/7
b+r = 1728897
hy, = -0821

Hy, = 6:048339

hy2= 001029
Hy? = 36°582411

Low. High.
P 7314131 7314131
(b—7)? 698222 698222
i “001029 002660
D? 8-013382 8015013
log D? 9038157 “9039042
log D "4519078 4519521
log D3 13557235 13558563
log p ‘4320814. "4320814
log p/D? 1:0763579 1-0762251
log M 3°8696230 3°8696634
log m “4234097 "4234163
log 7 16499673. 1-6499673
log couple 30193579 30192721

1045°580
1045°371

Couple

2090°951
148°326

Q = 1942:625

104:5°371

p? = 7314131
(b —r)2 = -698222
(b +r)? 89085
hy = ‘0516 = 002660
Hy = 6:02885 H,,2 = 36°347032
Low. High.
p 7314131 7314131
(b +7)? 2-989085 2-989085
H? 36°582411 36:347032
46°885627 46650248
1:6710397 1:6688539
8355198 -+8344269
2-5065595 2-5032808
4320814 “4320814
39255219 3-9288006
38696230 38696634
4234163 4234097
16499673 1:64.99673
1:8685285 1:8718410
73:880 T4446 -
74-446
148:326

In order to determine the moments of the attractions of the large balls M, M
upon the small ones m, m, the distances represented in figure E by p and 7, and
the true distances D between M, M and m, m are required, also the masses M, M

MDCCCXCV.—A.

58 PROFESSOR C. V. BOYS ON THE

Fig. E.

and m, m— that of displaced air. Then the moments are for any one attraction

out of the four possible,
GMmpr
Diez

These are most readily obtained from the observations in the manner set forth
on the last page, where every figure made use of isset down. Single multiplications
are performed on the arithmometer more quickly than by logarithms, hence natural
sines and cosines are employed. Continued multiplications are more conveniently
performed by logarithms, and the change from D? to D® can only be so effected.

The angle, @, is the amount through which the lead balls are turned from the
neutral position — the angle through which the gold balls are deflected.

R, the radius of motion of either lead ball, is half the distance between the axes of
the wires, and they are taken in the calculation as being identical, 7.¢., there is
supposed to be no eccentricity. In Experiment 5 I calculated the result both on
this supposition and more laboriously giving the true and slightly different values to
Ry and R,, the radius of motion of the upper and of the lower ball respectively. The
difference in the result only amounted to 3 parts in 2,000,000, and so, as I explained
on p. 26, a small eccentricity, if it exists, is of no consequence.

r, the radius of motion of either gold ball, is half the distance between the axes of
the fibres. The next few lines explain themselves; they simply give intermediate
quantities required for the solution of the different triangles. h, and hy are the
differences of levels of the centres of the lower gold and lead balls and upper gold and
lead balls respectively. H, is the difference of level of the lower lead and upper gold
ball and H,, the other great difference of level. The four couples obtained are those
due to the attraction of the two pairs at the same level and of the two pairs at
different levels. The latter are in the opposite direction to the former, and are
therefore subtracted. The result, 1942°625, when multiplied by G, is the actual
moment produced upon the torsion fibre by the action of the balls upon one another

NEWTONIAN CONSTANT OF GRAVITATION. 59

upon the supposition that the balls are all spheres, and act as if they were concen-
trated in their centres. The brass ball holders, as already explained, cause the forces
to be actually more than they appear to be, on the assumption that the lead balls act
as if they were concentrated in their centres, so that 1 + ‘0001866 is the factor by
which the couple must be multiplied to correct for the brass bal] holders. The
corresponding correction for the gold ball holder is only gggogo of the whole. One
small correction, too small to matter, but which I have calculated with some labour,
is the stability due to the vravitation of the table. This introduces a restraining
couple upon the balls alone in Experiment & of gzq'999 of the whole. Finally, there

263,000
the gold ball for the wires and the lead ball for the fibres. Combining all these,
the actual couple developed is found to be equal in Experiment 8 to 1942882

inch? gramme
apsaa US.

is the correction already mentioned on p. 31 of on account of the attraction of

second?

Q

3. The Dynamics of the Moving System.

As before, I shall take my example from Experiment 8.

Moment of inertia of counterweight No. 3o0rC. . = OlG5120

dee . . . . . . . . . . . . . . . . 37245°9 Ae eo Age
85547°17

Te e-w ott maleelib eRe Wisin pte etoreadiada i aicrr/6

T,” not taken.

Moment of inertia added to beam when balls are placed in position, called B.

( balls translated 5:302804 x ‘446652. . . . . . = 10578893
| + hooks translated 0°1190 x °3792 . .. . . . = ‘0017093
1 + balls rotated -4 x 5300252 x ‘126134? = ‘0337303
(ck hooks rotated 012 x 0252. = ‘0000075
Be ey eee = 10983364
Chala ah es a CONGR TD
Be Cea ee elo se
BL,? — CT,
OS a = SLITS,
ae
4? (B — C
S = = 001196138.
1 Ge Ee

12

60 PROFESSOR C. V. BOYS ON THE

The moment of inertia of the counterweight is directly obtained from its dimen-
sions. The moment of inertia added to the beam requires more explanation. When
the balls are hung on to the beam in the manner already described, they add to its
moment of inertia, both on account of their distance from the axis, and on account
of their own moments of inertia, about their own axes. Besides the balls the small
wire hooks and the quartz fibres produce their own effects. These are found in the
four lines bracketed B. In the first line the mass of the balls is made up as
follows :—

Mass of gold balls + wire holders, corrected for”
buoyancy as against brass weights, but not

absolutely, + 3} mass of displaced air. . . . 5°302204
se Mass Old Marva tbKeS)\ eae. ane ene aa eee ‘00060
5°302804

this is multiplied by the square of the radius +.

In the second line the radius of the support of the hook is obtained by direct
measurement of the beam itself. It is relatively unimportant. In the third line the
mass of the balls does not include the ball-holders or fibres or (perhaps wrongly) that
of any surrounding air. The radius of the ball is found by a screw micrometer. The
fourth line needs no explanation ; it is infinitesimal.

U is found from the formula placed next to it. This is the moment of inertia of
the mirror. It is not required in the calculation, but is found for the purpose
of comparison, It should be constant.

S represents the stiffness of the torsion fibre, 7.c., the couple that must be applied
in order to twist it through unit angle (57°:296).

If the unknown moment of inertia had been eliminated by the usual method, that
is by supposing the torsion constant while the mirror was made to swing either with
or without a known added moment of inertia (in this case, that due to the balls) then
T°’ and T,” would have been required. Taking T,” from the previous experiment
when it was found to be 116800,

a Br? i
U becomes ——*— = ‘035396
PT?
and
= 4B
S becomes oe = °001196375.
eee

Since the torsion is not the same when T,” and T,? are being found, as in one case
the fibre is much more strongly stretched than in the other, and is therefore longer
and thinner, and is not necessarily made of a material having the same rigidity, the
above figures are spurious.. They differ from the true figures found in the previous
page, but U, which is eliminated differs far more than S$, which is made use of. The

NEWTONIAN CONSTANT OF GRAVITATION. 61

reason of this is made clear if a correction, @ in terms of S, is included in the expres-
sions for U and §._ Since the fibre becomes stiffer when the balls are taken off, it is
simpler to consider this correction as a stiffening of the fibre when it is unloaded
instead of the reverse when it is loaded. The expressions are now :—

Ua Biv +45)

op aso |S):
‘ 4a? B
S = Ta? — T2(D OS)”

It now appears that in both, the denominator is affected to the same extent, which
is very small since T,” is small compared with T,”?. On the other hand the numerator
of S is not affected, while the correction applies to the whole numerator of U.

The very great effect of this upon the absolute value of S is well shown in Experi-
ment 9, where the additional weight was 7°975 instead of 5°314 grms. In con-
sequence of the extra amount of stretching S$ fell from ‘001196 to 001147, or nearly
5 per cent. The actual elongation of the torsion fibre in the two cases was ‘0394
and ‘0677 inch. The whole length of the fibre was 17 inches, so the amount of
stretch was ‘232 and ‘398 per cent. Even if the volume of the fibre remained
constant the diminution of torsional rigidity could not be accounted for with a
material of constant rigidity. This point is perhaps worth considering in connection
with Potsson’s ratio and the theory of elasticity, more especially in consequence of
the great hardness, freedom from structure and possible elongation without per-
manent deformation or change which are met with ina quartz fibre. I must, however,
defer its discussion for the present or leave it to some one more competent than
myself.

4. The Combination of the preceding Three Results.

The method of combining the results given in the first three sections of this part
is simple enough. From the first section, the deflection in scale divisions when the
lead balls are moved from the + to — positions is obtained. Let this be called P.
The second section gives Q the numerical coefficient of G; thus, Q G is the couple
exerted upon the fibre. From the third section, the actual couple S that would be
needed to twist the torsion fibre through an angle of 1 unit (57°3) is obtained
without any reference to G, and D being the actual distance in units or tenths of a
scale division from the scale to the mirror measured as explained on p. 17, it follows

G = PS/4QD.

The 4 in the denominator is due to the doubling of the angle by reflection and to
the doubling of the deflection by moving the lead balls from the + to the — positions.
G is thus obtained in inch?/gramme second* units; to convert it into

62 PROFESSOR C. V. BOYS ON THE

centimetre®/gramme second’ units it is merely necessary to multiply by 16°3861, the
number of cubic centimetres in a cubic inch.

To obtain from this the density of the earth I might have recalculated the
attraction of the earth treated as a rotating ellipsoid composed of similar shells of
equal density as given in Professor Poyntine’s paper, but since it is obvious that
G A is a constant, and is, taking Poyntrne’s figures, equal to 36°7970 X 107%, it is
merely necessary to divide this figure by G to find A.

Again, taking Experiment 8 to furnish an example, these operations are as follows :—

: PS 3695-4" x °00119598T

= —__ = = 2 =o
~ 4QD 4 x 1942882 x 139965 UEDA Xs

in inch?/gramme second” units.

Multiply by 16°3861, then G = 6°6579 x 10-% in C.GS. units, and A = 5°5268.

The more important quantities of the whole series of experiments are exhibited in
Table I, which, as the heading shows, is constructed on the Inch, Gramme, Second
system, in conformity with the actual measurements. The supplementary table is a
repetition of the most important quantities in C.G.S. units. Here below the constant
of gravitation G is to be found the series of values of A the mean density of the
earth. Appended are Cornv’s and Poyntno’s values, Cornv’s G being obtained from
his A in the same way that I obtained my A from my G.

An examination of the table shows that I have employed a fair variety of con-
ditions, the lead balls alone being unchanged throughout the series. Three pairs of
small masses were made use of. The lead balls were practically unchanged in
distance, though, after Experiment 7, they were brought nearer together by 39 inch
about. The effect of this on the deflection P and the coupie Q is at once evident in
Experiment 8. Three fibres were employed, though, as already mentioned, the
rigidity was very different in Experiment 9 owing to the great longitudinal strain.
The different torsional rigidities are tabulated under S.

The periods are tabulated under their squares, 7.¢., after correction for damping.
T,? is with the gold balls or cylinder suspended from the mirror and with the lead
balls at a + or — position, where, by producing a maximum couple, they do not
affect the period. Ty? is the corresponding period with the lead balls in their neutral
position where they accelerate the period. I might, following Reicu, have inde-
pendently calculated G from the acceleration produced in this way, but these periods
were not determined with the same care as the others, and in any case, the difference
is too small for an equally accurate result to have been obtained. T,? and T,” are the
square of the periods with counterweights and with nothing on the mirror.

The pairs of quantities tabulated under H,™ and h," are the four differences of
levels between the lead and gold balls. Thus 60296 in Experiment 5 is the

* 36954 = 36964 —1. See p. 56.
+ 00119598 = :00119615 (1 — 1/7850). See p. 35.

63

NEWTONIAN CONSTANT OF GRAVITATION.

OFS BG.¢ 0%-¢ 94.9
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64 PROFESSOR C. V. BOYS ON THE

difference of level of the upper lead and lower gold ball, while 6:0139 is the corre-
sponding difference between the other pair. Similarly ‘0059 is the difference of level
of the upper lead and upper goid balls, and ‘0216 the difference of level of the lower
pair of balls.

In order to eliminate as far as possible any systematic errors that might arise for
instance from imperfections of the copper central tube, which of course is very near
the gold balls, or from want of perfection in the lead balls, though nothing comparable
with the error of experiment need be feared on this account, I made some change in
the circumstances after every experiment. Thus, after Experiments Nos. 1 and 2
had been carried out, which were merely preliminary so that I might learn something
of the behaviour of the apparatus, I arranged the balls in Experiment 3 as follows :—

Lead ball, No. 1, Wall side, High level,
san 2 Arche. cows mae
Golde =. 8, Walla sz anohmes
wate. ,, 4, Arche ds elrowane
Neutral reading of lid 267°.

The arch side is the right as seen from the telescope, or the left as seen from the
back when the optical compass is in use. This expression depending upon the
structure of the cellar avoids ambiguity.

The corresponding arrangement in the whole series of experiments with the dates
at which they were carried out is given in Table IT.

As would be expected, I had not at first all the details so complete as at the end
of the series of experiments. Thus, in Experiment 8, the air drawing arrangement
for steadying the mirror or starting it into motion, had not been thought of. At
that time, for want of a better arrangement, I had to enter the corner and
withdraw the back window, fig. 12, so as to allow the accidental movement of
the air to start a swing of great amplitude. As I have already indicated, the
decrement is, in spite of all I can do to prevent it, inconveniently high, so that
periods extending over forty-five minutes cannot be taken unless the mirror has
an oscillation of large amplitude at starting, far larger than two or three
reversals of the lead balls in time with the oscillation would set up. The plan
was essentially bad owing to temperature, disturbance, and tremor, nevertheless
the observations made at the time were fairly consistent, thus two periods in
the + position on October 16th, gave 241:93 and 241:90. The next day I put up
the felt. screens and two periods were 241°9(4) in the + position, and 241°88 in the
negative. I then introduced a different method of producing a swing of great
amplitude, viz., in the air tube then screwed into the back window, fig. 12, I fitted a
glass stop-cock which could be turned on or off without touching the metal windows
or screens. I did this hoping that a clockwork fan belonging to a lamp would
produce a gentle draught upon the end of the mirror when set in action opposite a

GRAVITATION.

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66 _ PROFESSOR C. V. BOYS ON THE

funnel-shaped end to the pipe. This did not work, and I was therefore compelled at

the time to produce the draught by some ready means; gentle movement of a sheet

of paper at a distance from the instrument produced the desired motion, but my

going near the instrument at all was essentially bad. The periods obtained after .
this were :—

Oct. 29 . . . 241°99 + position.

Pane er OO =

30. 6h a a Qhiesees oe ae

Ge Gg OURO Se Se eee

I noticed slight differences between periods taken with the lead balls in the + and
— positions with my preliminary apparatus, but, though I am not able to explain it,
I am glad to say that, with the more perfect setting and screening now in use, it has
practically disappeared. The two periods taken with the counterweight gave identical
results, 64°954 seconds.

The soldered fibres used in all the later experiments seem a definite improvement,
as the creeping of the zero, which was never very troublesome, almost entirely ceased.

The traffic and the trains are not the only causes of disturbance. Wind, by
pressing upon the building and neighbouring trees, of course shakes the ground ; but
on Sept. 9-10, a particularly quiet night, I had to leave, owing to a sudden dis-
turbance produemg a pendular motion of 15 divisions, or 150 units, and for some time
there was no quiet. As the motion was clearly produced by a lurch of the whole
instrument and table carrying it, and was greater in amount than any traflic in the
busiest part of the day had ever produced, and was moreover free from the high
period tremor characteristic of human disturbance, I at once set it down to an earth-
quake. I was marking transits of every 10 divisions at the time. The moment of
the last mark was 15h. 44m. 14°3s., allowing for the error of the clock as determined
at the Observatory. The next mark was due in 3 seconds, but I was, of course,
unable to record it. In the ‘Standard’ of Sept. 12th there was an account of a
violent earthquake at Jassy, which was felt also at Bucharest, at six o’clock in the
morning. I have not ascertained the exact time at which the earthquake was felt in

Xoumania, or the amount to allow for difference of longitude, but these, no doubt,
can be supplied from Vienna.*

Experiment 11 was a purely comparative one. Everything being left as in Experi-
ment 10, a tube was connected with the stop-cock in the bell-jar J, and with a
hydrogen bottle and drying bottle, so that dry hydrogen could be fed in to displace
the air in the central tube. The object was to see if any advantage would be derived
from the smaller viscosity of hydrogen ; but, though the resistance fell so as to change

* Mr. C#artes Daytson informs me that the shock was recorded at Bucharest at 3h. 40m. 35s., a.M.,
but that the epicentrum must have been some distance from there. The time interval between Bucharest
and Oxford appears very small, the usual rate of travel being 3 km. a second, or a little more.

NEWTONIAN CONSTANT OF GRAVITATION. 67

the decrement from °842 to ‘937, which in itself was a great advantage, so much
difficulty seemed inherent in the method that I determined not to prosecute it. The
values found this night for T,” were

MEME no 6 ee SOM
Inhydrogen . . . 35401

The deflections owing to disturbance could not be so accurately determined as usual;
they were
Tinta a ere aa ero 20
In hydrogen . . . 385238

The only observation of real interest in connection with the hydrogen experiment
was the effect of the gas upon the mirror. The mirror was bent to a small extent,
causing the image of the divisions to practically disappear. A movement of the eye-
piece outwards of about 3 inch was needed to make them appear sharp again. On
letting the gas escape the focus went back to its old place, and this was repeated
without variation three or four times. I imagine that the glass became convex under
the influence of the hydrogen in consequence of the glass being penetrated by the
quickly-moving molecules, and so becoming expanded in the front or unprotected
side, while the silver and lacquer at the back prevented this action, much as paper or
lace will protect glass from the cutting action of a sand-blast. The bending may have
been produced by a contraction of the lacquer or silver, but this seems hardly con-
ceivable. An interesting line of inquiry is suggested by this experiment, but 1 have
not been able to do more at present.

An examination of the results shows that they hover about two values, experi-
ments 3, 4, 5, 6 and 12 being about 5°520 for A, and the remainder about 5°528. It
is impossible to trace any connection between the arrangement of the apparatus, &c.,
and this small irregularity. It is necessary, therefore, to review the deflections and
periods of each and the conditions, whether of disturbance or quiet, under which they
were carried out. No. 3 has already been discussed, and the wonder is that it should
agree so well with the others when the imperfect conditions are borne in mind, and
when it is remembered that the torsion fibre in this experiment had only one-third of
the rigidity of those used later, while the gold balls were only half as heavy.

As already mentioned, the periods in Experiment 4 were lost, so that an absolute
result could not be calculated. The values of 2r in the two cases only differed by
00002 inch, an amount which is probably beyond the certainty of measurement, and
therefore the results for 4 are merely obtained from those from Experiment 5, by
multiplying or dividing by the ratio of the deflections.

Deflections and periods for Experiment 4 were taken over several days. The
deflections were :—

K 2

68 PROFESSOR C. V. BOYS ON THE

Ang. 21. | Aug. 23. | Aug. 25. | Aug. 26. | Aug. 27. | Aug. 29.

3669:0 | 3667-7 36658 3669°7 3668°3 36683

3669°6 3668 (36649) 3669:0
a: 3666°7 3665°7 aS ore 3669°4
3667°8

Temperature at 1! 40.43 @. | 179-04 C.| 16°58 C. | 16°56 C. | 16°59 C. | 18°24 0.

end of night

The mean of all but the one in brackets, which depends on a single value only, is
36681. The deflection for Experiment 5 is 3668°6, practically an identical quantity,
so that the G and A of the two are almost the same. The two results should properly
be considered as one. Both unfortunately depend upon unsatisfactory period obser-
vations which, when squared, varied from 37200 to 37240. On this account the
results from Experiments 4 and 5, which are higher than any of the others for G and
lower for A, should have had a bad mark put against them. In Experiment 6 the
deflections were nearly as consistent as those in Experiment 4, while the periods were
now nearly the same in the + and — positions, being, when squared, 37245 in the —
and 37247 in the + positions, The conditions of this experiment seemed decidedly
favourable, and I see no reason inherent in the observations that could lead me to
doubt the accuracy of the results.

In Experiment 7 the only change was twisting the lead balls so that the sides that
were inwards should be outwards. The sudden change in the result for A from
5°5189 to 5°5291 might seem to be due to some irregularity of density in the lead
balls. But the extraordinary agreement between this result and the three following,
where every kind of change was made in the conditions, including the turning of the
balls again, and the change from high to low and low to high, and where, moreover,
the extra steadiness of temperature due to the screening of the octagon house was
introduced, shows that this argument will not hold. I cannot account for this small
difference. In Experiment 8 all the conditions were most perfect. The figures for
this have already been given, and so need not be repeated. I may, however, compare
the squares of the periods of Experiments 6, 7, and 8, throughout which the beam
mirror and gold balls were never touched, to show how much better the agreement

was at this time than before.

| Experiment. Date. — position. + position.
|_
6 Sept. 14. 37245 37247°5
7 m do 37242
8 pee ae 37245'9

The last figure of this series was taken in determining 8. I may mention that a

NEWTONIAN CONSTANT OF GRAVITATION. 69

change of 3/5 inch in 2R was made in this experiment, the effect of which is at once
evident both in P the deflection, and in Q the geometrical factor.

In Experiment 9, the conditions were completely changed by the substitution of
gold cylinders for gold balls. As already mentioned, the torsional rigidity of the
fibre was altered 5 per cent. by the great tensile strain, yet with every quantity
redetermined the only change in the result was about 1 part in 1500. The old
conditions were realised again in Experiment 10, except that I had taken the fibre to
London, re-soldered the broken ends and waited three months, but the result only
differed from that of Experiment 8, by 1 part in 60,000. Perfect conditions were
met with again, the mean deflections for the two nights, January 6 and January 7,
being 3516°5 and 3516°3. The last experiment on January 21 was disturbed, and the
points of rest varied several units in the course of the night. I was compelled,
moreover, on leaving the apparatus at 17", to take off the gold balls, replace them
by the counter-weights, and after about three hours’ sleep, to return again and
take the counter-weight period. This was far too soon for the temperature to have
settled after disturbance, and in addition to this cause of error, I had only 10 minutes
in which to take the period, and had then to hurry off with the drum record still wet,
in order to be in London where I had to lecture at noon. I cannot, therefore, look
upon this experiment with the same confidence as Nos. 7 and 10, and so with the
exception of Experiment 6, all those that give the lower value for A have something
against them. Under these circumstances, I cannot do otherwise than look to
Experiments 7, 8, 9, and 10 as being the most likely to give a true value. Moreover,
as Nos. 8 and 10 were both made under most favourable yet very different conditions,
their closely agreeing figures carry more weight than the other two. I therefore
conclude that A = 55270 and G = 6°6576 X 10~*. The fifth figure in such case is,
of course, a purely arithmetical phenomenon, but I do not think that the fourth
figure can be more than 1, or at the outside 2 in error.

I had hoped to have made a greater number of experiments under more widely
differing conditions, but the strain which they entail is too severe, for not only have
I had to give up holidays for the last three years, but to leave London on Saturdays
and occasionally to sit up all Saturday and Sunday nights at the end of a week’s
work. The conditions, therefore, are too difficult for such an extended series as I
should like to make to be possible, and I must after one more effort, leave the problem
to others who have leisure, and what is of far greater consequence, a quiet country
place undisturbed by road and railway traffic, and who possess the knowledge and
manipulative skill which the experiment requires.

Conclusion.

I think it might be useful, now that the autumn has passed and I have been unable
to make a new series of observations, if I were to state my views a3 to any change of

70 PROFESSOR C. V. BOYS ON THE

detail that might conduce to greater accuracy. I am still convinced that G may be
determined with an accuracy of 1 in 10,000 by means of apparatus such as I have
described.

In the general design I am unable to suggest any improvement. The weakest spot
is caused by the resistance of the air making time work difficult, especially where
visible shaking interferes with the usefulness of oscillations of small amplitude. I
doubt if a practical gain is to be obtained by the use of hydrogen, and I am sure that
a high vacuum is out of the question. The only remedy, therefore, is to employ
larger suspended balls, and with them a longer beam. For the same argument that
shows that with any length of beam the limit of sensibility imposed by the strength
of the fibre is increased by reducing the weight of the suspended balls, for the rigidity
of a fibre varies nearly as the square of its strength, shows also that if the fibres are
not far from their breaking weight, the size of the balls cannot be increased without
reducing the sensibility. _ But increase of size would be advantageous because, while
the forces depend upon the cube of the diameter, the resistance to movement depends
upon the square. The result is a less serious decrement with larger balls. Now, in
order to employ these -and yet maintain the period with the necessarily stronger
fibre, a longer beam must be employed. Of course, unless the diameter of the large
attracting balls are increased in the same proportion the angle of deflection will fall.
I do not think that the beam needs to be lengthened to more than about two
inches. If this length were adopted it would be better to aim at 5 centims., for since
this is half a decimetre, a more accurate determination of the length could be obtained
by reference to the standard decimetre at Sevres, than would be possible if it were not
very nearly an exact submultiple. Whether or not the lead balls and the whole
apparatus should be doubled in size is a mere question of cost. The expenses
would run up very rapidly with very moderate increase of sensibility. I should feel
disposed to be content with lead balls about six inches in diameter, but I would
certainly have an Elmore tube for the centre one T, and, by preference, for the large
eylinder C. The slight diminution of angular deflection which would result from this
change, would be more than compensated by the doubled optical definition, but there
might be some difficulty in obtaining a thin rectangular mirror 5 X 1 centims., in
which no optical defect could be detected.

It may appear that I am reversing all my arguments and practice in now advocating
an increase of size, but it must be remembered that the object is not so much to
increase the sensibility, or even to be able to make better geometrical determinations,
for both of these, in my apparatus, exceed the square of the periods in the degree of
accuracy with which they are known. The object is solely to be less influenced by
the viscosity of the air, but this would not have limited the accuracy of my periods so
seriously if I had not been disturbed by trains.

I should have had less confidence in this doubling of the size, if my supposition
that the disturbing moments, due to convection, were proportional to the seventh

NEWTONIAN CONSTANT OF GRAVITATION. i

power of the linear dimensions, had been correct. Since it varies only as the fifth
power, and the quietness of the air is so great in my apparatus (p. 11), there can be
no objection on this account to the double size; but I would strongly urge that in
such a case, a room more uniform in temperature than the one at Oxford should be
employed. It would also be well to lay non-connecting mats on those parts of instru-
ments on which the hands are apt to rest when the balls are being transferred, or
other manipulative operations are being carried out, so as to reduce, as far as possible,
access of heat, and hence the interval that must elapse before observations of
deflections or periods can be undertaken. I do not think any ready-made room is
likely to be found available. A disused adit, at a great distance from existent
mining operations, would be perfect, if it could be made use of. The instrument
could then be walled up in a room to itself, and the heat from the observer and the
travelling lamp excluded far more perfectly than in my case. An adit would be
convenient also, in that it would allow of the use of a greater distance from the scale
to the mirror than could be obtained in an ordinary room. This should not be less
than 20 metres.

I should recommend a slight change in the upper end of the lid pillars with the
object of giving the ball holder two adjustments, one radially, and one at right angles
to a radius, so that eccentricities observed by the microscope of the optical compass
could be corrected.

I also think more pains should be taken with the beam mirror to insure its rotating
about its own centre of gravity, both when the gold balls and when the counter-
weight are suspended. This would remove any doubt as to its constancy of move-
ment of inertia when made to oscillate under the three conditions, and would at the
same time make observable eccentricity of the gold balls impossible.

Finally, I have suffered much from the great loss of time that results from the
accidental fall of a gold ball down the central tube. It can only be replaced after
lifting out the torsion head, torsion fibre, and beam mirror, so that all the centering
adjustments are lost, besides which, there is the serious risk of breaking the torsion
fibre whenever this operation is carried out. I would make the lower end of the
central tube funnel-shaped inside, and employ a much larger holding down screw,
with a central hole more than large enough to allow the gold ball to escape through
it. This could, of course, be plugged at other times. In order to put the gold balls
into their places without removing the torsion fibre, I would have a large hole in the
torsion head behind (away from the big telescope) the torsion rod, and this would be easy
with the larger central tube. Then if a special overhead wheel were placed with its
edge vertically over the centre of this hole, the gold ball could be let down as
described in the paper and transferred, as usual, on to one of the side hooks by the
use of a simple tool made of a bent pin.

In every other respect the apparatus behaves so perfectly, and the operations are
conducted with such facility, that I am unable to offer any other useful suggestion.

2A ON THE NEWTONIAN CONSTANT OF GRAVITATION.

DESCRIPTION OF PLATES 1 AND 2.

PLATE 1.

Fig. 1 is a vertical section, and fig. 2 a sectional plan of the apparatus. Fig. 3 is a front view of a
portion of it. Figs. 4, 5, 6 show details of the lid, pillars, and ball-holders on a larger scale. Fig. 7
represents the beam-mirror, counterweight, and eye-hooks full size. Figs. 8 to 10 show the window
apertures in the central tube, beam raiser, &c., on a larger scale. Figs. 11 and 12 are the front and
back windows used when deflections and periods are being observed. Figs. 13 and 14 show the back
window for use with the optical compass. Fig. 15 represents the tubular screens; figs. 16 and 17, the
mould for pressing the 44-inch lead balls.

PLATE 2.

Figs. 18, 19, 20, and 21 are plan, side, and end elevations of the cellar with the apparatus in position.
Fig. 22 is a horizontal section of the octagon house, the position of the apparatus being shown in dotted
lines. Fig. 23 is an isometric projection of the geometrical clamps holding the scale and dummy.
Figs. 24, 25, 26 are plan, front and side views, of the rotating and focussing slides and scale of the
optical compass in position on the lid of the instrument, which is represented in chain lines. Figs. 27,
28, 29 are plan, front and side views, of the traversing slides and microscopes of the optical compass in
position on the focussing slide, which is represented in chain lines.

ScALE oF Fries. PLATES 1 AND 2.

|
Scale . : | t a 3 1 | + inch to foot. |
Figure hrhal 1 4 7 18
16 2 5 | 19 |
17 3 6 20
22 | 24 8 21
23 | 25 | 9 |
26 10
| 27 11
28 12
| 29 | 3 |
| | 14

beat

Toye: | Phil. Trans. 1895.A. Plate 1.

Fig.l6.

Section or @.(..a.

s YI

vo

LZ

SSSSSSSSS ee MW

La
ALLL Na

ee
I. Wa

cs =

KC

N

West, Newmar photo lath.

Phil. Trans. 1895. A. Plate2.

{

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ms th.

West, Newman shoto li

Phil. Trans. 1895.A. Plate 2.

al

| Boys.

Scale of Feet

be 8 od

II. On the Photographic Spectrum of the Great Nebula in Orion.

By J. Norman Lockyer, C.B., F.R.S.

Received June 13,—Read June 21, 1894.

CoNnTENTS.

PAGE.
ee Descriptionofabheyphovoora ph sire waren wemr teria enn y ar iierie es i sunny ar lnton Dairies ((3
leptablerotwaveclensthse mote. ce sack mb ater Meh ty hase ae ee Rec a eel
III. The origins of the lines recorded . . . . . AD lauperee SSMaL tint mig fensse | ies eet cm CDH Lf
IV. The variation of the spectrum in ‘different regions 1 themebul ae wee seca eet Seed S
Y. Discussion of the results in relation to the meteoritic hypothesis . . ...... 81
(a) The complex origin of the spectra of nebule . . .......2,.7 ~. «282
(b) The passage to bright-line stars . . cot Nap einsitae: Wana aoe ica rot enmea eee fara aittoy™
(c) Relation to stars of Groups II. and III. Ne eaienebi lly iets ess sila Orisa ee leon ota)
WeleeGeneraliconclusionsi, PRVIths, otk cheat eats hc ae Meet aINaR a teenth Sem riage “EAERA Synet neta, SQ)T!

J. DESCRIPTION OF THE PHOTOGRAPHS.

Iv February, 1890, I communicated to the Royal Society a preliminary note on some
photographs of the spectrum of the Orion Nebula, taken at Westgate-on-Sea.*

The detailed discussion of the photographs has been reserved with the hope of
securing others, but owing to other pressing work no further photographs have been
obtained.

As the photographs in question show a greater number of lines than others which
have been described, and especially as they appear to have an important bearing on
the study of certain types of stellar spectra, I have thought it desirable that the
publication of the results should no longer be delayed.

The instrument employed was the thirty-inch reflector, and a spectroscope by
Hineer, having one prism of 60° and two half-prisms of 30°.

Mawson’s instantaneous plates were used. The exposures were carried up to four
hours, and five photographs were taken, some of them with shorter exposures than
that named, in consequence of the sky becoming clouded or irregularities in the driving

* «Roy. Soc. Proc.,’ vol. 48, p. 199.
MDCCCXCV.—A, L 5 3.95

74 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

clock, which was not then completely finished. One plate was exposed for four hours,
on February 11, 1890, but, unfortunately, in consequence of the high wind, the slit
was covered for an unknown part of this time by the velvet used to keep out stray
light, and this was not at once discovered, as the finder for directing the telescope is
at the lower end of the reflector tube, away from the spectroscope. This photograph
only shows three or four of the more prominent lines, but they are all sharply defined.
The other photographs were taken on February 2, 8, 9, and 10, the last with an
exposure of three hours.

As a collimator has not yet been fitted to the tube of the reflector the exposure of
the plate to the flame of burning magnesium was made by closing the mirror cover,
and burning magnesium at its exact centre. One half of the slit was exposed to the
nebula, and the other half to the burning magnesium.

The part of the nebula photographed was the bright portion in the region of the
trapezium. In some photographs, in consequence of clock irregularities, the stars
of the trapezium have imprinted their spectra upon the plates, but these in no way
interfere with the spectrum of the nebula, since a longish slit was used, and the
spectra of the stars are narrow.

There is a remarkable and almost absolute similarity between the photographs
obtained. The best one, taken on February 10, shows all the lines of the other
photographs with cthers in addition, and this has therefore been selected for the
determination of wave-lengths.

The probable mean position of the slit during the three hours’ exposure of this
photograph is shown in fig. 1, but the irregularities in the driving caused all the
stars in the trapezium to cross the slit at different times.

Fig. 1. Showing mean position of slit in photograph of February 10, 1890.

It has not been found possible to reproduce the negative with advantage in
consequence of its small size, but fig. 3 (see p. 80) gives a good idea of the appearance
of the eleven principal lines shown in the photograph, and the position of the stellar
spectra on the plate. Further reference to this diagram will be made later.

The principal lines are the three ordinarily seen in the visible spectrum, the lines of

SPECTRUM OF THE GREAT NEBULA IN ORION. 75

hydrogen at H,, H;, H., and H,, and the strong line in the ultra-violet near \ 373.
H, is by far the strongest line in the spectrum. The wave-length of the least
refrangible line on the photograph was taken as 5006°5, as determined at Ken-
sington, and this, together with the hydrogen lines, the line at 44471, and the
ultra-violet magnesium triplet in the comparison spectrum, formed the basis of the
curve for determining the positions of the fainter lines. The photograph was
measured with a micrometer reading to 0°00001 inch.

All the lines are shown in the table which follows. In all, fifty-four lines have
been recorded, and, of these, about twenty are seen without difficulty. The remainder
require a favourable light, but no line has been inserted in the table which has not
been measured several times by two observers. The spectrum extends from the
ultra-violet to the green, and the intensities of the lines on the photographs
naturally do not correspond to the visual ones; the F line, for instance, appears
stronger than the brightest line in the visible spectrum at 15006. The photographic
intensities are recorded in the table, six representing the strongest and one the
feeblest line.

Some of the wave-lengths referred to in the preliminary paper have been slightly
changed by the new reduction.

76 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC
Il. TABLE oF WAVE-LENGTHS.

Tasie [.—Lines Photographed in the Spectrum of the Orion Nebula, Feb. 10, 1890.

Micrometer Wave- Photographic | Probable | Wave-length of pro- Re
: 5 : Sits me marks.
reading. length. intensity. origins. bable origins.
3°3672 3707 2
3 8632 8715 1
3°3565 3729 6
33455 | 3743 ul |
3°3410 | 3752 | 1 A 3749°8 H,,
3°3310 3770 | 1 H 3769°4 H,
3°3200 | 3796 2 H 3796-9 Hg
3°3020 383 2 H 38345 H,
3°2950 | 3847 ut
3°2910 3855 | 1
3°2850 | 3868 | 4
3°2762 | 3887 + H 3887°8 He
3°2690 3902 2
3°2656 3910 1
3°2565 3933 2 Ca 3933 K line, Solar Spect.
3°2525 3941 | 1
3°2495 3949 | 1
3:24.15 3968 | 5 Ca 38968 H.
3°2356 3984 1
32295 4.000 3
3:2251 4010 2
3 2197 4025 3
3°2136 | 4041 1
372185 | 4054. 2
32035 | 4067 2
31969 | 4086 1
Ss 1915 | 4101 6 H 4101 Hs
31849 | 4120 1
31818 | 4129 1
31771 4142 1
31722 4154 2
31682 4167 1 |
3°1560 42.04. 1
31491 4226 1 (Cer | 4.226 Flame line
31464 4234 H | |
| 31360 4269 2 | |
| 31160 4340 6 H 4340 Hy
3-103 4385 1 | Fe 4383 Strongest flame line of
3° 1020 4389 2 iron
| 30972 4410 ] |
3:0929 4426 2 |
30810 4471 4 | Lorenzonr’s f.
30750 4495 3 |
30645 4539 2
| 3:04.50 4.627 2
| 3:0275 4715 2
| 3:0230 4735 1 C 4736
3°0070 4824. 3
| 3°0040 4839 2
| 3°0000 4861 6 ace | 4861 He
2:9935 4897 3
2-9892 4.923 3
2°9835 4957 4
2:9750 5006°5 5 Mg 5006°5 “Chief ” line

SPECTRUM OF THE GREAT NEBULA IN ORION. Ot

Ill. THe Ortcins oF THE LINES.

Tt will be seen from the table, that hydrogen enters largely into the composition of
the vapours of the nebula. H, H,, H;, H., and the ultra-violet series, certainly as far
as H, (new notation),* are all present.

It is worthy of remark, however, that while, as previously stated, H, is the strongest
line in the whole spectrum, and H,, H;, and H, are also strong, the ultra-violet
hydrogen lines are amongst the weakest.

Next to H,, the line \ 373 is the most intense. In 1887, I suggested that this line
was one of the members of the triplet seen in the spectrum of burning magnesium.
As I stated in a preliminary communication, the wave-length could not be finally
determined from the photographs already obtained, but it was probably near ) 3729.

This value, however, will require correction for motion in the line of sight. If Mr.
KEELER'S valuest for the motion be accepted, and the earth’s orbital velocity be
allowed for, the correction will be about 0:22 tenth metres towards the red. This will
bring the nebular line slightly nearer the least refrangible member of the magnesium
triplet. Further measures of photographs taken with higher dispersion are necessary
in order to settle this point.

The lines next in importance to those already mentioned, are near wave-lengths
4471, 4495 and 3868. The first of these, the strongest between H, and H,, is
probably the line observed by Dr. CopELAND in 1886. With reference to this line,
I wrote as follows in a paper communicated to the Royal Society on Nov. 9, 1889.1

“The observations of Dr. CopELAND have now, I think, established the identity of
the yellow line, in the nebula of Orion at all events with D;. In a letter to
Dr. CopELAnD, I suggested that the line at \ 447 was, in all probability, LoRENzont’s
f of the chromosphere spectrum, seeing that it was associated both in the nebula and
chromosphere with hydrogen and D,. This he believes to be very probable. The line
makes its appearance in the chromosphere spectrum about 75 times to 100 appearances
of D,, or the lines of hydrogen.”

For the other strong lines near ) 3868 and ) 4495, no origins have been found.

From the final reduction of the photographs, as given in the table, it appears that
the line formerly said§ to be “near \ 4027,” is at 44025. It can, therefore, no
longer be attributed to manganese. Its origin is at present unknown, but, as will
appear later, it is a line frequently met with in the spectra of other celestial bodies.
The line at \ 4690 referred to above, does not appear in the revised list, which only
contains lines measured without great difficulty. Further, only a small proportion of
the lines now mapped can be ascribed to metallic origins, but these, it will be seen, are

* Voce, ‘ Ast. Nach.,’ 3198, 1893.

+ ‘Roy. Soc. Proc.,’ vol. 49, p. 400, 1891.
£ Ibid., vol. 47, p. 30.

§ Ibid., vol. 48, p. 200.

78 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

the chief lines in the spectra of the elements concerned. The table shows that a large
number of the lines appear to have no terrestrial equivalent, but they are present in the
spectra of other celestial bodies. These coincidences are discussed in a subsequent part
of the paper.

IV. THe VARIATION OF THE SPECTRUM IN DIFFERENT REGIONS OF THE NEBULA.

The earlier investigations of the photographic spectrum of the Orion Nebula
seemed to indicate that the spectrum was different for different regions.

In my own observations in 1891, with the 30-inch reflector at Westgate, the
variations were very striking.

I stated in a paper communicated to the Royal Society in December, 1889,* “TI
obtained momentary glimpses of many bright lines between H, and H,, on October 31.”
These were also seen by Mr. Fow Ler, and it was observed that, as the nebula was
swept across the slit, in some parts the lines were seen together, while in other parts
first one group and then another made their appearance. In the same paper I
referred also to the variations in the same field of view of some of the lines. These
observations were made with an enlarged form of pocket spectroscope, with a
dispersion that does not split D. I found that in certain parts of the nebula, in the
same field, certain lines were knotted, as often seen in prominences on and off the sun,
and in other parts broken ; in the former case, whilst the F line thickened equally on
both sides, the chief nebular line thickened only on the more refrangible side.t

This result is shown in fig. 2.

* ‘Roy. Soc. Proc.,’ vol. 48, p. 195.

+ In another paper (‘ Phil. Trans., ’A, 18938, vol. 184, p. 714), I wrote as follows with regard to the
chief line: “I have convinced myself of the fluted nature of the line by new observations made with
instruments best fitted to show it, while the Lick telescope is, perhaps, the ideal telescope not to employ
in such an inquiry. Hence, although the visibility of magnesium is not fundamental for my argument,
I still hold that it is more probably the origin of the nebular line than an unknown form of nitrogen.”
The recent remarks of Professor Krrier (‘ Ast. and Ast. Phys.,’ January, 1894, p. 61), and Mr.
CampBeE.t (‘ Ast. and Ast. Phys.,’ May, 1894, p. 385), as to the relative efficiency of telescopes in regard
to the observation of spectrum lines, seem to indicate that the matter has not been sufficiently thought
out. I have not seen a statement as to the percentage of light utilised in the case of the Lick telescope,
but I may say that at the time my observations were made, the mirrors of my telescope were newly-
silvered, so that probably only a small percentage of light was lost. Neglecting the loss of hght due to
absorption in the case of the refractor, and to reflection in the case of the reflector, the brightness of the
image formed on the slit of the spectroscope by the Westgate telescope is about sixteen times that of
the imaye formed by the Lick telescope, and it is scarcely necessary to add that having this great
illuminating power, the collimator of the spectroscope has been designed to take full advantage of it.
[Professor CAMPBELL, who has succeeded Professor KEgLEer at the Lick Observatory, is of the same
opinion as myself. He writes (‘Astr. and Ast.-Phys.,’ 1893, p. 53): “The 36-inch telescope presents
several positive disadvantages. . . . . The ratio of the focal length 19:1 is much larger than
exists in small telescopes, and hence the latter would form much brighter images on the slit plate.”
Note added 4.1.95. ]

SPECTRUM OF THE GREAT NEBULA IN ORION. 79

This was confirmed by Messrs. FowLer and Baxanpatt at Kensington, with the
10-inch equatorial, on October 31 and November 1, and again by Mr. Fow er with
the 30-inch on November 2.

Fig. 2. Difference in the appearance of the lines at 4862 (F) and 5006'5.

It is also recorded in the Observatory note-book that at times these lines appeared
of unequal length, the spectroscope employed in the observations having a long slit,
and that sometimes 500 and 495 were seen without H,. In the photographic
investigation of variations in the spectrum, the question is complicated by differences
in sensitive films, and in the case of a silver-on-glass reflector by the conditions of
the mirrors. My own experience has shown that when mirrors are tarnished, the ©
ultra-violet portion of the spectrum is weakened in greater proportion than the violet
and blue.

One of the most striking variations previously recorded is that of the strong line
in the ultra-violet near \ 373. This was the strongest line in the photograph taken
by Dr. Hucerns in March, 1882,* but it was not shown in Dr. Draper's photograph
taken in the same year.t

Dr. DRAPER says: “I have not found the line at 3730, of which he (Dr. Hucers)
speaks, though I have other lines which he does not appear to have photographed.
This may be due to the fact that he had placed his slit on a different region of the
nebula, or to his employment of a reflector and Iceland spar prism, or to the use of a
different sensitive preparation. Nevertheless, my reference spectrum extends beyond
the region in question.”

A later photograph (1889), taken by Dr. Huaains,t did not show the line in
question, the slit being placed on a different part of the nebula. As already stated,
the line is one of the strongest in my photographs, though it is not quite as strong as
Hy. The spectrum photographed by Dr. Huccins, in 1889, differed entirely from
those photographed by him in 1882 and 1888, the slit being again placed on a
different region of the nebula.

My own photographs are specially interesting, as they indicate differences even in
the small area of the nebula which is covered by the slit during a single exposure.

* ‘Roy. Soc. Proc.,’ vol. 33, p. 427.

+ ‘Amer. Journ. of Science,’ vol. 23, p. 339.
ft ‘Roy. Soc. Proe.,’ vol. 46, p. 41.

80 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

5

Some of the more important variations are indicated in fig. 3. The stars, the spectra
of which are registered on the plate, will be readily identified by a comparison of
figs. 1 and 8, the spectra of the trapezium stars being shown at the bottom of the
diagram, and that of the star G. P. Bonp 685 (HERSCHEL’s €) at the top.

It will be seen, for example, that the line near ) 495 falls off in intensity about
the middle of its length, while the lines of hydrogen show no such reduction in the
same part of the nebula. If we first consider the phenomena, in the neighbourhood
of the star G. P. Bonn 685 (HERSCHEL’S e), near the trapezium, it will be seen
that here the lines 4471 and 4495 are most intense. In this region there is also a
distortion of the two lines at 4471 and 4495; they are sharply bent towards the
red end of the spectrum, whilst the other lines remain straight. Unfortunately, the
spectrum of this star is only shown on the photograph of February 10, and, in the
absence of other photographs, it is possible that the displacement of the two lines in
question may be due to a distortion of the gelatine film. The displacement of the
lines, if real, would indicate a velocity of about 200 miles per second, in the line of
sight. Both lines are brightest where they are most disturbed.

Fig. 3. Diagram showing the principal lines in the photograph of the spectrum of the Orion nebula,

February 10, 1890, with their relative intensities. The spectra of the stars in the trapezium are
shown at the bottom of the diagram, while that at the top is the spectrum of the star Bonp 685.

It will be seen, also, that where the lines of the nebula cross the continuous
spectrum of the star, they are considerably broadened. This is seen in all the
principal lines from d 378 to \ 495.

Where the chief line (500) crosses the spectrum of the star, there is a decided
indication of a reversal. As it approaches the star, the line bifureates and reunites
on the other side, leaving a short dark line where it crosses the spectrum of the star,
as shown in fig. 3. This reversal is not seen in the case of the hydrogen lines, but if
it be subsequently confirmed in the case of 500, it will be an indication that some of
the nebulous matter lies in front of the star in question (Bonp 685; HERSCHEL e).

SPECTRUM OF THE GREAT NEBULA IN ORION. 81

Coming now to the region of the nebula about the stars of the trapezium, it will be
seen from fig. 8 that the bright lines are considerably widened where they intersect
the spectra of the trapezium stars. In this case the hydrogen line at \ 4340 is
widened very little on the less refrangible side, while, on the more refrangible side,
the widening is nearly as great as its own breadth. Further, on each side of the line
there is a decided break in the continuous spectrum of the stars, giving the appearance
of a broad absorption band, with the bright hydrogen line running through it. This
appearance is almost exactly reproduced at H;.

Dr. Draper* appears to have noticed a peculiarity in the hydrogen lines where
they crossed the spectra of the trapezium stars in his photographs of 1882. He says :—

“The hydrogen line near G, wave-length 4340, is strong and sharply defined ; that
at h, wave-length, 4101, is more delicate ; and there are faint traces of other lines in
the violet. Among these lines there is one point of difference, especially well shown
in a photograph where the slit was placed in a north and south direction across the
trapezium; the H, line, \ 4340, is of the same length as the slit, and, where it
intersects the spectrum of the trapezium stars, a duplication of effect is noticed. If
this is not due to flickering motion in the atmosphere, it would indicate that
hydrogen gas was present even between the eye and the trapezium.

“ T think the same is true of the H; line, \ 4101.”

The line at 500 is only feebly impressed in the neighbourhood of the trapezium
stars, and no reversal is visible.

It is clear, therefore, that the spectrum of the nebula varies very considerably in
different regions.

Y. Discussion oF RESULTS IN RELATION TO THE MeEtTEorRITIC HYPorHEsts.

In my paper, “On the Photographic Spectra of some of the Brighter Stars,” com-
municated to the Royal Society in November, 1892,t I made reference to the spectra
of nebulee in relation to the meteoritic hypothesis. The statements were based upon
an incomplete reduction of the photographs of the spectrum of the Orion nebula, and
I now proceed to show how the hypothesis bears the test when the final reductions
are considered.

On the hypothesis :—

(a) The normal spectrum of the nebule, including planetary nebule, should have
a complex origin.

(b) The bright-line stars are simply nebulee further condensed.

(c) With further condensation a group of stars of increasing temperature, with
spectra consisting of mixed bright and dark flutings, is produced.

(d) Still further condensation results in a group of stars of increasing temperature,
with spectra of dark lines, differing from the solar spectrum.

% ¢ Amer. Journ. of Sci.’ (3), vol. 23, p. 339, 1882.
+ ‘Phil. Trans.,’ A, 1898, vol. 184, p. 713.
MDCCCXCV.—A, M

82 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

(a) The Complex Origin of the Spectra of the Nebule.

As pointed out in the paper referred to, the bright lines should have three origins,
namely :—

(1) Non-condensable gases driven out of the meteorites.

(2) Low temperature vapours produced by a large number of feeble collisions.

(8) High temperature vapours produced by a small number of end-on collisions.

It will be seen from the tables that the requirements of the hypothesis in this
respect are fully satisfied.

The lines of hydrogen and the flutings of carbon are what we should expect from
the large interspaces ; the flutings of magnesium and the low temperature lines of
iron and calcium bring us face to face with phenomena connected with low tempera-
tures, and they may be ascribed to the partial collisions ; while the lines coincident
with chromospheric lines must be regarded as high temperature products, since the
solar chromosphere may be taken as indicating the spectrum we might expect to be
associated with the high temperature vapours produced by the end-on collisions.

The undoubted presence of the lines D, and \4471 left but little doubt as to the
chromospheric relationship of some of the lines in the nebular spectrum, but the flood
of new light thrown by the photographs taken with the prismatic cameras during the
total eclipse of the sun on April 16th, 1893, put the matter beyond all question.

The discussion of the eclipse photographs will form the subject of a separate
communication, but it may be here stated that the spectrum of the nebula shows a
number of coincidences with lines seen in the spectrum of the chromosphere and
prominences.

(b) The Passage to the Bright-Line Stars.

The association of the nebulee with the bright-line stars in the classification of the
heavenly bodies was, I think, first suggested by me in 1887.*

So far as the planetary nebulee are concerned, this grouping has been abundantly
confirmed by Professor Pickrrine’s work on the bright-line stars, and by the visual
observations of Professor KEELER.

Professor PrcKERINGt tabulates the lines, and concludes with the statement that,
“Owing to the similarity of the spectra of the planetary nebulee and the bright-line
stars, they may be conveniently united in a fifth type.” It is clear then, that in this
particular, Professor PrcKERING accepts my proposed classification.

Mr. KEELER writes,{ ‘‘ The spectra of the nuclei of the planetary nebule have a
remarkable resemblance to the Wotr-Raver and other bright-line stars, and an

* © Roy. Soe. Proc.,’ vol. 43, p. 144.
+ ‘Ast. Nach.,’ 3025, 1891.
t ‘ Proc, Ast. Soc. Pacific,’ vol. 2, No. 11, Nov. 29, 1890.

SPECTRUM OF THE GREAT NEBULA IN ORION. 83

intimate connection between these objects, if established by further observations,
would place the bright-line stars first in the order of development. The D; line
appears in the central condensation of a number of bright nebule, and with sufficient
light would probably be seen in many of them, and this line is also predominant in
most of the bright-line stars.”

One of the main points of this paper is to show that the relationship indicated
between the planetary nebule and bright-line stars also holds good for such a nebula
as that of Orion.

The bright lines seen in the visual spectra of the two classes of nebulee have long
been known to be identical, and a comparison of the Westgate photographs with the
results obtained by Professor PickERING, and the more recent work of GorHarD,* and
of Professor CAMPBELL, at the Lick Observatory, on the spectra of the planetary
nebulee,t has shown that the similarity also extends to the photographic region.

The fact that some of the nebular lines were apparently coincident with lines in the
bright-line stars, was recognized at an early stage in the reduction of the Westgate
photographs, and in the preliminary note I wrote as follows: ‘ It is a very striking
fact that some of the chief lines are apparently coincident, although the statement
is made with reserve, with the chief bright lines in P Cygni, a magniticent photo-
graph of which I owe to the kindness of Professor PICKERING; it is one of the
Henry Draper Memorial photographs.”

The bright lines here referred to were those of hydrogen, and lines at 4025 and
4471. All these have since been photographed at Kensington, in the spectrum of
P Cygni, and there is no longer any doubt as to their identity with bright lines in
the nebula. Additional bright lines in the spectrum of P Cygni, photographed at
Kensington, are also seen in the nebula, as shown in the following table :—

Tasie II.—Comparison of Orion Nebula with P Cygni.

Orion nebula. P Cygni (Kensington).
3968 3968 H.
4015
4025 4025
4035
4101 4101 Hs
| 4147
| 4340 4340 H,
| 4471 AAT 1
4715 A715
4840
486 | 4361 He
4.923 4923

* © Astr, and Ast.-Phys.,’ 1893, p. 51.
+ Ibid., p. 276.
M 2

84 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

Table III. shows in a complete form the details of the coincidences of the lines in
the spectrum of the Westgate photograph of the Orion nebula with those of
planetary nebule and bright-line stars, as given by PickERING and CAMPBELL.
Only those lines of the nebula which show coincidences are included in this table,
but the spectra of the planetary nebulee and bright-line stars are tabulated in full.*

it will be seen that all the lines of the planetary nebule, photographed by
PICKERING, appear in the Orion nebula, while of the twenty lines photographed by
CAMPBELL, twelve are present. Of fifteen lines in the spectra of the bright-line
stars, eleven appear in the nebula.

Tase II1.—Comparison of Orion Nebula with Planetary Nebulze and Bright-line

Stars.
Planetary nebule. Planetary Bright-line Bright-line Bright-line
Orion nebula. (CAMPBELL.) nebule. stars, Type I.| stars, Type II. | stars, Type III.
(Rowrann’s Seale.) | (Prckerinc.) | (PICKERING.) (PICKERING. ) (PICKERING. )
3868 (4) 3867-8
3887 (4) 3888 388 389 389
3949 (1) Ae af 395 ih 395
3968 (5) | 3969 397 398 397
4025 (3) 4026 He 402 4.02
4067 (2) 4.067 ae 406 406 407
4101 (6) 4102 410 410 410
4120 (1) an ie oye a 412
4204 (1) be “a 420 420 421
4340 (6) ABAL 434 4.34 434 434
sis 4363-4
4389 (2) 4390
4426 (2 a6 ae ate se 443
4471 (4) 4472-3 447 ie 44.7
bie os ae 451 451
Se 454 455 455
4574.
4.595
4610
4631-40 462 464 464
4663
ae 4686-8 25 469 469
4715 (2) 4714-6 470
i 4743
4861 (6) 4862 486 486 486
4957 (4) 4958
5006°5 (5) 5007 501

* Professor PickerinG has been good enough to furnish me with glass copies of his beautiful photo-
graphs of the spectra of some of the bright-line stars. The positions of the various lines which he
gives are in the main confirmed by the new measures which have been made at Kensington. I am in
communication with him as to additional lines which have been mapped.

[In consequence of the delay in printing this paper, I am enabled to state that Professor CAMPBELL has
communicated some most important observations to ‘ Astr. and Ast.-Phys.,’ 1894, p. 448, on the Wotr-
Rayer stars, which show that the number of coincidences with lines in the nebula of Orion and planetary
nebule is increased by 7.—Note added 4.1.95. ]

SPECTRUM OF THE GREAT NEBULA IN ORION. 85

(c) Relation to Stars of Groups II. and LIL.

With further condensation, the interspaces between the meteorites will be reduced,
and the bright-line stars will pass to stars with absorption spectra in which the dark
lines correspond with the bright lines of the nebulee. There will, however, be inter-
mediate stages (Group II. and the early stages of Group III.), as I have already
pointed out.* At these stages, some of the high-temperature lines do not appear
either as bright or dark lines, and this, no doubt, for the reason that the radiation
from the interspaces is masked by the absorption of the vapours in the immediate
neighbourhood of the meteoritic stones. In these stars the hydrogen lines are
normally feeble dark lines, but the amount of radiating area in a cross section is so
nearly equal to the amount of absorbing area that disturbances which, according to
the meteoritic hypothesis, produce the increase of light in the variable stars of the
group, are sufficient to make the hydrogen lines appear bright.

When we pass to the more condensed bodies, we find a group of stars, of which
y Cygni is a typical case, in which the dark lines are very numerous,t but different
from those which appear in the solar spectrum. This difference, however, is not
taken account of in VocEw’s classification of stellar spectra. It may be added that
photographs of the spectra of other stars resembling y Cygni have been obtained since
the date of the paper referred to.

At a still further stage of condensation we get stars in which there are only a
relatively small number of lines, and these are lines which appear in the nebule.
This similarity became evident at an early stage of the discussion of the photographie
spectrum of the Orion nebula, and a comparison with the spectrum of a Andromedze
was given in the paper communicated to the Royal Society, in November, 1892.1

The first suggestion of such a relation appears to have been made by Dr. ScHEINER,
of Potsdam,§ who pointed out that the strong line at \ 4471, which had been observed
in the Orion nebula by Dr. CopELAND, was also seen in the Potsdam photographs of
the spectrum of Rigel. This line is one of the brightest in the nebula photographs
now under discussion, and is seen in the spectra of a large number of stars of the type
of Rigel and Bellatrix.

The spectra of such stars in the region between K and 472 are described in my
paper referred to above; and in Table IV. they are compared with the spectrum of
the Orion nebula. It will be seen that out of 31 lines in the nebula in the region
compared, 20 are coincident with stellar lines.||

* © Phil. Trans.,’ A, 1893, vol. 184, p. 711. + Ibid., p. 698. ab) Tilak, (0) CUS),

§ ‘ Ast. Nach.,’ 2923, p. 328, 1889.

|| It may be added that D,, which appears bright in the nebula, was observed by Mr. Fowter asa
dark line in the spectrum of 7 and ¢ Orionis, on Dec. 12, 1893, and in Rigel on March 4, 1894. It does
not, however, appear in the spectrum of Sirius or # Lyre. Ds has also been photographed asa dark line
in the spectra of Band « Orionis, by Mr. Campsety at the Lick Observatory. ‘Astr. and Ast. Phys.,’ May,
1894 p. 395.

86

PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

Taste IV.—Comparison of Orion Nebula with Stars of Groups II. and IIL.
(Region K to \ 472 Angstrém).

Group IITy.
Orion nebula. |Group II.) Group IIIz.
| a Cygni. Rigel. Bellatrix. | 6 Orionis. | « Virginis.
|
K 3933 (2) | 3933-6 3933°6 3933 (6) | 3933 (6) | 3933 (8) | 3933 (1) | 3933 (1)
3941 (1)
3949 (1)
30 3961 (6)
Jo o6 a o¢ 3963 (2) | 3963 (8) | 3963 (2)
(He) 3968 (5) | 3968 3968 3968 (6) | 3968 (6) | 3968 (6) | 3968 (6) | 3968 (6)
3984.
ye oc 3994 (1) | 8994 (8) | 3994 (2)
4000 (3)
4010 ae 4008 (2) | 4008 (5) | 4008 (2) | 4008 ()
ae 4024 (2)
4025 (3) 4025 (1) | 4025 (8) | 4025 (6) | 4025 (4) | 4025 (4)
4041 (1) ae ; 4040 (2)
4054: (2)
4067 (2) 4069 (2) | 4069 (2) | 4069 (2)
“fs 4071 (2)
ie 4075 (2) | 4075 (2) | 4075 (2)
4086 (1) te 4088 (5)
00 a0 ye ae fe fe 4094 (2)
H3 4101 (6) | 4101 4101 410L (6) | 4101 (6) | 4101 (6) | 4101 (6) | 4101 (6)
we oo O° oC O° 4104 (2)
. oo 4114 (4)
ac oC 50 4119 (2)
4120 (1) | 56 4120°5 (2) | 4120°5 (4) | 4120°5 (2) | 4120-5 (2)
ny | 4121°5 (2)
56 | 4127 (3) | 4127 (8)
Ab) || S .. | 4180 (8) | 4180 (3) |
4142 (1) | 4143 4143 | 4143 (1) | 4143 (2) | 4143 (5) | 4143 (2) | 4143 (2)
4154 (2) | |
4167 (1) | Oc ais 4168 (8)
ee | 4172 (4) | 4172 (1) |} 4172 (1)
ae | 4177 (4) | 4177 () | 4177 Q)
420-4 (1)
4226 (1) |
4234 (1) | 4283 4233 | 4233 (5) | 4233 (2) | ie
06 ots ye | 4241-5 (2) 30 | 4241°5 (2)
iA : a lees .. | 4253 (2)
4269 (2) 6 o0 fe 4267 (2) | 4267 (4) | 4267 (1) | 4267 (1)
<i a ae | 4298 (3)
a oe MA 4302 (3)
aye 50 4307 (3)
ie 20 4314 (3) 00 ae 4314 (1) | 4314 (1)
= be 4337 (2 |
H, 4340 (6) | 4340 4340 4340 (6) | 4840 (6) | 4340 (6) | 4340 (6) | 4340 (6)
2) si S. .. | 4345 (2)
te a 4351 (4) | 4351 (1) | 4351 (2) | 4351 (a) |
4385 (1) | 4383 383 | 4383 (38) | (4)
4389 (2) | 4388 4388 | 4888 (1) | 4388 (8) | 4388 (5) | 4388 (2) | 4388
Se te fe 43943 (3) 6 43943 (2)
4410 (1)
fe : : oe 4414°5 (2) |4414°5 (1) | 44145 (8)

SPECTRUM OF THE GREAT NEBULA IN ORION. 87

Taste ITV.—Comparison of Orion Nebula with Stars of Groups IJ. and III,
(Region K to \ 472 Angstrém)—(continued.)

|

Group IITy.

Orion nebula. Group II.) Group IIIa.
|

|
|
|

| a Cygni, Rigel. Bellatrix, | 6 Orionis. | « Virginis. |
o6 pease 30 4417 (3) 00 4417 (2)
4426 (2) |
ac eoeacte 36 o¢ 50 4437 (3) |
4471 (4) | 4471 4471 4471 (1) | 4471 (4) | 4471 (6) | 4471 (5) | 4471 (4)
oc lenrea oe 4481 (5) | 4481 (5) | 4481 (8)
4495 (4) |
4539 (2) | 4541 45.4] 4541 (2) 4541 (1) | 4541 (1)
oe ES . 4549 (4)
4555°5 (3 fe 4553 (3)
4558°5 (3
a - 4583 (4) |
4627 (2) | 4629 4629 Aig) (8) || se 4629 (2)
4715 oc fe 56 Be 4714 (3)

In the accompanying map (fig. 4) an attempt is made to show the gradual change
of the bright lines of the nebulz and bright-line stars into dark ones as condensation
proceeds. Not all the lines seen in the various spectra, but only those which best
illustrate the results of progressive condensation, are dealt with. In the spectrum of
the Orion nebula and planetary nebule, the lines shown in the map are those which
afterwards appear as bright lines in the bright-line stars, or as dark lines in some of
the more condensed bodies. The lines mapped as belonging to the bright-line stars
are those which appear twice in Professor PICKERING’S lists, to which reference has
been made, except in the case of the important line at 4471, which has been
included because it appears in P Cygni as well as in one of PICKERING’s types of
bright-line stars. The dark lines shown in the spectra of stars of Groups II., II«.,
TIIg., Ily., 1V«., and IV£.,* are only those which show remarkable coincidences
either amongst themselves or with the bright lines at the foot of the map. The
approximate intensities of the various lines in the map are represented by their
thicknesses.

If we consider, first, the question of the hydrogen lines, it will be seen that they
begin to thin out as bright lines in the bright-line stars, and make their appearance
as thin dark lines in Group II. From Group II. to Group IV. they thicken pretty
regularly ; but other causes besides temperature may possibly affect their apparent
thickness, as I have previously pointed out.t

In addition to the lines of hydrogen, other lines, including the H and K lines of

* See ‘ Phil. Trans.,’ vol. 184, 1893, p. 725.
+ Ibid., p. 688.

88 PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

calcium, and the lines at \ 4388 and \ 4471, appear as dark lines at an early stage in
Group II.

Other lines, however, do not appear dark until a later stage; \ 4025, \ 4069, and
) 4269, for example, do not make their appearance as dark lines until Group IIIy.,
and others, such as 4205, do not appear until Group IV. is reached.

Some of the dark lines, as 14025 and 4471, have their maximum intensity in
Group IITy., whilst others are much less regular in their intensities in passing through
the different groups,

CRIV, & ANonoUcoe

javincitis
% ORIONIE

GR. tly yo

B

OR, Ms 76

GR. ill &TAURE

O ORIONIS

.l_ SRTLLINE STARS

GR.i, ORION NEBULA

CR.1, PLAN. NEBULA

Fig. 4. Diagram showing the gradual change of bright to dark lines in condensing swarms of meteorites.

In general, it may be taken that the absence of some of the lines from Group II.
and the earlier stages of Group III. is due to the approximate equality of the
radiating and absorbing areas of the vapours producing such lines.

With the aid of a series of photographs taken with special exposures, it is possible
to extend the comparison of the stars of Groups III. and IIIy. with the nebula into
the ultra-violet region of the spectrum. These photographs have been reduced by
Mr. SHackieton. The coincidences are shown in Table V. In this table Groups IT.

SPECTRUM OF THE GREAT NEBULA IN ORION. 89

and III. are omitted, for the reason that their spectra beyond K are only photo-
graphed with great difficulty.*

The wave-lengths of the lines of the nebula are copied from Table I., and are
expressed on CorNv’s scale ; those of the lines in the ultra-violet spectra of stars of
Group III. are based on wave-lengths of the ultra-violet lines of hydrogen on
RoWLAND’s scale, according to Professor HALE.t

The wave-lengths have been left in these different scales, because the differences
are only minute, and, in general, in the ultra-violet region, less than the assumed
accuracy of the wave-lengths as determined by the instruments at our disposal.

* Phil. Trans.,’ A, vol. 184, 1893, p. 701.
+ ‘ Astr, and Ast.-Phys.,’ vol. 11, 1892, p. 618.

MDCCCXCY.—A

90

PROFESSOR J. N. LOCKYER ON THE PHOTOGRAPHIC

Tape V.—Comparison of the Orion Nebula with Stars of Group III. in the
Ultra-Violet Region.

Orion nebula.

3707 (2)
3715 (1)
3729 (6)
3743 (1)
(Hx) 3752 (1)

(Hi) 3770 (1)
(H0) 3796 (2)

(Hy) 3833 (2)

3847 (1)

3855 (1)

Group IITy.

3868 (4)

(He) 3887 (4)

3902 (2)

a Cygni. Rigel. Bellatrix. 6 Orionis. a Virginis.
37118 (Hy) 37118 (Hv)
3721-9 (Hy) 37219 (Hn)
37342 (HX) 37342 (BX)
| 93750°2 (He) 3750°2 (He)
3770°8 (Hz) 3770°'8 (H1)
37981 (He) 37981 (He), 37981 (He) 37981 (He) 37981 (He)
| 3806°6 3806
3819°5 | 3819°5 3819°5
3820°2 |
38278 |
3829°5 |
3832:0 | |
3835°5 (Hy) 3835°5 (Hy) 3835°5 (H») 3835°5 (Hy) 3835'5 (Hy)
3838°3
3840°4.
3 3842°7
3845°5
3849°6
3853°6 38536
3856°1 3856'1 3856
3859°5
3862°8 38628
3865°6
3867-9 3867°5 3867
3869°8
3871-7 3871-2
3876°5
3878°7
3882°5
3889-14 (Ho) 38891 (H¢) 3889'1 (H¢) 3889'1 (Hc) 3889'1 (Ho)
3900°8 |
3903°4
3906°2
3913°5
39188
3919-2
3921
3926°7
3930:2 3929-4.
3931°8 3931-2
3933°6 3933°6 3933°6 3933°6 3933°6

i i

SPECTRUM OF THE GREAT NEBULA IN ORION. 91

VI. General Conclusions.

(1) The spectrum of the nebula of Orion is a compound one consisting of hydrogen
lines, low temperature metallic lines and flutings, and high temperature lines. The
mean temperature, however, is relatively low.*

(2) The spectrum is different in different parts of the nebula.

(3) The spectrum bears a striking resemblance to that of the planetary nebule and
bright-line stars.

(4) The suggestion, therefore, that these are bodies which must be closely
associated in any valid scheme of classification is strengthened.

(5) Many of the lines which appear bright in the spectrum of the nebula appear
dark in the spectra of stars of Groups II. and IIL, and in the earlier stars of
Group LV.; and a gradual change from bright to dark lines has been found. ~

(6) The view, therefore, that bright-line stars occupy an intermediate position
between nebulz and stars of Group III. is greatly strengthened by these researches.

I have to express my great obligations to Mr. Fowxer for the zeal and patience
which he displayed in taking the photographs under somewhat unfavourable con-
ditions. He is responsible for the determination of the wave-lengths of the lines and
has assisted in the discussion.

Messrs. BAXANDALL and SHACKLETON, computers to the Solar Physics Committee,
have assisted in the preparation of the tables and the map illustrating the changes of
spectrum with increasing condensation.

* © Roy. Soc. Proc.,’ vol. 43, p. 152, 1887.

II. Propagation of Magnetization of Iron as affected by the Electric Currents
in the Iron.

By J. Horxryson, F.R.S., and E. Witson.*
Received May 17,—Read May 31, 1894.

Part I.

Ir is not unfamiliar to those who have worked on large dynamos with the ballistic
galvanometer, that the indications of the galvanometer do not give the whole changes
which occur in the induction. Let the deflections of the galvanometer connected to
an exploring coil be observed when the main current in the magnetic coils is reversed.
The first elongation will be much greater than the second in the other direction, and
probably the third greater than the second—showing that a continued current exists
in one direction for a time comparable with the time of oscillation of the galvanometer.
These effects cannot be got rid of, though they can be diminished by passing the
exciting current through a non-inductive resistance and increasing the electromotive
force employed. This if carried far enough would be effective if the iron of the cores
were divided so that no currents could exist in the iron; but the currents in the iron,
if the core is solid, continue for a considerable time and maintain the magnetism of
the interior of the core in the direction it had before reversal of current. It was one
of our objects to investigate this more closely by ascertaining the changes occurring at
different depths in a core in terms of the time after reversal has been made.

The experiments were carried out in the Siemens Laboratory, King’s College,
London ; and the electro-magnet used is shown in fig. 1. It consists in its first form,
the results of which though instructive are not satisfactory, of two vertical wrought-
iron cores, 18 inches long and 4 inches diameter, wound with 2595 and 2613 turns
respectively of No. 16 B.W.G. cotton-covered copper wire—the resistance of the two
coils in series being 16°3 ohms. The yoke is of wrought-iron 4 inches square in
section and 2 feet long. The pole-pieces are of wrought-iron 4 inches square, and all
surfaces in contact are truly planed. One of the pole-pieces is turned down at the
end, which butts on the other pole-piece, for half an inch of its length to a diameter
of 4 inches; and three circular grooves are cut in the abutting face having mean

* The experimental work of this paper was in part carried out by three of the Student Demonstrators
of the Sizmexs Laboratory, King’s College, London, Messrs. Brazit, Arcuison, and Greennam. We
wish to express our thanks to them for their zealous co-operation.

19.2.90

04 7.
0) D 10 () 5 0
OT§a afte, Reversal, Seco, a Vevers

Ne ae

f su) 5 0 a} 5 T 10
Veco, n > Peversn Se onds after| Reverse

4 S| 2)5 “Ho

Ss

VR | Of pet VR | [ae] APT dale.

ELLYN ELT

BS A is
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SESS
= |S N S
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67349 s9dde

Ds

Beeee

Amperes in nail Winding. =

rs

PROPAGATION OF MAGNETIZATION OF IRON,

95

Mec leale eol [e |
ee Pe) ee ei
_ fae eee

SL nl \ewsrbaemecn secre | | | |

|e ea ae

Voll

PTR CL ee

_, JENS E Rae
WN Pes

CAP IFR

mse aia
eer | Sar
(Se

_eecnas reer revertat.| | | |

96 MESSRS. J. HOPKINSON AND HE. WILSON ON THE

diameters of 2°6, 5°16, and 7°75 centims. respectively, for the purpose of inserting
copper coils the ends of which are brought out by means of the radial slot shown in
fig. 2. When the pole-pieces are brought into contact as shown in fig, 1, we have
thus three exploring coils within the mass and a fourth was wound on the circular
portion outside. These exploring coils are numbered 1, 2, 3, 4 respectively, starting
with the coil of least diameter.

Fig. 3 gives a diagram of the apparatus and connections, in which A is a reversing
switch for the purpose of reversing a current given by ten storage cells through the
magnet windings in series; B is a Thomson graded galvanometer for measuring
current ; and C is a non-inductive resistance of about 16 ohms placed across the
magnet coils for the purpose of diminishing the violence of the change on reversal.
The maximum current given by the battery was 1:2 amperes. A D’Arsonyal gal-
vanometer of Professor AyRton’s type, D, of 320 ohms resistance; a resistance
box E; and a key F were placed in circuit with any one of the exploring
coils 1, 2, 3, 4, for the purpose of observing the electromotive force of that circuit.
The method of experiment was as follows :—The current round the magnet limbs was
suddenly reversed and readings on the D’Arsonval galvanometer were taken on each
coil at known epochs after the reversal. The results are shown in fig. 4, in which
the ordinates are the electromotive forces in C.G.S. units and the abscissee are in
seconds.

The portion of these curves up to two seconds was obtained by means of a ballistic
galvanometer having a periodic time of fifty seconds, the key of its circuit being
broken at known epochs after reversal. From the induction curve so obtained the
electromotive force was found by differentiation.

The curve A which is superposed on curve 4 of fig. 4 gives the current round the
magnet in the magnetizing coils. It is worth noting, that, as would be expected, it
agrees with the curve 4. The potential of the battery was 1:2 amperes xX 16°3 ohms
= 19°6 volts. Take the points two seconds after reversal, the electromotive force in
one coil is 330,000 ; multiplying this by 5208, the number of coils on the magnet, we
have in absolute units 1,718,640,000 as the electromotive force on the coil due to
electromagnetic change, or, say, 17'2 volts. Subtracting this from 19°6 we have 2:4.
The electromotive force observed is 125 X 16°3 = 2°02. The difference between
these could be fully accounted for by an error of + second in the time of either
observation.

The general character of the results was quite unexpected by us. Take coil No. 2
for example, the spot of light, on reversing the current in the magnet winding, would
at once spring off to a considerable deflection, the deflection would presently diminish,
attaining a minimum after about 6 seconds; the deflection would then again increase
and attain a maximum greater than the first after 8 seconds, it would then diminish
and rapidly die away.

To attempt a thorough explanation of the peculiarities of these curves would mean

PROPAGATION OF MAGNETIZATION OF IRON. 97

solving the differential equation connecting induction with time and radius in the iron
with the true relation of induction and magnetizing force. But we may inversely from
these curves attempt to obtain an approximation to the cyclic curve of induction of
the iron.

Let 7 be the mean length of lines of force in the magnet. Let n be the number of
convolutions on the magnet, and let c be the current in amperes in the magnetizing
coils at time ¢. Then at this epoch the force due to the magnetizing coils is 4mnc/10/.
Call this H).

Next consider only one centimetre length of the magnet in the part between the
pole-pieces which is circular and has coils 1, 2, 3, wound within its mass, and coil
4 wound outside. The area of each of the electromotive force curves of the coils 1, 2,
3, 4, up to the ordinate corresponding to any time, is equal to the total change of the
induction up to that time. ,

In fig. 2 let Aj, Ay, As, A, be the areas in sq. centims. of coil 1 and the ring-shaped
areas included between the coils 1, 2, 3, 4 respectively. Then the induction at time ¢,
as given by the integral of curve 1, divided by A, is the average induction per
sq. centim. for this epoch over this area. Also, the induction at time ¢, as given by
the integral of curve 2, minus the induction for the same time, as given by the
integral of curve 1, divided by Aj, is the average induction per sq. centim. for this
area. Similarly, average induction per sq. centim. for As, A, can be found for any epoch.

Consider area A,. It is obvious that all currents induced within the mass
considered external to this area, due to changes of induction, plus the current in
the magnetizing coil per centim. linear, at any epoch, go to magnetize this area, and,
further, the induced currents in the outside of the area A, itself go to magnetize the
interior portion of this area. We know the electromotive forces at the radii 1, 2, 3,
4, and the lengths in centims. of circles corresponding to these radii. From a know-
ledge of the specific resistance of the iron we can find the resistance, in ohms, of rings
of the iron corresponding to these radii, having a cross-sectional area of 1 sq. centim.
Let these resistances be respectively 1), 72, 13,7, At time ¢, let e,, e, es, e, be the
electromotive forces in volts at the radii 1, 2, 3, 4, then 2s 5 = ; ah, = are at this

1 2 3 4

epoch the amperes per sq. centim. at these radii. Let a curve be drawn for this epoch,
having amperes per sq. centim. for ordinates and radii in centims. for abscissee. Then
the area of this curve, from radius 1 to radius 4, gives approximately the amperes per
centim. due to changes of induction, and (neglecting the currents within the area
considered) the algebraic sum of this force (call it Hy), with the force due to the
magnetizing coils (H,) at the epoch chosen, gives the resultant magnetizing force
acting upon area A,. If H is this resultant force, we have H=H,+ H, Next
draw a curve showing the relation between the induction per sq. centim. (B) and the
resultant force (H) for different epochs. This curve should be an approximation to
the cyclic curve of induction of the iron.

MDCCCXCV.—A. O

98 MESSRS. J. HOPKINSON AND E. WILSON ON THE
Fig. 10.

)ppe care

ares bie Co

Amp

Vig. 13a.

aaateaees

% 5

Fang zl
ay z |

SS = 1 Ls

7
1 End Gees ee Lee are
cae dela

Flagtt t
Fig. 16
N

3
aleceale = Bf

PROPAGATION OF MAGNETIZATION OF IRON. -| 9)

Fig. 12a.

ie lito 2
EO memeer |

100 MESSRS. J. HOPKINSON AND E. WILSON ON THE

The attempt to obtain an approximation to the cyclic curve of induction from the
curves in fig. 4 was a failure, that is to say, the resulting curve did not resemble a
cyclic curve of magnetization. This is due to imperfections of fit of the two faces, in
one of which the exploring coils are imbedded. That this imperfection of fit will tend
to have a serious effect upon the distribution of induction over the whole area is
obvious on consideration. Take the closed curve abcd in fig. 5, where AB is the
junction between the pole pieces. If the space between the faces was appreciable, the
force along be and ad in the iron could be neglected in comparison with the forces in
the non-magnetic spaces ab, cd. The magnetizing force is sensibly 4zc, where ¢ is the
current passing through the closed curve. This may be made as small as we please.
Therefore, the force along ab is equal to the force along de. In our case the space
between the faces is very small, but has still a tendency towards an equalizing of
the induction per unit area over the whole surface.

To test this the following experiment was tried. At a distance of 24 inches from
the abutting surfaces of the pole pieces four holes were drilled in one of the pole
pieces in a plane parallel with the abutting surfaces, as shown in fig. 6. By means of
a hooked wire we were able to thread an insulated copper wire through these holes,
so as to enclose only the square area A, which is bounded by the drilled holes and has
an area of ‘61 sq. inch. The wire is indicated by the dotted lines. Fig. 7 gives two
curves taken by the D’Arsonval in the manner already described for a reversal of the
same current in the copper coils of the magnets. No. 1 (fig. 7) is the curve obtained
from No. 1 coil (fig. 2) near the air space. No. 2 (fig. 7) is the curve obtained from
the square coil shown in fig. 6. The difference is very marked and shows at once the
effect of the small non-magnetic space which accounts for the large initial change of
induction previously observed on the coils 1, 2, 3 in fig. 4. Similar holes were drilled
in the yoke of the magnet in a plane midway between the vertical cores, having the
same area of ‘61 sq. inch; and on trial exactly the same form of curve was produced
as is shown in No. 2 of fig. 7. This method of drilling holes in the mass is open to
the objection that the form of the area is square.

Whilst the above experiments were being made the portion of the magnet to take
the place of the pole-pieces previously used was being constructed as follows :—In
fig. 8 the portion of the magnetic circuit resting upon the vertical cores consists of a
centre rod A, of very soft Whitworth steel surrounded by tubes Ag, Ag of the same
material. The diameter of A, is 1 mch. ‘The outside diameter of A, is 25 inches;
and A, is 4 inches outside diameter between the cores of the magnet, but is 4 inches
square at each end where it rests upon the magnet limbs. At the centre of the rod
A, (longitudinally) a circular groove is turned down 1 millim. deep and 5 millims.
wide, and also a longitudinal groove 1 millim. deep and 1 millim. wide is cut as
shown in the figure for the purpose of leading a double silk covered copper wire from
terminal T, to 9 convolutions at the centre and along the rod to terminal T,. A
similar groove is cut in the outside of the tube Ay, and a copper wire is carried from

PROPAGATION OF MAGNETIZATION OF IRON. 101

terminal T, to 9 convolutions round the centre of the tube again along the groove to
terminal T,. Nine convolutions were also wound round the outside tube Ag, the ends
of which are connected to the terminals T;, T, respectively.

The tubes and rod were made by Sir J. WuitwortH and Co., of Manchester,
and a considerable force was required to drive the pieces into their proper position.
Our best thanks are due to Professor KENNEDY and his assistants for the putting
together of these pieces by means of a 50-ton hydraulic testing machine. We are
aware that the surfaces are somewhat scored by the hydraulic pressure, and the
magnetic qualities may be slightly different for layers of the soft steel near these
surfaces, but they serve just as well for the purpose of our experiments.

Fig. 8.

Systematic experiments were then commenced. The magnetizing coils on the
magnets were placed in parallel with one another, and a total current of 1°75 amperes
(that is, °87 ampere in each coil), due to 5 storage cells, was reversed through the
coils. The arrangement of apparatus is shown in fig. 3, except that the pole-pieces
are replaced by the soft steel tubes shown in fig. 8, and the non-inductive resistance
C is removed. We have now three exploring coils instead of four, and these are
marked 1, 2, 3 respectively, starting with the coil of smallest diameter. For the
purpose of obtaining the current curve, the D’Arsonval was placed across a non-
inductive resistance of $ ohm in the circuit of the magnetizing coils. Fig. 9 gives
a set of curves obtained with the 5 cells, and also another set obtained by a reversal
of 1°8 amperes given by 54 cells—a non-inductive resistance being placed in the
circuit to adjust the current.

The effect of reversing the same maximum current with two different potentials is
very marked. Take coil No. 1. With 5 cells the maximum rate of change of
induction occurs at 9 seconds after reversal, at which epoch the current in the copper
coils is about 1 ampere, the maximum current being 1°75. With 54 cells the
maximum rate of change of induction occurs at 4 seconds, and here the current in the
copper coils is nearly a maximum. We therefore chose to work with 54 cells, thus
avoiding a magnetizing force due to the current in the copper coils varying a
considerable times after reversal.

102 MESSRS. J. HOPKINSON AND E. WILSON ON THE

[o}

PSs SES
ia See
Zap a=

iN

tmperes tre Copper Coils. —

A

PROPAGATION OF MAGNETIZATION OF IRON. 103

Fig. 19a.

J2SSe eas
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Beye ee
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Secreta

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4
ait| t72 6

Benes
= a
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104 MESSRS J. HOPKINSON AND E. WILSON ON THE

Table I. gives a list of the experiments made with total reversal of current due te
54 cells, the magnetizing coils being kept in parallel with one another, and the
- magnitude of current through them adjusted by means of a non-inductive resistance.

In fig. 10 the maximum current in the copper coils is ‘0745 ampere, which, after
reversal, passes through zero and attains a maximum at about 3 seconds. It will be
observed that the change of induction with regard to each of the coils 1, 2, 3 is
rapid to begin with, but that it gradually decays and becomes zero at about 46 seconds
after reversal.

Fig. 11 is interesting in that it gives the particular force at which coils 1 and 2
show a second rise in the electromotive force curves, No. 1 being a maximum at
about 25 seconds, and No. 2 at about 8 seconds after reversal. These “humps”
become a flat on the curve for a little smaller force, and, as shown in fig. 10,
they have disappeared altogether. In this case the current in the copper coils has
attained a maximum at about 4 seconds after reversal.

In fig. 12 the maximum current in the copper coils is ‘24 ampere, corresponding
with a force in C.G.S. units of 4:96. This is got from = es The current
in the copper coils has attained its maximum value at about 4 seconds after
reversal, and changes of induction were going on up to 35 seconds.

In the following attempt to obtain an approximation to the cyclic curve of
hysteresis, from these curves, we bave taken the volume-specific resistance of the
soft steel to be 13 X 107° ohm. We have taken the diameter of coils 1, 2, 3 to be
respectively 1°22, 3°18, and 5:08 centims.,* and we find that the corresponding
resistances, in ohms, of rings of the steel having 1 sq. centim. cross-section and
mean diameters equal to the coils are, respectively, 103°7 x 107°, 259°4 x 107%, and
4164X10~°. From a knowledge of the electromotive forces at the three radu, for
a given epoch, we are able to find the amperes per sq. centim. at those radii. In fig.
124 a series of curves have been drawn for different epochs, giving the relation
between amperes per sq. centim. and radii in centims., and the areas of these curves
between different limits have been found, and are tabulated in Table II. It is
necessary here to state that the path of these curves through the four given points
in each case is assumed ; we have simply drawn a fair curve through the points.
But what we wish to shew is that the results obtained with the curves, drawn as
shown in fig. 12, are not inconsistent with what we know with great probability to
be true.

The results shown in fig. 12B have been obtained as follows: take curve ],
fig. 128; the electromotive force curve of coil 1, fig. 12, has been integrated,
and the integral up to the ordinate corresponding to any time is equal to the total

* Tn Part IJ. of this paper the smallest radius was taken to be 127. cr our purpose the difference

is not worth the expense of correction.

PROPAGATION OF MAGNETIZATION OF IRON. 105

change of the induction up to that time, which divided by the area of the coil in sq.
centims. gives the average induction per sq. centim. In obtaining the areas we had
to assume the path of the electromotive force curve up to 2 seconds, but this we can
do with a good deal of certainty.

With regard to the forces we see that after 3 seconds the induced currents have
to work against a constant current in the copper coils. In obtaining the forces due
to induced currents we have only taken the area of the curves in fig. 124 between
the radii 1°22 centims. and 5°08 centims. ; that is, we have neglected the effect of
the currents within the area of coil No. 1 altogether. The resultant force (H) is
the algebraic sum of the force (H,) due to the currents between the radii taken, and
the force (H,) due to the current in the copper coils, and is set forth for different
epochs in Table II. The inductions per sq. centim. have been plotted in terms of
this resultant force (H), and curve I., fig. 128, shows this relation.

Next, take curves II. and III., fig. 128. In obtaining the inductions for these
curves, the difference between the integrals of curves No. 1 and 2, fig. 12, for a given
epoch, has been taken. This gives the induction for this epoch, which, when divided
by the ring-shaped area between coils 1 and 2, gives the average induction per unit
of that area.

In obtaining the forces in curve IL., fig. 128, we have taken the areas of the curves in
fig. 124 between the radii 3:18 centims. and 5°08 centims.; that is, we have neglected
the forces within the area under consideration as before. Here the error is of more
importance, and may partly account for the difference between the forces of
curves I., IJ. In curve III. we have taken the areas of curves in fig. 124 between
the radii 2°2 and 5:08; that is, we have taken account of the force due to induced
currents over a considerable portion of the area considered. Coupled with the
uncertainty in form of the curves in fig. 124 we have the uncertainty as to how
much to allow for the forces due to induced currents over the particular area
considered. The difference in the ordinates of curves I. and II. may partly be
accounted for by errors arising from the assumed path of the electromotive force
curve up to 2 seconds, which is more uncertain in curve 2, fig. 12, than in curve 1 ;
and partly to possible slight inequality between the muterials of the rod and its
surrounding tube.

In fig. 13 the maximum current in the copper coils is ‘77 ampere, corresponding
with a force in C.G.S. units of 16. The current in the copper coils, after passing
through zero, attains its full value at about 9 seconds after reversal, and the change
of induction ceases at 19 seconds.

No. 1 curve, fig. 13, has been integrated, and the maximum induction per
sq. centim. found to be 14,500 C.G.S. units. We have taken a given cyclic curve
for soft iron corresponding with this maximum induction, and have tabulated the
forces obtained therefrom in Table ILI. for the different values of B got from the
integration of No. 1 curve. We then plotted in fig. 134 the amperes per sq. centim,

MDOCCCXCV.-—-A. P

106 MESSRS. J. HOPKINSON AND E. WILSON ON THE:

Fig. 20.

Fig. 20e.
B

PROPAGATION OF MAGNETIZATION OF IRON. 107
Fig. 21a.

Fig. 21.

SI s
os

Se
SS

Foe Hina |_|
Jada
ivi

Biles lobaliok |1f
= eae
Litt tt td

Walts | pe one. 0 |

DTT EE
LT festetelerlere| “|_|

108 MESSRS. J. HOPKINSON AND HE. WILSON ON THE

at the different radii for different epochs, and in each case, by drawing a curve fairly
through them, we were able to produce areas in fair correspondence with areas as
got by means of the given cyclic curve. The comparative areas are tabulated in
Table IIT.

In fig. 9 the maximum current in the copper coils due to the 54 cells is
1°8 amperes, corresponding with a force of 20°7 in C.G.S. units. In this case the
current had passed through zero and attained a maximum at 6 seconds after reversal;
the change of induction being zero also at this time. We have worked out the
current per sq. centim. for the different radii at different epochs, as before, and have
plotted them in fig. 94. Fig 98 gives the relation of B to H, found from the curves,
and it also shows a fair approximation to the cyclic curve for soft iron, although in
this case the points are fewer in number and were more difficult to obtain, owing to
the greater rapidity with which the D’Arsonval needle moved as compared with the
earlier curves.

With a reversal of 2°3 amperes the whole induction effects had died out at
5 seconds after reversal. Coil No. 1 showed a maximum electromotive force at about
34 seconds. Coil No. 2 gave a dwell, and attained a maximum at 2 seconds, and
then died rapidly away. Coil No. 3 attained an immediate maximum and died
rapidly to zero at 5 seconds.

With a reversal of 65 amperes the whole inductive effects had died out at about
3 seconds after reversal. No. 1 coil showed a maximum electromotive force at about
1? seconds. No. 2 gave a dwell and attained a maximum at about 14 seconds and
rapidly died away to zero at about 2 seconds. No. 3 attained an immediate maximum
and died rapidly to zero at about 2 seconds.

The variations in form of these curves and of the times the electromotive forces
take to die away are intimately connected with the curve of magnetization of the
material. When the magnetizing force is small (1°7) the maxima occur early because
the ratio induction to magnetizing force is small. As the magnetizing force increases
to 3 and 4°96 the maxima occur later because this ratio has increased, whilst when
the force is further increased to 16 and 37:2, as shown in figs. 13 and 9, the maxima
occur earlier because the ratio has again diminished.

The results, both of these experiments and of those which follow, have a more
general application than to bars of the particular size used. From the dimensions
of the partial differential equation which expresses the propagation of induction in
the bar, one sees at once that if the external magnetizing forces are the same in two
bars differing in diameter, then similar magnetic events will occur in the two bars,
but at times varying as the square of the diameters of the bars. But one may see
this equally without referring to the differential equation. Suppose two bars, one
n times the diameter of the other, in which there are equal variations of the
magnetizing forces ; consider the annulus between radii 7), 7, and n7,, nr, in the two,
the resistance per centimetre length of the rods of these annuli will be the same for

PROPAGATION OF MAGNETIZATION OF IRON. 109

their area, and their lengths are alike as 1:n; the inductions through them, when
the inductions per centimetre are the same, are as the areas, that is, as 1:n*. Hence
if the inductions change at rates inversely proportional to 1: n’, the currents between
corresponding radii will be the same at times in the ratio of 1: n”, and the magnetizing
forces will also be the same.

Magnets of sixteen inches diameter are not uncommon ; with such a magnet, the
magnetizing force being 37 and the magnetizing current being compelled to at once
attain its full value, it will take over a minute for the centre of the iron to attain its
full inductive value.

On the other hand, with a wire or bundle of wires, each 1 millim. diameter, and
a magnetizing force between 3 and 5, which gives the longest times with our bar,
the centre of the wire will be experiencing its greatest rate of change in about
soo second. This is a magnetizing force similar to those used in transformers, and
naturally leads us to the second part of our experiments.

Part I].—ALTERNATE CURRENTS.

This part of the subject has a practical bearing in the case of alternate current
transformer cores, and the armature cores of dynamo-electric machines.

The alternate currents used have periodic times, varying from 4 to 80 seconds, and
were obtained from a battery of 54 storage cells by means of a liquid reverser,* shown
in elevation and plan in figs. 14 and 15. It consists of two upright curved plates of
sheet copper, AA, between which were rotated two similar plates, BB, connected
with collecting rings, DD, from which the current was led away by brushes to the
primary circuit of the magnet. The copper plates are placed in a weak solution of
copper sulphate in a porcelain jar. The inner copper plates, and the collecting rings,
are fixed to a vertical shaft, S, which can be rotated at any desired speed by means
ot the gearing shown in the figure. The outer plates are connected to the terminals
of the battery of storage cells, and the arrangement gives approximately a sine curve
of current when working through a non-inductive resistance.

The experiments were made with the same electro-magnet and Whitworth steel
tubes described in Part I. of this paper. Fig. 16 gives a diagram of connections in
which M is the current reverser, G is the Thomson graded current meter for
measuring the maximum current in the copper coils, and W is the electro-magnet. A
small, non-inductive resistance, placed in the primary circuit served to give the curve
of current by observations on the D’Arsonval galvanometer, D, of the time variation
of the potential difference between its ends. The D’Arsonval galvanometer was also
used, as in Part I., for observing the electromotive forces of the exploring coils 1, 2,
and 3 (see fig. 8, Part 1.), R being an adjustable resistance in its circuit for the
purpose of keeping the deflections on the scale.

* This form of reverser is due to Professor Ewinq.

110 MESSRS. J. HOPKINSON AND E. WILSON ON THE

Fig. 22a.

ee

eoNeh 5

ERE @ae
BARB

Beee deers

PROPAGATION

OF MAGNETIZATION OF IRON.

ps
le
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704

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20000
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afl

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177 peres |t7r| Ce
N a
ete Zz

i

112 MESSRS. J HOPKINSON AND E. WILSON ON THE

The method of experiment was as follows :—The liquid reverser, M, was placed so
as to give a maximum current on the meter G, which was adjusted by non-inductive
resistance, N, to the desired value, and, in all cases, when changing from higher to
lower currents, a system of demagnetization by reversals was adopted. Time was
taken, as in Part I., on a clock beating seconds, which could be heard distinctly.

As an example, take fig. 19, in which the periodic time is 80 seconds, and the
maximum current in the copper coils °23 ampere. The E.M.F. curves of the exploring
coils are numbered 1, 2, and 3 respectively, and the curve of current in the copper
coils is also given.

As in the case of simple reversals (Part I.) we may from these curves attempt to
obtain an approximation to the cyclic curve of induction of the iron. In all cases
where this is done we have taken coil 1 and considered the area. within it—that is to
say, from a knowledge of the E.M.F.’s at different depths of the iron, due to change
of induction at any epoch, we have estimated the average magnetizing force acting in
this area, and this we cali H,. The curves from which these forces have been
obtained are given in fig. 194, and have been plotted from Table VI. The algebraic
sum of this force, H,, and the force H,, given at the same epoch by the current in
the copper coils, is taken to be the then resultant force magnetizing this area. Also
the integral of curve 1, fig. 19, gives the average induction over this area at the same
epoch. Curve , fig. 19B, is the cyclic curve obtained by plotting the inductions in
terms of the resultant force H.

A word is necessary with regard to the last column in Table VI. This gives the
total dissipation of energy by induced currents in ergs per cycle per cub. centim. of
the iron. We know the watts per sq. centim. at different depths of the iron for
different epochs. Let a series of curves be drawn (fig. 19) for chosen epochs giving
this relation: the areas of these curves from radii 0 to 5:08 give for the respective
epochs the watts per centim. dissipated by induced currents. In symbols this is
— dy; where r is the radius, and ec the E.M.F. and current. It is now only

Sq. centim. :
necessary to integrate with regard to time in order to obtain the total dissipation : we
éc

have chosen a half period as our limits. This gives us || dr dt, and is got

from the area of curve z, fig. 19p. The ordinates of this curve are taken from the
last column of Table VI.

The curves in figs. 21, 22, have been treated in a similar manner to that already
described in connection with fig. 19. But in fig. 20 the procedure is a little different.
In this case the periodic time is 20, and the maximum force per centim. linear, due to
the current in the copper coils, is 4°87. With this frequency and current the effects
of induced currents in the iron are very marked: we have taken a given soft
iron cyclic curve, of roughly the same maximum induction as given by the integral of
curve No. 1, fig. 20, and have tabulated the forces obtained therefrom in Table VII,

PROPAGATION OF MAGNETIZATION OF TRON. 113

In fig. 20a we have plotted the amperes per sq. centim. at the different radii, and for
the several epochs, and in each case, by drawing a curve fairly through these points,
as shown in the figure, we are able to produce areas in fair correspondence with the
areas obtained by means of the given cyclic curve. The comparative areas are given
in Table VII.

The results shown in fig. 22 are by no means so satisfactory as the results given by
other figures, but we have thought it better to insert them here, as we do not wish
to make any selection of results which might give an idea of average accuracy greater
than these experiments are entitled to.

Referring now to the summary of results in Table V., we note the marked effect of
change of frequency upon the average induction per unit area of the innermost coil
No. 1, when dealing with comparatively small maximum inductions. Compare the
results given in figs. 19 and 20. The maximum force per centim. linear due to the
current in the copper coils is 4°8 in each case, but the average induction per
sq. centim. of coil No. 1 is reduced from 7690 to 1630 by a change of frequency from
go to 35. Thisis, of course, not the case on the higher portion of the induction curve,
as is shown by the results of figs. 21 and 22, although the resultant force H is
reduced by the induced currents.

In fig. 23 the maximum amperes in the copper coils is ‘24, and the periodic time is
reduced to 4. An inspection of these curves shows the marked effect of change of
frequency, coil No. 2 being exceedingly diminished in amplitude as compared with
No. 3.

Asan example of the practical bearing of this portion of the paper, suppose we
have a transformer core made out of iron wire, 1 millim. in diameter, the wires

being perfectly insulated from one another. The outside diameter of our outer tube
: rs (oushs : 3 6 be Ne
is 101°6 millims. Similar events will therefore happen at times, varying as Gia) :
Take the case of fig, 19, in which the periodic time is 80 seconds, and the maximum
average induction per sq. centim. is about 7000.

(101-6)?

a
practice. The ergs dissipated per cycle per cub. centim. are 3820 by induced currents,
and about 3000 by magnetic hysteresis. We see further, from fig. 20, that at 500

periods per second only the outside layers of our 1 millim. wire are really useful.

= 129 periods per second, and this is an example which might arise in

As another example, take the case of an armature core of a dynamo electric
machine in which a frequency of 1000 complete periods per minute might be taken.

In fig. 21 the periodic time is 80, and the maximum average induction per
sq. centim. is 15,000.

We have
sy = SO) (o/ LOS)

8

I

e
i=)
—
S
eo

36 = nearly 3 millims.
MDCCCXCV.—A. Q

114 MESSRS. J. HOPKINSON AND E. WILSON ON THE

The ergs dissipated per cycle per cub. centim. are 26,000 by induced currents, and
about 17,000 by magnetic hysteresis. This shows that according to good practice,
where the wires in armature cores are of an order of 1 or 2 millims. diameter, the loss
by induced currents would be but small as compared with the loss by magnetic
hysteresis. This, of course, assumes the wires to be perfectly insulated from one
another, which is not always realised in practice.

Both the armature cores of dynamos and the cores of transformers are now usually
made of plates instead of wire; roughly speaking a plate in regard to induced
currents in its substance is comparable to a wire of a diameter double the thickness
of the plate. We infer that the ordinary practice of making transformer plates
about 4 millim. thick, and plates of armature cores 1 millim. thick, is not far wrong.
Not much is lost by local currents in the iron, and the plates could not be much
thicker without loss.*

TABLE I,
Ae rere era Maxinium force in Maximum induction |
a gs paler ab = C.G.S. units. per sq. centim.
magnetizing coils. H R
d
Fig. 10 sea a 0745 ioe
Pris! ki ee ei eas 138 3:0
2 eRableme ine 24, 4:96 | 8,000
49 101 12,820
Sy SS Mas ee ills | 774 16:0 14,495
BS PORTALS) 1:80 37:2 | 15,480
| 2°31 47-6 | |
65 1345 |

* The question of dissipation of energy by local currents in iron has been discussed by Professors
J.J, Tuomson and Ewr1ns. See the ‘ Electrician,’ April 8th and 15th, 1892.

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MDCCCXCV,—A,

IV. On the Dynamical Theory of Incompressible Viscous Fluids and the
Determination of the Criterion.

By OssorneE Reynotps, V.A., LL.D., F.RS., Professor of Engineering in Owens
College, Manchester.

Received April 25—Read May 24, 1894.

Section I.
Introduction.

1. THE equations of motion of viscous fluid (obtained by grafting on certain terms to
the abstract equations of the Eulerian form so as to adapt these equations to the case
of fluids subject to stresses depending in some hypothetical manner on the rates of
distortion, which equations NAVIER* seems to have first introduced in 1822, and
which were much studied by Cavcuyt and Porsson{) were finally shown by
St. Venant§ and Sir Gasrret SToKEs,|| in 1845, to involve no other assumption than
that the stresses, other than that of pressure uniform in all directions, are linear
functions of the rates of distortion, with a co-etlicient depending on the physical state
of the fluid.

By obtaining a singular solution of these equations as applied to the case of
pendulums in steady periodic motion, Sir G. SrokeEs was able to compare the
theoretical results with the numerous experiments that had been recorded, with the
result that the theoretical calculations agreed so closely with the experimental
determinations as seemingly to prove the truth of the assumption involved. This
was also the result of comparing the flow of water through uniform tubes with the
flow calculated from a singular solution of the equations so long as the tubes were
small and the velocities slow. On the other hand, these results, both theoretical and
practical, were directly at variance with common experience as to the resistance

* ‘Mém, de Académie,’ vol. 6, p. 389.
+ ‘Mém. des Savants Ktvangers,’ vol. 1, p. 40.
t ‘Mém. de l’Académie,’ vol. 10, p. 345,
§ «B.A. Report,’ 184.6.
|| ‘Cambridge Phil. Trans.,’ 1845.
9 ‘Cambridge Phil. Trans.,’ vol, 9, 1857.
R 2 6.5.95

124 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

encountered by larger bodies moving with higher velocities through water, or by
water moving with greater velocities through larger tubes. This discrepancy
Sir G. Sroxes considered as probably resulting from eddies which rendered the
actual motion other than that to which the singular solution referred and not as
disproving the assumption.

In 1850, after Jouxe’s discovery of the Mechanical Equivalent of Heat, Stoxrs
showed, by transforming the equations of motion—with arbitrary stresses—so as to
obtain the equations of (‘‘ Vis-viva”) energy, that this equation contained a definite
function, which represented the difference between the work done on the fluid by the
stresses and the rate of increase of the energy, per unit of volume, which function,
he concluded, must, according to JouLE, represent the Vis-viva converted into heat.

This conclusion was obtained from the equations irrespective of any particular
relation between the stresses and the rates of distortion. Sir G. SroKss, however,
translated the function into an expression in terms of the rates of distortion, which
expression has since been named by Lord Rayiyrcu the Dissipation- Function.

2, In 1883 I succeeded in proving, by means of experiments with colour bands—
the results of which were communicated to the Society*—that when water is caused
by pressure to flow through a uniform smooth pipe, the motion of the water is direct,
i.é., parallel to the sides of the pipe, or sinuous, 7.e., crossing and re-crossing the pipe,
according as U,,, the mean velocity of the water, as measured by dividing Q, the
discharge, by A, the area of the section of the pipe, is below or above a certain value
given by

iKpu/Dp,

where D is the diameter of the pipe, p the density of the water, and K a numerical
constant, the value of which according to my experiments and, as I was able to show,
to all the experiments by PorseuILLE and Darcy, is for pipes of circular section
between

1900 and 2000,

or, in other words, steady direct motion in round tubes is stable or unstable according
as

DUT
Qi tec or > 2000,

the number K being thus a criterion of the possible maintenance of sinuous or
eddying motion.

3. The experiments also showed that K was equally a criterion of the law of the
resistance to be overcome—which changes from a resistance proportional to the

* ¢Phil. Trans.,’ 1883, Part III., p. 935.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 125

velocity and in exact accordance with the theoretical results obtained from the
singular solution of the equation, when direct motion changes to sinuous, 7.¢., when

DU,
PES SS IS

BL

4. In the same paper I pointed out that the existence of this sudden change in the
law of motion of fluids between solid surfaces when

DU, = —K
Pp
proved the dependence of the manner of motion of the fluid on a relation between
the product of the dimensions of the pipe multiplied by the velocity of the fluid and
the product of the molecular dimensions multiplied by the molecular velocities which
determine the value of
-

for the fluid, also that the equations of motion for viscous fluid contained evidence of
this relation.

These experimental results completely removed the discrepancy previously noticed,
showing that, whatever may be the cause, in those cases in which the experimental
results do not accord with those obtained by the singular solution of the equations,
the actual motions of the water are different. But in this there is only a partial
explanation, for there remains the mechanical or physical significance of the existence
of the criterion to be explained.

5. [My object in this paper is to show that the theoretical existence of an inferior
limit to the criterion follows from the equations of motion as a consequence :—

(1) Of a more rigorous examination and definition of the geometrical basis on
which the analytical method of distinguishing between molar-motions and _heat-
motions in the kinetic theory of matter is founded ; and

(2) Of the application of the same method of analysis, thus definitely founded, to
distinguish between mean-molar-motions and relative-molar-motions where, as in the
case of steady-mean-flow along a pipe, the more rigorous definition of the geometrical
basis shows the method to be strictly applicable, and in other cases where it is
approximately applicable.

The geometrical relation of the motions respectively indicated by the terms
mean-molar-, or MzEAN-MerAn-Mortov, and relative-molar or RELAtTIVE-Mr&AN-Mortion
being essentially the same as the relation of the respective motions indicated by the
terms molar-, or MEAN-Morron, and relative-, or HEAT-Morion, as used in the theory
of gases.

I also show that the limit to the criterion obtained by this method of analysis and
by integrating the equations of motion in space, appears as a geometrical linut to the

126 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

possible simultaneous distribution of certain quantities im space, and in no wise
depends on the physical significance of these quantities. Yet the physical significance
of these quantities, as defined in the equations, becomes so clearly exposed as to
indicate that further study of the equations would elucidate the properties of matter
and mechanical principles involved, and so be the means of explaining what has
hitherto been obscure in the connection between thermodynamics and the principles
of mechanics.

The geometrical basis of the method of analysis used in the kinetic theory of gases
has hitherto consisted :—

(1) Of the geometrical principle that the motion of any point of a mechanical
system may, at any instant, be abstracted into the mean motion of the whole system
at that instant, and the motion of the point relative to the mean-motion ; and

(2) Of the assumption that the component, in any particular direction, of the
velocity of a molecule may be abstracted into a mean-component-velocity (say w)
which is the mean-component velocity of all the molecules in the immediate
neighbourhood, and a relative velocity (say €), which is the difference between u
and the component-velocity of the molecule ;* wv and € being’so related that, M being
the mass of the molecule, the integrals of (ME), and (Mw€), &c., over all the molecules
in the immediate neighbourhood are zero, and =[M (wu + €)?] = }{M(u? + €*)].t

The geometrical principle (1) has only been used to distinguish between the energy
of the mean-motion of the molecule and the energy of its internal motions taken
relatively to its mean motion; and so to eliminate the internal motions from all
further geometrical considerations which rest on the assumption (2).

That this assumption (2) is purely geometrical, becomes at once obvious, when it is
noticed that the argument relates solely to the distributicn in space of certain
quantities at a particular instant of time. And it appears that the questions as to
whether the assumed distinctions are possible under any distributions, and, if so,
under what distribution, are proper subjects for geometrical solution.

On putting aside the apparent obviousness of the assumption (2), and considering
definitely what it implies, the necessity for further definition at once appears.

The mean component-velocity (w) of all the molecules in the immediate neighbour-
hood of a point, say P, can only be the mean component-velocity of all the molecules in
some space (S) enclosing P. w is then the mean-component velocity of the mechanical
system enclosed in §, and, for this system, is the mean velocity at every point within
S, and multiplied by the entire mass within § is the whole component momentum
of the system. But,according to the assumption (2), 7 with its derivatives are to be
continuous functions of the position of P, which functions may vary from point to
point even within S$; so that wv is not taken to represent the mean component-velocity
of the system within S, but the mean-velocity at the point P. Although there seems
to have been no specific statement to that effect, it is presumable that the space S has

* “Dynamical Theory of Gases,” ‘Phil. Trans.,’ 1866, pp. 67. + ‘Phil. Trans.,’ 1866, p. 71.

FLUIDS AND THE DETERMINATION OF THE CRITERION, 127

been assumed to be so taken that P is the centre of gravity of the system within S.
The relative positions of P and S being so defined, the shape and size of the space 8
requires to be further defined, so that wu, &., may vary continuously with the position
of P, which is a condition that can always be satisfied if the size and shape of S may
vary continuously with the position of P.

Having thus defined the relation of P to S and the shape and size of the latter,
expressions may be obtained for the conditions of distribution of u, for which = (ME€)
taken over § will be zero, 7.e., for which the condition of mean-momentum shall be
satisfied.

Taking §,, 7, &c., as relating to a point P, and 8, wu, &c., as relating to P, another
point of which the component distances from P, are a, y, 2, P, is the C.G. of S,, and
by however much or little S may overlap S,, 8 has its centre of gravity at a, y, z,
and is so chosen that u, &c., may be continuous functions of «, y, z w may,
therefore, differ from u, even if P is within §,. Let w be taken for every molecule of
the system §,. Then according to assumption (2), ¥ (Mw) over 8, must represent the
component of momentum of the system within §,, that is, in order to satisfy the
condition of mean momentum, the mean-value of the variable quantity wu over the
system S, must be equal to u, the mean-component velocity of the system §), and
this is a condition which in consequence the geometrical definition already mentioned
can only be satisfied under certain distributions of uw. For since w is a continuous
function of x, y, z, M (uw — u,) may be expressed as a function of the derivatives of wu at P,
multiplied by corresponding powers and products of «, y, z, and again by M ; and by
equating the integral of this function over the space 8, to zero, a definite expression
is obtained, in terms of the limits imposed on #, y, z, by the already defined space 8,
for the geometrical condition as to the distribution of w under which the condition of
mean momentum can be satisfied.

From this definite expression it appears, as has been obvious all through the
argument, that the condition is satished if wv is constant. It also appears that there
are certain other well-defined systems of distribution for which the condition is
strictly satisfied, and that for all other distributions of ~ the condition of mean-
momentum can only be approximately satisfied to a degree for which definite
expressions appear.

Having obtained the expression for the condition of distribution of u, so as to
satisfy the condition of mean momentum, by means of the expression for M (wu — w’),
&c., expressions are obtained for the conditions as to the distribution of €, &c., in
order that the integrals over the space 8, of the products M (w€), &c. may be zero when
={[M (uv — u,)| = 0, and the conditions of mean energy satistied as well as those of
mean-momentum. It then appears that in some particular cases of distribution of u,
under which the condition of mean momentum is strictly satisfied, certain conditions
as to the distribution of €, &c., must be satisfied in order that the energies of mean-

128 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

and relative-motion may be distinct. These conditions as to the distribution of € &c.,
are, however, obviously satisfied in the case of heat motion, and do not present
themselves otherwise in this paper.

From the definite geometrical basis thus obtained, and the definite expressions
which follow for the condition of distribution of uw, &c., under which the method of
analysis is strictly applicable, it appears that this method may be rendered generally
applicable to any system of motion by a slight adaptation of the meaning of the
symbols, and that it does not necessitate the elimination of the internal motion of
the molecules, as has been the custom in the theory of gases.

Taking wu, v, w to represent the motions (continuous or discontinuous) of the matter
passing a point, and p to represent the density at the point, and putting w, &c., for
the mean-motion (instead of w as above), and w’, &c., for the relative-motion (instead
of €as before), the geometrical conditions as to the distribution of u, &c., to satisfy
the conditions of mean-momentum and mean-energy are, substituting p for M, of
precisely the same form as before, and as thus expressed, the theorem is applicable to
any mechanical system however abstract.

(1) In order to obtain the conditions of distribution of molar-motion, under which
the condition of mean-momentum will be satisfied so that the energy of molar-motion
may be separated from that of the heat-motion, wu, &c., and p are taken as referring to
the actual motion and density at a point in a molecule, and §, is taken of such
dimensions as may correspond to the scale, or periods in space, of the molecular

distances, then the conditions of distribution of wu, under which the condition of mean-
momentum is satisfied, become the conditions as to the distribution of molar-motion,
under which it is possible to distinguish between the energies of molar-motions and
heat-motions.

(2) And, when the conditions in (1) are satisfied to a sufficient degree of approxi-

mation by taking w to represent the molar-motion (w in (1)), and the dimensions of
the space 8 to correspond with the period in space or scale of any possible periodic or

eddying motion. The conditions as to the distribution of u, &c. (the components of
mean-mean-motion), which satisfy the condition of mean-momentum, show the
conditions of mean-molar-motion, under which it is possible to separate the energy
of mean-molar-motion from the energy of relative-molar- (or relative-mean-) motion

Having thus placed the analytical method used in the kinetic theory on a definite
geometrical basis, and adapted so as to render it applicable to all systems of motion,
by applying it to the dynamical theory of viscous fluid, I have been able to show :—
Feb. 18, 1895.]

(a) That the adoption of the conclusion arrived at by Sir GABRIEL Stoxes, that the
dissipation function represents the rate at which heat is produced, adds a definition
to the meaning of w, v, w—the components of mean or fluid velocity—which was
previously wanting ;

FLUIDS AND THE DETERMINATION OF THE CRITERION. 129

(b) That as the result of this definition the equations are true, and are only true
as applied to fluid in which the mean-motions of the matter, excluding the heat-
motions, are steady ;

(c) That the evidence of the possible existence of such steady mean-motions, while
at the same time the conversion of the energy of these mean-motions into heat is
going on, proves the existence of some discriminative cause by which the periods in
space and time of the mean-motion are prevented from approximating in magnitude
to the corresponding periods of the heat-motions, and also proves the existence of
some general action by which the energy of mean-motion is continually transformed
into the energy of heat-motion without passing through any intermediate stage ;

(d) That as applied to fluid in unsteady mean-motion (excluding the heat-motions),
however steady the mean integral flow may be, the equations are approximately true
in a degree which increases with the ratios of the magnitudes of the periods, in time
and space, of the mean-motion to the magnitude of the corresponding periods of the
heat-motions ;

(e) That if the discriminative cause and the action of transformation are the result
of general properties of matter, and not of properties which affect only the ultimate
motions, there must exist evidence of similar actions as between the mean-mean-
motion, in directions of mean flow, and the periodic mean-motions taken relative to
the mean-mean-motion but excluding heat-motions. And that such evidence must be
of a general and important kind, such as the unexplained laws of the resistance of
fluid motions, the law of the universal dissipation of energy and the second law of
thermodynamics ;

(7) That the generality of the effects of the properties on which the action of trans-
formation depends is proved by the fact that resistance, other than proportional to
the velocity, is caused by the relative (eddying) mean-motion.

(g) That the existence of the discriminative cause is directly proved by the
existence of the criterion, the dependence of which on circumstances which limit the
magnitudes of the periods of relative mean-motion, as compared with the heat-motion,
also proves the generality of the effects of the properties on which it depends.

(i) That the proof of the generality of the effects of the properties on which the
discriminative cause, and the action of transformation depend, shows that—if in the
equations of motion the mean-mean-motion is distinguished from the relative-mean-
motion in the same way as the mean-motion is distinguished from the heat-motions—
(1) the equations must contain expressions for the transformation of the energy of
mean-mean-motion to energy of relative-mean-motion ; and (2) that the equations,
when integrated over a complete system, must show that the possibility of relative-
mean-motion depends on the ratio of the possible magnitudes of the periods of relative-
mean-motion, as compared with the corresponding magnitude of the periods of the
heat-motions.

(7) That when the equations are transformed so as to distinguish between the

MDCCCXCY,—A. s

130 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

mean-mean-motions, of infinite periods, and the relative-mean-motions of finite periods,
there result two distinct systems of equations, one system for mean-mean-motion, as
affected by relative-mean-motion and heat-motion, the other system for relative-mean-
motion as affected by mean-mean-motion and heat-motions.

(7) That the equation of energy of mean-mean-motion, as obtained from the first
system, shows that the rate of increase of energy is diminished by conversion into
heat, and by transformation of energy of mean-mean-motion in consequence of the
relative-mean-motion, which transformation is expressed by a function identical in
form with that which expresses the conversion into heat; and that the equation of
energy of relative-mean-motion, obtained from the second system, shows that this
energy is increased only by transformation of energy from mean-mean-motion
expressed by the same function, and diminished only by the conversion of energy
of relative-mean-motion into heat.

(x) That the difference of the two rates (1) transformation of energy of mean-mean-
motion into energy of relative-mean-motion as expressed by the transformation
function, (2) the conversion of energy of relative-mean-motion into heat, as expressed
by the function expressing dissipation of the energy of relative-mean-motion, affords
a discriminating equation as to the conditions under which relative-mean-motion
can be maintained.

(/) That this discriminating equation is independent of the energy of relative-mean-
motion, and expresses a relation between variations of mean-mean-motion of the first
order, the space periods of relative-mean-motion and jz/p such that any circumstances
which determine the maximum periods of the relative-mean-motion determine the
conditions of mean-mean-motion under which relative mean-motion will be maintained
—determine the criterion.

(m) That as applied to water in steady mean flow between parallel plane surfaces,
the boundary conditions and the equation of continuity impose limits to the maximum
space periods of relative-mean-motion such that the discriminating equation affords
definite proof that when an indefinitely small sinuous or relative disturbance exists
it must fade away if

P D U, |p

is less than a certain number, which depends on the shape of the section of the
boundaries, and is constant as long as there is geometrical similarity. While for
greater values of this function, in so far as the discriminating equation shows, the
energy of sinuous motion may increase until it reaches to a definite limit, and rules
the resistance.

(n) That besides thus affording a mechanical explanation of the existence of the
criterion K, the discriminating equation shows the purely geometrical circumstances
on which the value of K depends, and although these circumstances must satisfy
geometrical conditions required for steady mean-motion other than those imposed by

FLUIDS AND THE DETERMINATION OF THE CRITERION. 131

the conservations of mean energy and momentum, the theory admits of the determi-
nation of an inferior limit to the value of K under any definite boundary conditions,
which, as determined for the particular case, is

o17.

This is below the experimental value for round pipes, and is about half what might
be expected to be the experimental value for a flat pipe, which leaves a margin to meet
the other kinematical conditions for steady mean-mean-motion.

(0) That the discriminating equation also affords a definite expression for the
resistance, which proves that, with smooth fixed boundaries, the conditions of
dynamical similarity under any geometrical similar circumstances depend only on the
value of

dp 5.
z Fis b%,

where 0 is one of the lateral dimensions of the pipe ; and that the expression for this
resistance is complex, but shows that above the critical velocity the relative-mean-
motion is limited, and that the resistances increase as a power of the velocity higher
than the first.

Section II.

The Mean-motion and Heat-motions as distinguished by Periods.—Mean-mean-
motion and Relative-mean-motion.—Discriminative Cause and Action of Trans-
formation.—Two Systems of Equations.—A Discriminating Equation.

6. Taking the general equations of motion for incompressible fluid, subject to no
external forces to be expressed by

du

a, d A
pa =T le (Pic + pu) + ay (Pye + puv) + = (Pie + puw) | |
dy d Gp d
Pig =~ [ap (Ba + pm) + 5 (Par + p20) + 5 (Py + pow) b & . (1),
a |
dz J

U L 1
Pp a ania ee (Diz -F pwi) ae a (Py: oF pwr) ay

dz

(Pes + pwr)

with the equation of continuity

O=du/dx + dojdy--dwdz. . . . . . +. (2);

where p,,, &c., are arbitrary expressions for the component forces per unit of area,
resulting from the stresses, acting on the negative faces of planes perpendicular to
$2

132 PROFESSOR 0. REYNOLDS ON INCOMPRESSIBLE VISCOUS

the direction indicated by the first suffix, in the direction indicated by the second
suffix.
Then multiplying these equations respectively by u, v, w, imtegrating by parts,
adding and putting
2E for p(w+v? + w’)

and transposing, the rate of increase of kinetic energy per unit of volume is given by

[ ~ (pre) +5 5 (ups) +— ~ (pez) ;

(Gj tuntegt: ar + na 3m >
+ (wpe) + £ (wpe) + Z(mp.)
[ Poe ae ht a
2" + Page FPA PP, ey
| tea gg tie Gy + Pep |

The left member of this equation expresses the rate of increase in the kinetic
energy of the fluid per unit of volume at a point moving with the fluid.

The first term on the right expresses the rate at which work is being done by the
surrounding fluid per unit of volume at a point.

The second term on the right therefore, by the law of conservation of energy,
expresses the difference between the rate of increase of kinetic energy and the rate
at which work is being done by the stresses. This difference has, so far as I am
aware, in the absence of other forces, or any changes of potential energy, been equated
to the rate at which heat is being converted into energy of motion, Sir GABRIEL
Stokes having first indicated this* as resulting from the law of conservation of
energy then just established by JouLs.

7. This conclusion, that the second term on the right of (3) expresses the rate at
which heat is being converted, as it is usually accepted, may be correct enough, but
there is a consequence of adopting this conclusion which enters largely into the
method of reasoning in this paper, but which, so far as I know, has not previously
received any definite notice.

* “Cambridge Phil. Trans.,’ vol. 9, p. 57.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 133

The Component Velocities in the Equations of Viscous Fluids.

In no case, that Iam aware of, has any very strict definition of wu, v, w, as they
occur in the equations of motion, been attempted. They are usually defined as the
velocities of a particle at a point («, y, z) of the fluid, which may mean that they are
the actual component velocities of the point in the matter passing at the instant, or
that they are the mean velocities of all the matter in some space enclosing the point,
or which passes the point in an interval of time. If the first view is taken, then the
right hand member of the equation represents the rate of increase of kinetic energy,
per unit of volume, in the matter at the point; and the integral of this expression
over any finite space 8, moving with the fluid, represents the total rate of increase
of kinetic energy, including heat-motion, within that space; hence the difference
between the rate at which work is done on the surface of S, and the rate at which
kinetic energy is increasing can, by the law of conservation of energy, only represent
the rate at which that part of the heat which does not consist in kinetic energy of
matter is being produced, whence it follows :—

(a) That the adoption of the conclusion that the second term in equation (3) ex-
presses the rate at which heat is being converted, defines u, v, w, as not representing
the component velocities of points in the passing matter.

Further, if it is understood that u, v, w, represent the mean velocities of the matter
in some space, enclosing «, y, z, the point considered, or the mean velocities at a point
taken over a certain interval of time, so that } (pu), = (pv), = (pw) may express the
components of momentum, and zz (pv) — y= (pw), &e., &e., may express the com-
ponents of moments of momentum, of the matter over which the mean is taken ;
there still remains the question as to what spaces and what intervals of time ?

(6) Hence the conelusion that the second term expresses the rate of conversion of heat,
defines the spuces and intervals of time over which the mean component velocities must
be taken, so that E may include all the energy of mean-motion, and exclude that of
heat-motions.

Equations Approximate only except in Three Particular Cases.

8. According to the reasoning of the last article, if the second term on the right of
equation (3) expresses the rate at which heat is being converted into energy of mean-
motion, either pu, pv, pw express the mean components of momentum of the matter,
taken at any instant over a space S, enclosing the point «, y, z, to which w, v, w
refer, so that this point is the centre of gravity of the matter within S, and such
that p represents the mean density of the matter within this space; or pu, pv, pw
represent the mean components of momentum taken at «, y, z over an interval of time 7,
such that p is the mean density over the time 7, and if ¢ marks the instant to which
u, v, w refer, and t’ any other instant, =| (¢ — ¢’) p|, in which p is the actual density,
taken over the interval r is zero. The equations, however, require, that so obtained,

134 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

p; u, ¥, w, Shali be continuous functions of space and time, and it can be shown that
this involves certain conditions between the distribution of the mean-motion and the
dimensions of Sp and 7.

Mean- and Relative-Motions of Matter.

Whatever the motions of matter within a fixed space S may be at any instant, if
the component velocities at a point are expressed by u, v, w, the mean component
velocities taken over S will be expressed by

— (pu)

>

Fe Cet RM MGA tities. (ah)

If then u,v, w, are taken at each instant as the velocities of x, y, z, the instantaneous
centre of gravity of the matter within 8, the component momentum at the centre of
gravity may be put

pu pu + pun. ve Yo. anitiiy cake OS

where w’ is the motion of the matter, relative to axes moving with the mean velocity,
at the centre of gravity of the matter within 8. Since a space S§ of definite size and
shape may be taken about any point a, y, z in an indefinitely larger space, so that
x, y, 21s the centre of gravity of the matter within 8, the motion in the larger space

may be divided into two distinct systems of motion, of which wu, v, w represent a
mean-motion at each point and w’, v’, w’ a motion at the same point relative to the
mean-motion at the point,

If, however, w, v, w are to represent the real mean-motion, it is necessary that
= (pu’), = (pu’), = (po’) summed over the space 8, taken about any point, shall be
severally zero; and in order that this may be so, certain conditions must be fulfilled.

For taking «, y, 2 for G the centre of gravity of the matter within S and 2”, 7, 2’
for any other point within §, and putting a, b, ¢ for the dimensions of S in
directions «, y, 7, measured from the point 2, y,z, since w, v, w are continuous functions
of x, y, 2, by shifting 8 so that the centre of gravity of the matter within it is at

wv, y’, v, the value of u for this point is given by

au

(v’ — x)? + &e. (6)

da?

wl—

isi, +@ —o(F) + —y() +6 -9(Z) +

dy} g /9

where all the differential coefficients on the left refer to the point «, y, z; and in the
same way for v and w.

Subtracting the value of w thus obtained for the point a’, y’, 2’ from that of w at the

FLUIDS AND THE DETERMINATION OF THE CRITERION. 135

same point the difference is the value of wv’ at this point, whence summing these
differences over the space S about G at «, y, z, since by definition when summed over
the space S about G

5 oe — tills Ooi Sale? Sela © oo oo)

du

S (pu') = — {45 [p(@— ey ](Ts) + 32le-9 (Ga)

du

|
+$2lo(e—2)I(Fs) +4eb 1 (aay
|

ihatis .

2 (pw) « a? (de ) b? (du 2 (du
= (p) is < . da Sli 2 al 4F 9 ( + ke. }

In the same way if ¥(___) be taken over the interval of time 7 including ¢; and
for the instant ¢

“= oe and pu = pu + pw’;

then since for any other instant ¢’

where 3 [p(t — ¢’)] = 0, and S[p (u —u)] = 0.
It appears that

du

= (pw’) =— =[S p(t — te WP + &e. |

> (pu! (22
i a al | a
Sia) <-l1r a) &e. |

(8B).

From equations (84) and (8B), and similar equations for & (pv’) and = (pw’), it appears
that if
2 (pu) = = (pu') = = (pw) = 0,

where the summation extends both over the space S and the interval 7, all the terms
on the right of equations (84) and (8B) must be respectively and continuously zero, or,
what is the same thing, all the differential coefficients of u, v, w with respect to
x, y, z and t of the first order must be respectively constant.

This condition will be satisfied if the mean-motion is steady, or uniformly varying

136 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

with the time, and is everywhere in the same direction, being subject to no variations
in the direction of motion ; for suppose the direction of motion to be that of x, then
since the periodic motion passes through a complete period within the distance 2a,
= (pu’) will be zero within the space

2a dy dz,

however small dy dz may be, and since the only variations of the mean-motion are in
directions y and 2, in which b and c may be taken zero, and du/dt is everywhere
constant, the conditions are perfectly satisfied.

The conditions are also satisfied if the mean-motion is that of uniform expansion or
contraction, or is that of a rigid body.

These three cases, in which it may be noticed that variations of mean-motion
are everywhere uniform in the direction of motion, and subject to steady variations
in respect of time, are the only cases in which the conditions (84), (8B), can be perfectly
satisfied.

The conditions will, however, be approximately satisfied, when the variations of

u, v, w of the first order are approximately constant over the space S.

In such case the right-hand members of equations (84), (8B), are neglected, and it
appears that the closeness of the approximations will be measured by the relative
magnitude of such terms as

a u/dx, &e., t d?u/dt? as compared with du/dx, du/dt, &e.

Since frequent reference must be made to these relative values, and, as in periodic
motion, the relative values of such terms are measured by the period (in space or time)
as compared with a, b, c and 7, which are, ina sense, the periods of w’, v’, w’, I shall
use the term period in this sense, taking note of the fact that when the mean-motion
is constant in the direction of motion, or varies uniformly in respect of time, it is not
periodic, 7.e,, its periods are infinite.

9. It is thus seen that the closeness of the approximation with which the motion of
any system can be expressed as a varying mean-motion together with a relative-
motion, which, when integrated over a space of which the dimensions are a, 6, ¢, has

no momentum, increases as the magnitude of the periods of uw, v, w in comparison with
the periods of w’, v’, w’, and is measured by the ratio of the relative orders of magni-
tudes to which these periods belong.

Heat-motions in Matter are Approximately Relative to the Mean-motions.

The general experience that heat in no way affects the momentum of matter, shows
that the heat-motions are relative to the mean-motions of matter taken over spaces of

FLUIDS AND THE DETERMINATION OF THE CRITERION. 137

sensible size. But, as heat is by no means the only state of relative-motion of matter,
if the heat-motions are relative to all mean-motions of matter, whatsoever their periods
may be, it follows—that there must be some discriminative cause which prevents the
existence of relative-motions of matter other than heat, except mean-motions with
periods in time and space of greatly higher orders of magnitude than the corres-
ponding periods of the heat-motions—otherwise, by equations (84), (8B), heat-motions
could not be to a high degree of approximation relative to all other motions, and we
could not have to a high degree of approximation,

du du du a)
Pre Ty + Pyx ly + Pex 7B
dv dv dv ad
(ae Bog, Page = ag ee 2 pe 8 2. IO)
dw dw dw

Piz ihe + Pyz dy Pz iB J

where the expression on the right stands for the rate at which heat is converted into
energy of mean-motion.

Transformation of Energy of Relative-mean-motion to Energy of Heat-motion.

10. The recognition of the existence of a discriminative cause, which prevents the
existence of relative-mean-motions with periods of the same order of magnitude as
heat-motions, proves the existence of another general action by which the energy of
relative-mean-motion, of which the periods are of another and higher order of
magnitude than those of the heat-motions, is transformed to energy of heat-motion.

For if relative-mean-motions cannot exist with periods approximating to those of
heat, the conversion of energy of mean-motion into energy of heat, proved by Jouts,
cannot proceed by the gradual degradation of the periods of mean-motion until these
periods coincide with those of heat, but must, in its final stages, at all events, be the
result of some action which causes the energy of relative-mean-motion to be trans-
formed into the energy of heat-motions without intermediate existence in states of
relative-motion with intermediate and gradually diminishing periods.

That such change of energy of mean-motion to energy of heat may be properly
called transformation becomes apparent when it is remembered that neither mean-
motion nor relative-motion have any separate existence, but are only abstract
quantities, determined by the particular process of abstraction, and so changes in the
actual-motion may, by the process of abstraction, cause transformation of the
abstract energy of the one abstract-motion, to abstract energy of the other abstract-
motion.

All such transformation must depend on the changes in the actual-motions, and so
MDCCCXCV.—A. T

138 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

must depend on mechanical principles and the properties of matter, and hence the
direct passage of energy of relative-mean-motion to energy of heat-motions is evidence
of a general cause of the condition of actual-motion which results in transformation—
which may be called the cause of transformation.

The Discriminative Cause, and the Cause of Transformation.

11. The only known characteristic of heat-motions, besides that of being relative
to the mean-motion, already mentioned, is that the motions of matter which result
from heat are an ultimate form of motion which does not alter so long as the mean-
motion is uniform over the space, and so long as no change of state occurs in the
matter. In respect of this characteristic, heat-motions are, so far as we know,
unique, and it would appear that heat-motions are distinguished from the mean-
motions by some ultimate properties of matter.

It does not, however, follow that the cause of transformation, or even the
discriminative cause, are determined by these properties. Whether this is so or not
can only be ascertained by experience. If either or both these causes depend solely
on properties of matter which only affect the heat-motions, then no similar ettect
would result as between the variations of mean-mean-motion and relative-mean-
motion, whatever might be the difference in magnitude of their respective periods.
Whereas, if these causes depend on properties of matter which affect all modes of
motion, distinctions in periods must exist between mean-mean-motion and relative-
mean-motion, and transformation of energy take place from one to the other, as
between the mean-motion and the heat-motions.

The mean-mean-motion cannot, however, under any circumstances stand to the
relative-mean-motion in the same relation as the mean-motion stands to the heat-
motions, because the heat-motions cannot be absent, and in addition to any trans-
formation from mean-mean-motion to relative-mean-motion, there are transformations
both from mean- and relative-mean-motion to heat-motions, which transformation
may have important effects on both the transformation of energy from mean- to
relative-mean-motion, and on the discriminative cause of distinction in their periods.

In spite of the confusing effect of the ever present heat-motions, it would, however,
seem that evidence as to the character of the properties on which the cause of trans-
formation and the discriminative cause depend should be forthcoming as the result of
observing the mean- and relative-mean-motions of matter.

12. To prove by experimental evidence that the effects of these properties of
matter are confined to the heat-motions, would be to prove a negative; but if these
properties are in any degree common to all modes of matter, then at first sight it
must seem in the highest degree improbable that the effects of these causes on the
mean- and relative-mean-motions would be obscure, and only to be observed by
delicate tests. For properties which can cause distinctions between the mean- and

FLUIDS AND THE DETERMINATION OF THE CRITERION. 139

heat-motions of matter so fundamental and general, that from the time these motions
were first recognized the distinction has been accepted as part of the order of nature,
and has been so familiar to us that its cause has excited no curiosity, cannot, if they
have any effect at all, but cause effects which are general and important on the
mean-motions of matter. It would thus seem that evidence of the general effects of
such properties should be sought in those laws and phenomena known to us as the
result of experience, but of which no rational explanation has hitherto been found ;
such as the law that the resistance of fluids moving between solid surfaces and of
solids moving through fluids, in such a manner that the general-motion is not
periodic, is as the square of the velocities, the evidence covered by the law of the
universal tendency of all energy to dissipation and the second law of thermo-
dynamics.

13. In considering the first of the instances mentioned, it will be seen that the
evidence it affords as to the general effect of the properties, on which depends transforma-
tion of energy from mean- to relative-motion, is very direct. For, since my experiments
with colour bands have shown that when the resistance of fluids, in steady mean flow,
varies with a power of the velocity higher than the first the fluid is always in a state
of sinuous motion, it appears that the prevalence of such resistance is evidence of the
existence of a general action by which energy of mean-mean-motion with infinite
periods is directly transformed to the energy of relative-mean-motion, with finite
periods, represented by the eddying motion, which renders the general mean-motion
sinuous, by which transformation the state of eddying-motion is maintained, not-
withstanding the continual transformation of its energy into heat-motions.

We have thus direct evidence that properties of matter which determine the cause
of transformation, produce general and important effects which are not confined to the
heat-motions. ;

In the same way, the experimental demonstration I was able to obtain, that
relative-mean-motion in the form of eddies of finite periods, both as shown by colour
bands and as shown by the law of resistances, cannot be maintained except under
circumstances depending on the conditions which determine the superior limits to the
velocity of the mean-mean-motion, of infinite periods, and the periods of the relative-
mean-motion, as defined in the criterion

DU,,/p = K,

is not only a direct experimental proof of the existence of a discriminative cause which
prevents the maintenance of periodic mean-motion except with periods greatly in excess
of the periods of the heat-motions, but also indicates that the discriminative cause

depends on properties of matter which affect the mean-motions as well as the heat-
motions.

140 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

Expressions for the Rate of Transformation and the Discriminative Cause.

14. It has already been shown (Art. 8) that the equations of motion approximate
to a true expression of the relations between the mean-motions and stresses, when the
ratio of the periods of mean-motions to the periods of the heat-motions approximates
to infinity. Hence it follows that these equations must of necessity include whatever
mechanical or kinematical principles are involved in the transformation of energy of
mean-mean-motion to energy of relative-mean-motion. It has also been shown that
the properties of matter on which depends the transformation of energy of varying
mean-motion to relative-motion are common to the relative-mean-motion as well as to
the heat-motion. Hence, if the equations of motion are applied to a condition in
which the mean-motion consists of two components, the one component being a mean-
mean-motion, as obtained by integrating the mean-motion over spaces §, taken about
the point x, y, z, as centre of gravity, and the other component being a relative-mean-
motion, of which the mean components of momentum taken over the space S, every-
where vanish, it follows :—

(1) That the resulting equations of motion must contain an expression for the rate
of transformation from energy of mean-mean-motion to energy of relative-mean-
motion, as well as the expressions for the transformation of the respective energies of
mean- and relative-mean-motion to energy of heat-motion ;

(2) That, when integrated over a complete system these equations must show that the
possibility of the maintenance of the energy of relative-mean-motion depends, whatsoever
may be the conditions, on the possible order of magnitudes of the periods of the relative-
mean-motion, as compared with the periods of the heat-motions.

The Equations of Mean- and Relative Mean-Motion.

15. These last conclusions, besides bringing the general results of the previous
argument to the test point, suggest the manner of adaptation of the equations
of motion, by which the test may be applied.

Put

“U=u+y, v=v+v, eee 4 5 5 (iil),
where
Li OP(HM PH) etonicss ees 6 6 6 6 6 5 (2),

the summation extending over the space S, of which the centre of gravity is at the

FLUIDS AND THE DETERMINATION OF THE CRITERION. 141

point x, y, z. Then since uv, v, w are continuous functions of x, y, z, therefore

u, v, w, and wu’, v, w’, are continuous functions of x, y, z. And as p is assumed
constant, the equations of continuity for the two systems of motion are :

du dv oa du’ . dv’ . dwt
da di a da aa di dy YG

=O ¢ s- ae (S)s

also both systems of motions must satisfy the boundary conditions, whatever they
may be.
Further putting Dees &c., for the mean values of the stresses taken over the space
S, and
Die = Px ae Pox . ° . . ° ° ° ° . . (14)

and defining S, to be such that the space variations of uv, v, w are approximately
constant over this space, we have, putting ww’, &c., for the mean values of the squares
and products of the components of relative-mean-motion, for the equations of mean-
mean-motion,

du d = 1 as — d LSE wes aot: 5
Pa = 15 (Pat puu + pu wu) + ay (Pus + puw + puv)

+ 5, (Da + pu + pww)| |. . (19),
See ee &e. |
&e. = &e. J

dz

which equations are approximately true at every point in the same sense as that in
which the equations (1) of mean-motion are true.

Subtracting these equations of mean-mean-motion from the equations of mean-
motion, we have

Wes 2 ie par es
fF {Doo + p (uw + wu) + p(u'u’ —wu')}

ar ae a = {Pye + p (wo + wr) + p (w'v’ — w’v')} &e., &e. (16),

1 ae — , ar pais f
LF, Bia + p (tin! + ui) + p (ul! — 0) |

which are the equations of momentum of relative-mean-motion at each point.

142 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

Again, multiplying the equations of mean-mean-motion by u,v, Ww respectively,

adding and putting 2E = p(w? + v? + w’), we obtain

p ge lt Peet WHY) + 5, [HD WHY] + EL (Pa |
<3 + E18 (Dy + BW) + ELE (Py FPO) +2 Dy + BW) JE

Bare dz
dae [6 Pat WH) + [Pe +WV)] +H [0 (p+ WW)

fF dy = da Sida a) ( —-; du a =

| Px Gi Pyx dy Pex dz

| = =] | | =e an
= - dy — dv — - dv : eH) ae — dv
+ OW ; ee Pape + Ain ee FD nasach TT iL
4 + Pry ae + Pw a + Py d. | 1 1 Oe m vee dy Oe r eo)

dy Yy lx
= dp = Oi. S 20 ed LD)
Pee: ar Ds ae J Te te OE ee hea dz |

which is the approximate equation of energy of mean-mean-motion in the same sense
as the equation (3) of energy of mean-motion is approximate. |

In a similar manner multiplying the equations (16) for the momentum of relative-
mean-motion respectively by w’, v’, w’, and adding, the result would be the equation
for energy of relative-mean-motion at a point, but this would include terms of
which the mean values taken over the space S, are zero, and, since all corresponding
terms in the energy of heat are excluded, by summation over the space S, in the
expression for the rate at which mean-motion is transformed into heat, there is no
reason to include them for the space §,; so that, omitting all such terms and putting

On’ = p(u? 4.02 +02)». b . . yey len

we obtain .

FLUIDS AND THE DETERMINATION OF THE CRITERION. 143

d — ad = @ == wl
(G+ in tee te )E a
f a (D'se + pw’) | +z, > ce (Dye + uv')| + F [ul (D'ye + uw’)

a {ie al ra (Pye + v'w’)) + = [e(py + ev + 5 Li (ep oun |

L she < [w’ ( Pez + ww)| + - [w’ (xa +w'r’)| + <[w (pz + w'w')| J

dy

a

dus 7! A du’
13 p TF dx a De dz

, du , dul , du’ f- —— Oe 0 6)
Paz g ie + Piyz ap (Dee a | puu In b PUY i we
|
r
|
|
J

i dv’ dv’
+ dv’ mek ae , LAT
| ae 2 Py dz + Pw dy te Pix dz
R

where only the mean values, over the space §,, of the expressions in the right member
are taken into account.

This is the equation for the mean rate, over the space §,, of change in the energy
of relative-mean-motion per unit of volume.

It may be noticed that the rate of change in the energy of mean-mean-motion,
together with the mean rate of change in the energy of relative-mean-motion, must
be the total mean-rate of change in the energy of mean-motion, and that by adding
the equations (17) and (19) the result is the same as is obtained from the equation (3)
of energy of mean-motion by omitting all terms which have no mean value as summed
over the space §).

The Expressions from Transformation of Energy from Mean-mean-motion to Relative-
mean-motion.

16. When equations (17) and (19) are added together, the only expressions that
do not appear in the equation of mean energy of mean-motion are the last terms on
the right of each of the equations, which are identical in form and opposite in sign.

These terms which thus represent no change in the total energy of mean-motion
can only represent a transformation from energy of mean-mean-motion to energy of
relative-mean-motion. And as they are the only expressions which do not form part
of the general expression for the rate of change of the mean energy of mean-motion,
they represent the total exchange of energy between the mean-mean-motion and the
relative-mean-motion.

It is also seen that the action, of which these terms express the effect, is purely

144 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

kinematical, depending simply on the instantaneous characters of the mean- and
relative-mean-motion, whatever may be the properties of the matter involved, or the
mechanical actions which have taken part in determining these characters. The
terms, therefore, express the entire result of transformation from energy of mean-
mean-motion to energy of relative-mean-motion, and of nothing but the transforma-
tion, Their existence thus completely verifies the first of the general conclusions
in Art. 14,

The term last but one in the right member of the equation (17) for energy of
mean-mean-motion expresses the rate of transformation of energy of heat-motions
to that of energy of mean-mean-motion, and is entirely independent of the relative-
mean-motion.

In the same way, the term last but one on the right of the equation (19) for
energy of relative-mean-motion expresses the rate of transformation from energy of
heat-motions to energy of relative-mean-motion, and is quite independent of the
mean-mean-motion.

17. In both equations (17) and (19) the first terms on the right express the rates
at which the respective energy of mean- and relative-mean-motion are increasing
on account of work done by the stresses on the mean- and _ relative-motion
respectively, and by the additions of momentum caused by convections of relative-
mean-motion by relative-mean-motion to the mean- and _ relative-mean-motions
respectively.

It may also be noticed that while the first term on the right in the equation (19)
of energy of relative-mean-motion is independent of mean-mean-motion, the corre-
sponding term in equation (17) for mean-mean-motion is not independent of relative-
mean-motion.

A Discriminating Equation.

18. In integrating the equations over a space moving with the mean-mean-motion
of the fluid the first terms on the right may be expressed as surface integrals, which
integrals respectively express the rates at which work is being done on, and energy
is being received across, the surface by the mean-mean-motion, and by the relative-
mean-motion.

If the space over which the integration extends includes the whole system, or such
part that the total energy conveyed across the surface by the relative-mean-motion is
zero, then the rate of change in the total energy of relative-mean-motion within the
space is the difference of the integral, over the space, of the rate of increase of this
energy by transformation from energy of mean-mean-motion, less the integral rate
at which energy of relative-mean-motion is being converted into heat, or integrating
equation (19),

FLUIDS AND THE DETERMINATION OF THE CRITERION. 145

Nate eel oe

ee a — 0 =
puu — + puv a + pu'w ree.

—— dw --7 dw —--, dw

=- zen a

Luly), i a |

— ({| 4 aF pow = + pLr z + pv Ww = dx dy dz
L + pw'w ae + pw Ai + pw'w' — i |

(i A Cae du! , du’)
Pee FZ + Bea + Px a, |

dv’

, pe |
+ {IX tee a 2 WY dy aD erga NS ChaChjdie). Te ek Tg ak (XO),

, aw! du’

LP * de +P, iy ot Ps GEE 3)

This equation expresses the fundamental relations :—

(1) That the only integral effect of the mean-mean-motion on the relative-mean-
motion is the integral of the rate of transformation from energy of mean-mean-
motion to energy of relative-mean-motion.

(2) That, unless relative energy is altered by actions across the surface within which
the integration extends, the integral energy of relative-mean-motion will be increasing
or diminishing according as the integral rate of transformation from mean-mean-
motion to relative-mean-motion is greater or less than the rate of conversion of the
energy of relative-mean-motion into heat.

19. For p’,,, &c., are substituted their values as determined according to the
theory of viscosity, the approximate truth of which has been verified, as already
explained.

Putting

eRe (ODS,

we have, substituting in the last term of equation (20), as the expression for the
rate of conversion of energy of relative-mean-motion into heat,

d du’) | dv’ | da’

_ {({ = (pH) dz dydz= ({f [2 (s a = =|
6 du \2 du {dv'\? dw’\? |
—»{\- oe $+ ) +2((7) +(7) + (a) |

du’ | d\2 dw’ dw’? dv’ du’ ;
aE (a a5 7) a GG a iE) v ie a d nl ‘| Lae dyad: se (2)

MDCCUXCV.—A. U

146 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

in which pw is a function of temperature only ; or since p is here considered as constant,

Lika (om) = — efeL (ie) + (i+ Cl] +(e ¥a)

if aw \2 » — du'\2
ae CG a al a G ate =| hae dy de... . . Can

da dy

whence substituting. for the last term in equation (20) we have, if the energy of
relative-mean-motion is maintained, neither increasing or diminishing,

Shp |

7 , du UT 7 7 U
UC = UC == “we ==
daz: uy dy ats d

—ST aU

| —— as — |
— p{|| +o gE 4 wee | dedyde

—-,dw , {dw , —
(LULU ea

|
{ + wu eal v a + ww FE

lu’\? /dv’\? /dw'\? |
a] du! de!
(c) 1 a a5 ( | |

E w’ dv’ i (2 u! du’

ree)

dz dx

dv’ du’\2
+ G aly D) J

which is a discriminating equation as to the conditions under which relative-mean-
motion can be sustained.

ag obra) ) + dudy dz = 0. . (24)

all |
|

20. Since this equation is homogeneous in respect to the component velocities of
the relative-mean-motion, it at once appears that it is independent of the energy of
relative-mean-motion divided by the p. So that if p/p is constant, the condition it
expresses depends only on the relation between variations of the mean-mean-motion
and the directional, or angular, distribution of the relative-mean-motion, and on the
squares and products of the space periods of the relative-mean-motion.

And since the second term expressing the rate of conversion of heat into energy of
relative-mean-motion is always negative, it is seen at once that, whatscever may be
the distribution and angular distribution of the relative-mean-motion and the varia-
tions of the mean-mean-motion, this equation must give an inferior limit for the rates
of variation of the components of mean-mean-motion, in terms of the limits to the
periods of relative-mean-motion, and p/p, within which the maintenance of relative-
mean-motion is impossible. And that, so long as the limits to the periods of relative-
mean-motion are not infinite, this inferior limit to the rates of variation of the mean-
mean-motion will be greater than zero.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 147

Thus the second conclusion of Art. 14, and the whole of the previous argument is
verified, and the properties of matter which prevent the maintenance of mean-motion
with periods of the same order of magnitude as those of the heat-motion are shown to
be amongst those properties of matter which are included in the equations of motion
of which the truth has been verified by experience.

The Cause of Transformation.

21. The transformation function, which appears in the equations of mean-energy of
mean- and relative-mean-motion, does not indicate the cause of transformation, but
only expresses a kinematical principle as to the effect of the variations of mean-mean-
motion, and the distribution of relative-mean-motion. In order to determine the
properties of matter and the mechanical principles on which the effect of the variations
of the mean-mean-motion on the distribution and angular distribution of relative-mean-
motion depends, it is necessary to go back to the equations (16) of relative-momentum
at a point; and even then the cause is only to be found by considering the effects of
the actions which these equations express in detail. The determination of this cause,
though it in no way affects the proofs of the existence of the criterion as deduced from
the equations, may be the means of explaining what has been hitherto obscure in the
connection between thermodynamics and the principles of mechanics. That such may
be the case, is suggested by the recognition of the separate equations of mean- and
relative-mean-motion of matter.

The Equation of Energy of Relative-mean-motion and the Equation of
Thermodynamics.

22. On consideration, it will at once be seen that there is more than an accidental
correspondence between the equations of energy of mean- and relative-rmean-motion
respectively and the respective equations of energy of mean-motion and of heat in
thermodynamics.

If instead of including only the effects of the heat-motion on the mean-momentum
as expressed by p,., &e., the effects of relative-mean-motion are also included by
putting p., for p,. + pw’, &e., and p,, for p,. + pw’, &e., in equations (15) and (17),
the equations (15) of mean-mean-motion become identical in form with the equations
(1) of mean-motion, and the equation (17) of energy of mean-mean-motion becomes
identical in form with the equation (3) of energy of mean-motion.

These equations, obtained from (15) and (17) being equally true with equations (1)
and (3), the mean-mean-motion in the former being taken over the space S, instead of
S, as in the latter, then, instead of equation (9), we should have for the value of the
last term—

U 2

Pera, + ce, = — yap 2 Uae ik (ammeter as Wey e = \((25)

in which the right member expresses the rate at which heat is converted into energy
of mean-mean-motion, together with the rate at which energy of relative-mean-motion
is transformed into energy of mean-mean-motion ; while equation (19) shows whence
the transformed energy is derived.

The similarity of the parts taken by the transformation of mean-mean-motion into
relative-mean-motion, and the conversion of mean-motion into heat, indicates that
these parts are identical in form; or that the conversion of mean-motion into heat is
the result of transformation, and is expressible by a transformation function similar
in form to that for relative-mean-motion, but in which the components of relative
motion are the components of the heat-motions and the density is the actual density
at each point. Whence it would appear that the general equations, of which equations
(19) and (16) are respectively the adaptations to the special condition of uniform
density, must, by indicating the properties of matter involved, atford mechanical
explanations of the law of universal dissipation of energy and of the second law of
thermodynamics.

The proof of the existence of a criterion as obtained from the equations is quite
independent of the properties and mechanical principles on which the effect of the
variations of mean-mean-motion on the distribution of relative mean-motion depends.
And as the study of these properties and principles requires the inclusion of condi-
tions which are not included in the equations of mean-motion of incompressible fluid,
it does not come within the purpose of this paper. It is therefore reserved for
separate investigation by a more general method.

The Criterion of Steady Mean-motion.

23. As already pointed out, it appears from the discriminating equation that the
possibility of the maintenance of a state of relative-mean-motion depends on p/p, the
variation of mean-mean-motion and the periods of the relative-mean-motion.

Thus, if the mean-mean-motion is in direction x only, and varies in direction y
only, if w’, v’, w’ are periodic in directions «, y, z, a being the largest period in space,
so that their integrals over a distance a in direction are zero, and if the co-efficients
of all the periodic factors are a, then putting

+ du/dy=C*,;

taking the integrals, over the space a of the 18 squares and products in the last
term on the left of the discriminating equation (24) to be

FLUIDS AND THE DETERMINATION OF THE ORITERION. 149
— 18uC, (27/a)? «a3
the integral of the first term over the same space cannot be greater than
pC,e°C 2a?

Then, by the discriminating equation, if the mean-energy of relative-mean-mction is
to be maintained,

pC,* is greater than 700 p/a?,
or

par ae ae y 5)
= (iy) = 700. Site Won ee ek OO)

is a condition under which relative-mean-motion cannot be maintained in a fluid of
which the mean-mean-motion is constant in the direction of mean-mean-motion, and
subject to a uniform variation at right angles to the direction of mean-mean-motion.
Tt is not the actual limit, to obtain which it would be necessary to determine the actual
forms of the periodic function for w’, v’, w’, which would satisfy the equations of
motion (15), (16), as well as the equation of continuity (13), and to do this the
functions would be of the form

/ 9
> E cos {o(nt + aaa ;
\ t

where r has the values 1, 2, 3, &e. It may be shown, however, that the retention of
the terms in the periodic series in which 7 is greater than unity would increase the
numerical value of the limit.

24. It thus appears that the existence of the condition (26) within which no
relative-mean-motion, completely periodic in the distance a, can be maintained, is a
proof of the existence, for the same variation of mean-mean-motion, of an actual
limit of which the numerical value is between 700 and infinity.

In viscous fluids, experience shows that the further kinematical conditions imposed
by the equations of motion do not prevent such relative-mean-motion. Hence for
such fluids equation (26) proves the actual limit, which discriminates between the
possibility and impossibility of relative-mean-motion completely periodic in a space a,
is greater than 700.

Putting equation (26) in the form

»/ (du/dy)* = 700 p/pa’,

it at once appears that this condition does not furnish a criterion as to the possibility
of the maintenance of relative-mean-motion, irrespective of its periods, for a certain
condition of variation of mean-mean-motion. For by taking a? large enough, such
relative-mean-motion would be rendered possible whatever might be the variation of
the mean-mean-motion.

150 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

The existence of a criterion is thus seen to depend on the existence of certain
restrictions to the value of the periods of relative-mean-motion—on the existence of
conditions which impose superior limits on the values of a.

Such limits to the maximum values of a may arise from various causes. If du/dy
is periodic, the period would impose such a limit, but the only restrictions which it is
my purpose to consider in this paper, are those which arise from the solid surfaces
between which the fluid flows. These restrictions are of two kinds—restrictions to
the motions normal to the surfaces, and restrictions tangential to the surfaces—the
former are easily defined, the latter depend for their definition on the evidence to be
obtained from experiments such as those of PorsEUILLE, and I shall proceed to show
that these restrictions impose a limit to the value of a, which is proportional to D,
the dimension between the surfaces. In which case, if

J (la/dyy? = U/D,
equation (26) affords a proof of the existence of a criterion
DLO Cee Gt aera yg (AT)

of the conditions of mean-mean-motion under which relative or sinuous-motion can
continuously exist in the case of a viscous fluid between two continuous surfaces
perpendicular to the direction y, one of which is maintained at rest, and the other in
uniform tangential-motion in the direction # with velocity U.

Section III.

The Criterion of the Conditions under which Relative-mean-motion cannot be main-
tained in the case of Incompressible Fluid im Uniform Symmetrical Mean-flow
between Parallel Solid Surfaces.—Expression for the Resistance.

25. The only conditions under which definite experimental evidence as to the value
of the criterion has as yet been obtained are those of steady flow through a straight
round tube of uniform bore; and for this reason it would seem desirable to choose
for theoretical application the case of a round tube. But inasmuch as the application
of the theory is only carried to the point of affording a proof of the existence of an
inferior limit to the value of the criterion which shall be greater than a certain
quantity determined by the density and viscosity of the fluid and the conditions of
flow, and as the necessary expressions for the round tube are much more complex
than those for parallel plane surfaces, the conditions here considered are those defined
by such surfaces.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 151

Case I. Conditions.

26. The fluid is of constant density p and viscosity m, and is caused to flow, by

a uniform variation of pressure dp/dx, in direction x between parallel surfaces,
given by

Yi Freeh Oye Y= hO gee My Wel eh oie “ates es, (28)

the surfaces being of indefinite extent in directions z and @.

The Boundary Conditions.
(1.) There can be no motion normal to the solid surfaces, therefore
O—=5 0 whten yi —s sje Oni ewe) eee ens ace (29)
(2.) That there shall be no tangential motion at the surface, therefore

C—O OW when Se0) 5 8 5 6 eon 5 (80))S

whence by equation (21), putting w for u’, py, = — pdu/dy.
By the equation of continuity du/dx + dv/dy + dw/dz = 0, therefore at the
boundaries we have the further conditions, that when y = + by,

Siti City = CCB O 5 6 6 2 os o (Sil),

Singular Solution.

27. If the mean-motion is everywhere in direction , then, by the equation of
continuity, it is constant in this direction, and as shown (Art. 8) the periods of mean-
motion are infinite, and the equations (1), (3), and (9) are strictly true. Hence if

|

DS ties OL! 8h oe eas See me eee ey (oP)
we have conditions under which a singular solution of the equations, applied to this
case, is possible whatsoever may be the value of b,, dp/dz, p and yp.

Substituting for p,,, p,:, &¢., in equations (1) from equations (21), and substituting
uv for u’, &c., these become

du dp du du
pan tele tas) HOOKS NESE: Pome)

152 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

This equation does not admit of solution from a state of rest ;* but assuming a
condition of steady motion such that du/dt is everywhere zero, and dp/d« constant,

the solution of
CERO op ON a IUD Eo |
p 2) i GBF o
if :
u = du/dz =0 wheny=+b,, } (34).
is |
J

1 dp y — by

U

p da 2;

This is a possible condition of steady motion in which the periods of wu according to
Art. 8 are infinite; so that the equations for mean-motion as affected by heat-
motion, by Art. 8, are exact, whatever may be the values of

ut, Do, p, , and dp/dza.

The last of equations (34) is thus seen to be a singular solution of the equations (15)
for steady mean-flow, or steady mean-mean-motion, when w’, v, w’, p’, &c., have
severally the values zero, and so the equations (16) of relative-mean-motion are
identically satisfied. :

In order to distinguish the singular values of u, I put

—b

whence ee aijoMece (BS).

dp ByT : b?—y? |
—=———U,, U = —U, 2 =
dx be Un, 2 Un Eee)

b
=U, | TRO —= PA Us ]

According to the equations such a singular solution is always possible where the
conditions can be realized, but the manner in which this solution of the equation (1)
of mean-motion is obtained affords no indication as to whether or not it is the only
solution—as to whether or not the conditions can be realised. This can only be
ascertained either by comparing the results as given by such solutions with the results
obtained by experiment, or by observing the manner of motion of the fluid, as in my
experiments with colour bands.

* Ina paper on the ‘Equations of Motion and the Boundary Conditions of Viscous Fluid,” read
before Section A at the meeting of the B.A., 1883, I pointed out the significance of this disability to be
integrated, as indicating the necessity of the retention of terms of higher orders to complete the
equations, and advanced certain confirmatory evidence as deduced from the theory of gases. The paper
was not published, as I hoped to be able to obtain evidence of a more definite character, such as that
which is now adduced in Articles 7 and 8 of this paper, which shows that the equations are incomplete,
except for steady motion, and that to render them integrable from rest the terms of higher orders must
be retained, and thus confirms the argument I advanced, and completely explains the anomaly.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 155

The fact that these conditions are realized, under certain circumstances, has afforded
the only means of verifying the truth of the assumptions as to the boundary con-
ditions, that there shall be no slipping, and as to pm being independent of the
variations of mean-motion.

Verification of the Assumptions in the Equation of Viscous Fluid.

28. As applied to the conditions of PorsruILLE’s experiments and similar experi-
ments made since, the results obtained from the theory are found to agree throughout
the entire range so long as w’, v’, w’ are zero, showing that if there were any slipping
it must have been less than the thousandth part of the mean flow, although the
tangential force at the boundary was 0°2 gr. per square centimetre, or over 6 lbs. per
square foot, the mean flow 376 millims. (1°23 feet) per second, and

du/dr = 215,000,

the diameter of this tube being 0°014 millim., the length 125 millims., and the
head 30 inches of mercury.

Considering that the skin resistance of a steamer going at 25 knots is not 6 Ibs.
per square foot, it appears that the assumptions as to the boundary conditions and
the constancy of » have been verified under more exigent circumstances, both as
regards tangential resistance and rate of variation of tangential stress, than occur in
anything but exceptional cases.

Evidence that other Solutions are possible.

29. The fact that steady mean-motion is almost confined to capillary tubes—and
that in larger tubes, except when the motion is almost insensibly slow, the mean-
motion is sinuous and full of eddies, is abundant evidence of the possibility, under
certain conditions, of solutions other than the singular solutions.

In such solutions w’, v’, w’ have values, which are maintained, not as a system of
steady periodic motion, but such as has a steady effect on the mean flow through the
tube ; and equations (1) are only approximately true.

The Application of the Equations of the Mean- and Relative-mean-motion.

30. Since the components of mean-mean-motion in directions y and z are zero, and
the mean flow is steady,

On — 0) dU da Nadia — 0% a. 9 =) eee(ee
MDCCCXCV.—-A. Ke

154 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

and as the mean values of functions of w’, v’, w’ are constant in the direction of flow,

d (ww) d (wu) d (w'u’)
Gi * da 2 da Ose ee,

By equations (21) and (37) the equations (15) of mean-motion become

du ere dp Pu Pu Opa! pO pee,
i= dk ote +i) —0[ Gorm + germ}
dv dp ds d —— | ‘
Poa eh 1 OO) ae wo) (38).
dw dp ad —-F7 =
oS = {eas foro}

The equation of energy of mean-mean-motion (17) becomes

a) _ 5b, [a (-di) , @ (oui 4 gas team! |
Eo ba +H 4 (3 Es Us bapla (uuvj+ > (u ww)
| |

dy dy
du \? du \2 ah, Sein
fly) +(e) freee ay tee a | J

Similarly the equation of mean-energy of relative-mean-motion (19) becomes

dk . y’ , Sap / , apap
LU (Pe FUE) HO (Ply FOR) HW (Diy + WY]

t / ‘ sae At / / Serhepey , , seer Tate,
_ ale (piuctuw)+0 (p', vw) +u' (pe tww’)|]
#2 ee 38 a) au iG ui (a ap | 1" dz ow da 1 da uy dz

vag Oh
— p fare tw a EER Ci ek ehali bo. 5 (Uh

Integrating in directions y and z between the boundaries and taking note of the
boundary conditions by which wu, w’, v’, w’ vanish at the boundaries together with the
integrals, in direction z, of

d /—~du i Mdyhw. —
s (w a ee (w'w’)], ae [u’ (p.ctu'w’)], &e.,
the integral equation of energy of mean-mean-motion becomes

fe inde = — {il “ + p \( y er —p {we v = uw’ = a oh jay dz. (41).

FLUIDS AND THE DETERMINATION OF THE CRITERION, 155

The integral equation of energy of relative-mean-motion becomes

Nae oee=— Mo fray + Joelle Cc) +) + Co)

/dw’ dv’ dw dw'\2 dv if
+(e+e) +(Gete) +(etG) lave... (2)

lz dz | \dx
If the mean-mean-motion is steady it appears from equation (41) that

_— dp
= [J ieay ae,

the work done on the mean-mean-motion w, per unit of length of the tube, by the
constant variation of pressure, is in part transformed into energy of relative-mean-
motion at a rate expressed by the transformation function

<7 [fe (we yr = + ww za) dy dz,

and in part transformed into heat at the rate

oil) + El)

While the equation (42) for the integral energy of relative-mean-motion shows
that the only energy received by the relative-mean-motion is that transformed from
mean-mean-motion, and the only energy lost by relative-mean-motion is that
converted into heat by the relative-mean-motion at the rate expressed by the last
term.

And hence if the integral of E’ is maintained constant, the rate of transformation
from energy of mean-mean-motion must be equal to the rate at which energy of
relative-mean-motion is converted into heat, and the discriminating equation becomes

[[p (we dy sett 7) ue= -»({l2 ia) + (7) a esi

dw’ dv'\2 du’ dw! \2 fdv’ du’\2
ve (re ar a) a CG ag dy ) a5 (GE au dy ) Jy cae (43).

The Conditions to be Satisfied by u and wv’, v’, w’.

31, If the mean-mean-motion is steady wu must satisfy :—
x2

156 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

(1) The boundary conditions

= \0) wheney) == Dy a yee ne ee CL

(2) The equation of continuity
dtd = OFF) aa a ee CO

(3) The first of the equations of motion (38)

d

PD. ( au du fae ——, | :
de ONG ae 73) p ley (wv’) + is (ww ) Peart (45)) 3

or putting

u=U+u—U and dp/dz =p U/dy?

as in the singular solution, equation (46) becomes

1? u—U) @ (& —U) 1 FF jy
al a Se )=p 15, 0) + 4, ways aR SoS eG (47) ;

dy? de

(4) The integral of (47) over the section of which the left member is zero, and

the mean value of » du/dy = »dU/dy wheny=+b,. . . (48).

From the condition (3) it follows that if w is to be symmetrical with respect to the
boundary surfaces, the relative-mean-motion must extend throughout the tube, so
that

> del , dwlw\ 4 . :
5 7 lz Sa ay? . . . . . .
le ay sles Je is a function of y (49).

And as this condition is necessary, in order that the equations (38) of mean-mean-
motion and the equations (16) of relative-mean-motion may be satisfied for steady
mean-motion, it is assumed as one of the conditions for which the criterion is sought.
The components of relative-mean-motion must satisfy the periodic conditions as
expressed in equations (12), which become, putting 2c for the limit in direction z,

re
)

‘ [7 (er | dx = | w’ dx = 0

~'0 “0 “0

IP [ u' dy dz = 0

(2) The equation of continuity

du'/da + dv'/dy -+ dw'/dz = 0.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 157
(3) The boundary conditions which with the continuity give

7

io — Oi da ay) (dy — dw! dz — 0 when y == a= en ee(ol)

(4) The condition imposed by ‘symmetrical mean-motion

i ( du | dw’

) de = 26f y?) GEA While alee a ODE

ANY dz

These conditions (1 to 4) must be satisfied if the effect on w is to be symmetrical
however arbitrarily wu’, v’, w’ may be superimposed on the mean-motion which results
from a singular solution.

(5) If the mean-motion is to remain steady w’, v’, w’ must also satisfy the kine-

matical conditions obtained by eliminating p from the equations of mean-mean-motion
(38) and those obtained by eliminating p’ from the equations of relative-mean-
motion (16).

Conditions (1 to 4) determine an inferior Inmit to the Criterion.

32. The determination of the kinematic conditions (5) is, however, practically
impossible ; but if they are satisfied, w’, v’, w’ must satisfy the more general conditions
imposed by the discriminating equation. From which it appears that when w’, v’, w’

are such as satisfy the conditions (1 to 4), however small their values relative to u
may be, if they be such that the rate of conversion of energy of relative-mean-motion
into heat is greater than the rate of transformation of energy of mean-mean-motion
into relative-mean-motion, the energy of relative-mean-motion must be diminishing.
Whence, when wu’, v’, w’ are taken such periodic functions of #, y, z, as under
conditions (1 to 4) render the value of the transformation function relative to the
value of the conversion function a maximum, if this ratio is less than unity, the
maintenance of any relative-mean-motion is impossible. And whatever further
restrictions might be imposed by the kinematical conditions, the existence of an
inferior limit to the criterion is proved.

Expressions for the Components of possible Relative-mean-motion.

33. To satisfy the first three of the equations (50) the expressions for w’, v’, w’, must
be continuous periodic functions of «, with a maximum periodic distance a, such as
satisfy the conditions of continuity.

Putting

/ = 2n/a; and 7 for any number from 1 to ~,

158 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

and
/ i *) da, d n ‘d, n 18, =
—_> le + a cos (nla) ++ G + a sin (nl) )
v =X {nla, sin (nlx) — nlB,, cos (nlx) } ( ; (53),
w =X {uly, sin (nlx) — nl 8, cos (nlx) } J)

w,v, w' satisfy the equation of continuity. And, if

a=B=y=6= da/dy = dB/dy = dy/dz = dd/dz = 0 when y= + tn (54)

and «8, ay, «6 are all functions of y? only ,
it would seem that the expressions are the most general possible for the components
of relative-mean-motion.

Cylindrical-relative-motion.

34. If the relative-mean-motion, like the mean-mean-motion, is restricted to
motion parallel to the plane of ay,

= 6 = w = 0, everywhere,
y , Ay

and the equations (53) express the most general forms for wu’, v' in case of such
cylindrical disturbance.

Such a restriction is perfectly arbitrary, and having regard to the kinematical
restrictions, over and above those contained in the discriminating equation, would
entirely change the character of the problem. But as no account of these extra
kinematical restrictions is taken in determining the limit to the criterion, and as it
appears from trial that the value found for this limit is essentially the same, whether
the relative-mean-motion is general or cylindrical, I only give here the considerably
simpler analyses for the cylindrical motion.

The Functions of Transformation of Energy and Conversion to Heat for Cylindrical
Motion.

d ( 1’)

dt \ /

35. Putting

for the rate at which energy of relative-mean-motion is converted to heat per unit of
volume, expressed in the right-hand member of the discriminating equation (43),

(\{ (,H’) dx dy dz
=n (fea) +(G) t+ (G+) +25 eee. 6)

FLUIDS AND THE DETERMINATION OF THE CRITERION. 159

Then substituting for the values of w’, v’, w’ from equations (53), and integrating in
direction a over 27//,and omitting terms the integral of which, in direction y, vanishes
by the boundary conditions,

[fo (ray ae = 2 ffs{epr (ae + 2) + 2 (ne [(S2) + (FY)

(GN? 1 (LEN oh aly 5
+ (Se) + (Ge) haya ines ee ae (7h)

In a similar manner, substituting for w’ v’, integrating, and omitting terms which
vanish on integration, the rate of transformation of energy from mean-mean-motion,
as expressed by the left member in the discriminating equation (43), becomes

5 ds ; dB, la,\ du
ez v a dy dz = 4 {(s E (1. = = Be: ) Al DCB: ~ 3 > (G3)

dy] dy

And, since by Art. 31, conditions (3) equation (47),

AO IO) se py, We) - Sa iice te Pom ey eet oe)

ae ly
integrating and sae the boundary conditions,
bay G30) ape poo) =p [arr ly ee era(60)
And since at the boundary u — U is zero,

AITO O oS a oe (GN),

Whence, putting U-++-w—U for w in the right member of equation (58), substituting
for 1 — U from (60), integrating by parts, and remembering that

PU Ii ° . rac
ie ae 3 a WHOA HY 1S COMA 4 oe. oo (OX),

also that

uv =t {nt (na — Bee) f ile ee meee (OS):

‘ IB. Lat, \®
=3|405 i 5 [dy [nt (cn = B.= a ett es = | (al) Cae Bia dy] . (64).

by J —by

160 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS

If wu’, v' ave indefinitely small the last term, which is of the fourth degree, may be

neglected.
Substituting in the discriminating equation (43) this may be put in the form

apa |)( 222) oa. (Bm Vl] are Sea ea
2pbUn _ 720 (: {ul ed ai (a) a Gi | * ee a ( i) ja (65)

ie 3 [dy [ 3 {nt( = 2 — a, aT fay

—ly 4 —2o

Limits to the Periods.

36. As functions of y the variations of @,, 8, are subject to the restrictions imposed
by the boundary conditions, and in consequence their periodic distances are subject
to superior limits determined by 20,, the distance between the fixed surfaces.

In direction x, however, there is no such direct connection between the value of b,
and the limits to the periodic distance, as expressed by 27/nl. Such limits necessarily
exist, and are related to the limits of «, and 8, in consequence of the kinemetical
conditions necessary to satisfy the equations of motion for steady mean-mean-
motion ; these relations, however, cannot be exactly determined without obtaining a
general solution of the equations.

But from the form of the discriminating equation (48) it appears that no such exact
determination is necessary in order to prove the inferior limit to the criterion.

The boundaries impose the same limits on «@,, 8, whatever may be the value of il ;
so that if the values of «,, 8, be determined so that the value of

26bUn
is a minimum

for every value of nl, the value of 7/, which renders this minimum a minimum-
minimum may then be determined, and so a limit found to which the value of the
complete expression approaches, as the series in both numerator and denominator
become more convergent for values of nl differmg in both directions trom 77.

Putting J, a, 8 for r/, «,, B, respectively, and putting for the limiting value to be
found for the criterion

20b)Um di
ke ihn | ae? (66)
bo op! ( (da\? /dB\? | da\? PB
: Me +B) +20) (F) + (5) |-+ (2) (5) bey
SK, a i | ae ay) dy | dy ) i i (67)

ar a (e@ — a) ay

ye a Ney “dy ;

when a and B are such functions of y that K, is a minimum whatever the value of J,
and / is so determined as to render K, a minimum-minimum.

FLUIDS AND THE DETERMINATION OF THE CRITERION. 161

Having regard to the boundary conditions, &c., and omitting all possible terms
which increase the numerator without affecting the denominator, the most general
form appears to be

@ = Y" (Qe. sin (25 + 1) p], )
B = 3," [by sin (2ép)}, ea rat ieeene ene anes 9" (08)

where |
P = ty/2by J

To satisfy the boundary conditions

s = 2r, when s is even, s = 2r + 1, when s is odd.
t= 2r + 1, when ¢ is odd, t = 2(r + 1), when ¢ is even.

Since a = 0, when p= + 37, >)
|
|

yo (Gs 41 s Csr43) = 0,
| GD:
and since dB/dy = 0, when p = + $7, : |

ay (4r or 2) Dir + 4 (r+ DV Oiyat — 04

From the form of K, it is clear that every term in the series for a and B increases
_ the value of K, and to an extent depending on the value of rv. K, will therefore be

minimum, when

(70),

a= ad, sin p + a, sin 3p
B= b, sin 2p +b, sin 4p |

which satisfy the boundary conditions if

dies Bagg Nati us Sus aU ati muse Des tee (Yet
by = a) ay)

Therefore we have, as the values of « and £, which render K, a minimum for
any value of l

a/a,=sinp-+sin 3p, B/b,= sin 2p + ¥sin 4p. 5)
And |
2by da 2b), dB _ a3
Rag = CEP + 3 cos 3p, BR Fc 2 cos 2p + 2 cos 4p (72)
2b, [adB Bdz 1 ; ; : ; |
—_— —_— g — —— y, 2
rap, ( dy dy ) aaa 3 sin p — 3 sin 3p + sin 5p + sin 7ps |

MDCCCXCV.—A. Y

162 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS
and integrating twice
bo
1
b

~—%

le (Me Gea Se Sree 1
ay ine. oy =) dy = — 1325 [= G05 ie hoe i pee EE
Putting

vir
2, for is
: : 3 4
the denominator of 5K,, equation (67), becomes
Cwm 1°325 Labo.
In a similar manner the numerator is found to be

bt (F) Ls (ear? + 1:25b,2) + 2L2(10a,2 + 8,2) + 82a,2 + 80,°3,

and as the coefficients of a, and b, are nearly equal in the numerator, no sensible error
will be introduced by putting

by = Chip
then
3 Lt + 2 x 5:°53L? + 50 /a\*
= 0-408L 6) ee)
which is a minimum if
Ol i) nis nec) 5 (75)
and
Kase BIER te, es eet eee (76).
Hence, for a flat tube of unlimited breadth, the criterion
pi205Un/e 18 ereater) than Dil 7) 2) 20 eee, emma

37. This value must be less than that of the criterion for similar circumstances.
How much less it is impossible to determine theoretically without effecting a general
solution of the equations ; and, as far as [ am aware, no experiments have been made
in a flat tube. Nor can the experimental value 1900, which I obtained for the round
tube, be taken as indicative of the value for a flat tube, except that, both theoretically
and practically, the critical value of U,, is found to vary inversely as the hydraulic
mean depth, which would indicate that, as the hydraulic mean depth in a flat tube is
double that for a round tube, the criterion would be half the value, in which case the
limit found for K, would be about 0°61 K. This is sufficient to show that the
absolute theoretical limit found is of the same order of magnitude as the experimental

FLUIDS AND THE DETERMINATION OF THE CRITERION. 163

value ; so that the latter verifies the theory, which, in its turn, affords an explanation
of the observed facts.

The State of Steady Mean-motion above the Critical Value.

38. In order to arrive at the limit for the criterion it has been necessary to consider
the smallest values of w’, v’, w’, and the terms in the discriminating equation of the
fourth degree have been neglected. This, however, is only necessary for the limit,
and, preserving these higher terms, the discriminating equation affords an expression
for the resistance in the case of steady mean-mean-motion.

The complete value of the function of transformation as given in equation (64) is

SU eG dp, det, OF ee aBy, eR
— 3 — —— 2 — 7a
—-> lp The [dy [inl (1, TF [5= - )e dy aR ie al ie) (4.5 7 B al dy) 5 (71a)

Whence putting U + wu — U, for w in the left member of equation (77), and inte-
grating by parts, remembering the conditions, this member becomes

Fe | ay (pu dy + © | we? Wy 6 3 5 2 0 > (78),

in which the first term corresponds with the first term in the right member of
equation (64), which was all that was retained for the criterion, and the second term
corresponds with the second term in equation (64), which was neglected.

Since by equation (35)

3U 5 1 dp
a MER lag eee
we have, substituting in the discriminating equation (43), either
1/dt (pH’) d; 2 (ie0
Ae (pH’) Lae a f (wv)? dy)
ee) p bo? dp __ 2b? [is Ke +o eh (79)
3 2 pera we) bo Y ?
ee ee * — | dy (we dy
—bo —bo
or
du dp
Lp ae Oe Meee ai) eo alc cs cud (OO))E

Therefore, as long as

164 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS FLUIDS.

is of constant value, there is dynamical similarity under geometrically similar circum-
stances.
The equation (79) shows that,

ap dp

5 dp .
Vv —_— + =I , iy
when OP ap de greater than K,

wv must be finite, and such that the last term in the numerator limits the rate of

transformation, and thus prevents further increase of wv’.
The last term in the numerator of equation (79) is of the order and degree

p Lia*/y? as compared with Lite*

Z
a (,H’) the first term in the numerator.

It is thus easy to see how the limit comes in. It is also seen from equation (79)

that, above the critical value, the law of resistance is very complex and difficult of

5 i
the order and degree of a

interpretation, except in so far as showing that the resistance varies as a power of the
velocity higher than the first.

V. On a Method of Determining the Thermal Conductivity of Metals, with
Applications to Copper, Silver, Gold, and Platinum.

By James H. Gray, M.A., B.Sc, late 1851 Exhibition” Scholar, Glasgow University,

Communicated by Lord Ketvin, P.RS.
Received May 24,—Read June 14, 1894; Re-cast, with Additions, January 31, 1895.

OF the different methods hitherto employed for the determination of thermal conduc-
tivity of metals, only those which were elaborated by Forses and by Anasrrim have
been successful in giving absolute results with fair approach to accuracy. The two
methods, in the hands of these and subsequent experimenters, have given closely
concordant results, both for copper and for iron. They, however, possess the dis-
advantages of being exceedingly elaborate, requiring, as they do, very extensive
preparations and comparatively large masses of the metals which are to be tested. _
For this reason, only the less costly metals can be tested, as it would be impracticably
expensive to obtain a bar of gold or platinum, for example, a metre or more in length,
and perhaps 2 square centims. section.

The method used in the present investigation (for which a grant of £50 was obtained
from the Government Research Fund) is free from these objections. It was suggested
by Lord Kevin as far-back as thirty years ago, about the same time that the late
Principal Forses began his experimental inquiry as to whether thermal conductivity
varied with temperature. The chief advantages of this method are that (1) it is
much simpler than the others ; (2) a test of the conductivity of any metal can be
made in two or three hours; and (3) (perhaps most important of all) only a few
grammes of the metal are necessary. Thus, even the rarest and most expensive
metals can be tested, at very moderate cost.

The method is essentially the experimental realization of the theoretical conditions
implied in the fundamental formula

— Y

Oe eA en?

where the symbols have their usual meaning. The metals to be tested are made in
the form of wires of circular section. One end is kept at a constant temperature v,
and the flow of heat Q, in a given time ¢, is measured. The length and section
being known, all the data are obtained for the determination of the absolute value of

30.5.95

166 MR. J. H. GRAY ON A METHOD OF DETERMINING

the thermal conductivity. It will be noted that this value is the proper mean
conductivity corresponding to the range of temperature between the ends of the wire.

Fig. 1 is a perspective drawing of the apparatus which has been used in the tests
of this method. Fig. 2 is a section (all the parts being drawn quarter full size)
containing the axis of the wire to be tested. Fig. 3 is a section, drawn full size,
through the middle of the apparatus, in a plane perpendicular to the section in fig. 2,
and showing in greater detail the wire, calorimeter ball, and that part of the heating
box at which the wire is soldered.

Fig. 1. Fig. 2.

2 3
_———

AWS

Quarter full size.

Referring to fig. 2, W is the wire to be tested. The upper end of W is soldered
into the bottom of the copper box B, and the lower end into the solid copper ball C,
the diameter of which is 5°5 centims. The sides of the copper box B are of thin
sheet copper, and the bottom of copper, 3 millims. thick. B is supported at the
middle by being fitted into a rectangular hole in a wooden screen, L, of dimensions
60 X 60 centims., by 2 centims. thick. In the hole of the copper block K, a small
thermometer is inserted for measuring the temperature of the other end of the wire.
The box B is filled with water and kept boiling briskly. The ball C is the calori-
meter by which the amount of heat conducted by the wire W is measured. In order
to measure the temperature of C, a very sensitive thermometer, which can be read to
one-fortieth of a degree Centigrade, is inserted in a hole drilled in C. This hole
reaches to a depth of 8°6 centims. from the circumference of the ball. The bulb
of the thermometer in the ball is surrounded by water or mercury. Surrounding

THE THERMAL CONDUCTIVITY OF METALS. 167

the heating box, B, is an asbestos covering, M, to prevent heat from reaching the
calorimeter from the sides of the box. In order to keep the temperature of the air
surrounding the calorimeter constant, the latter is surrounded by a water-jacket, R,
through which water at the temperature of the air is kept circulating. This water-
jacket is simply a cylindrical vessel, made of copper, with double walls, between
which the water circulates. The inside diameter is about 1 centim. greater than that
of the ball. The top of the water-jacket is covered with three or four layers of

Clay

Full size.

paper, so that the air surrounding the ball is completely separated from the outside
air, and is kept at a constant temperature. Surrounding the wire, all along its
length, is a tube of cardboard, G, of inside diameter 1 centim. Between the wire
and the inside of the tube cotton-wool is loosely packed, so as to prevent, as
effectually as possible, circulation of air about the wire.

From fig. 2 it will be seen that the heat from the Bunsen is prevented from

168 MR. J. H. GRAY ON A METHOD OF DETERMINING

reaching the wire or the ball by the wooden screen L. In the bottom of the box,
just above the Bunsen, are riveted a number of copper pins, so as to catch and
distribute the heat of the burner. Fig. 4 shows a plan of the box.

It will be convenient to classify the sources of error that may affect the results,
and to deal with them at this point.

1. There is, unless proper precautions be taken, loss of heat due to radiation from
the surface of the wire, and therefore the value obtained for the conductivity will be
too low.

2. The temperature indicated by the thermometer in the hot water may not be the
same as that of the end of the wire at the point where it enters the box. Also, the
temperature of the ball may not be the same throughout.

3. The thermometer may not indicate the average temperature throughout the ball.

4, There may be a lag in the thermometer.

5. There may be some error due to the solder at the ends of the wire.

1. Loss of heat due to radiation from the surface of the wire. As this was the most
obvious source of error, a long time was spent and much work done in investigating 1t.

The cardboard tube G (fig. 2) was found to be thoroughly efficient in preventing
radiation. It can be very easily made by rolling a long strip.of paper, which has
been previously gummed on one side, several times round a circular rod of a centimetre
diameter. The length of the tube is a little less than that of the wire. After the
gum has dried, a slit sufficiently wide to admit the wire is cut parallel to the length.
A circular piece of cardboard is fixed with gum to one end of the tube, as a flange for
attaching the tube to the bottom of the heating box. After it has been arranged
that the wire is in the central line, cotton-wool is put loosely in and the slit closed
up with gummed paper. The small volume of air in this tube takes almost imme-
diately the temperature of the wire all along its length.

To test the efficiency of the tube, a large number of experiments was made, the
results of which are given further on (pp. 180,181). It is clear that for a given differ-
ence of temperature between the ends, the loss by radiation from the surface of a wire
of given diameter will be greater the greater the length. If, then, there be no error
which becomes less the greater the length, and thus compensates for the radiation error,
a sufficient test of the efficiency of the tube will be to determine the conductivity with
different lengths of the same wire. The shorter lengths ought to give a distinctly
higher value, since the radiation from the surface is not only less than in the longer

THE THERMAL CONDUCTIVITY OF METALS. 169

lengths, but the quantity of heat conducted along the wire per second is greater, and
therefore the percentage error due to radiation rapidly diminishes.

In order to determine a superior limit for the error due to loss of heat by radiation,
a calculation is made below. The numbers used are taken so as to be as unfavourable
as possible, and give a value much higher than what would practically turn out.

in the case of copper wire, the surface was always somewhat tarnished, so the
emissivity may be taken as intermediate between those of polished and blackened
copper, that is ‘0008. The diameter aud length of wire were respectively ‘2 centim.
and 4 centims. The temperature at the hot end was 98° C., at the cold end 14° C.
The curve of temperature along the wire being logarithmic, the mean temperature
will be considerably less than half the sum of the highest and lowest temperatures,
which would assume that the curve is a straight line passing through the highest and
lowest points. Take, however, the curve to be a straight line; then the mean tempe-
rature above that of the air is 42°C. The quantity of heat Q, lost from the surface
S, of emissivity E, in one minute, is

Q = ES x 42 x 60
= 1:91 C.G.S. units approximately.

The quantity of heat conducted along the wire during this minute, as taken from
one of the tests, was ‘5 x 68°9, ‘5 being the rise in temperature, and 68°9 the capacity
_ of the calorimeter. The maximum percentage error due to radiation in a length of
4 centims. is therefore 5°5 per cent. This is on the assumption that there is no
jacket round the wire, but even then the actual loss would probably be less than
3 per cent. if currents of air be avoided. This rough calculation shows that radiation
from the surface of the wire need not be considered as an objection to the method.

2, Possible error due to the fact that the thermometers are not actually at the
ends of the wire, and so may not be indicating the proper temperatures.

The effect of this error would also be to give too low a value for the conductivity.
To guard against this the bottom of the box is made very thick, and the large block
K (fig. 2) is added so as to hold the thermometer. The difference of temperature
between the inside and outside surfaces of the bottom of the box is certainly
exceedingly small, if as much heat as the wire can take away is supplied to it.
Since the heat is supplied by boiling water, it is, however, possible that the copper
conducts so quickly that there is always a layer of water, it may be thin, immediately
in contact with the metal at a very much lower temperature than 100° C. This
point is particularly emphasized by Lord KELvIn in volume 8 of his Collected Papers,
where he remarks upon the exceedingly low values obtained by CLEMENT and by
Pécier for the conductivity of copper. These experimenters both attempted to
measure the conductivity by keeping one side of a slab of the metal in contact with
water at a constant temperature and measuring the rise in temperature of a known

MDCCCXCY.—A. Z

170 MR. J. H. GRAY ON A METHOD OF DETERMINING

quantity of water in contact with the other side. The result was that Ciiment’s
value was 200 times too small, while PrcLet, who tried to avoid CLEMENT'S error by
having the water violently stirred, succeeded in obtaining a value six times too
small. With the large surface to carry away the heat, PEcLET’s method is useless
for any substance having so high a conductivity as even the worst of the metals,
since the stirring could never be rapid enough without introducing fresh complications.

The direct tests applied to determine this error in the present investigation showed
that the temperatures on the inside and outside of the bottom of the box were the
same.

The following approximate calculation serves to show the order of magnitude of
the error due to the assumption that the thermometer in the ball indicates the
temperature of the end of the wire.

It is clear that the difference of temperatures between the wire where it enters the
ball, and the thermometer will be much less than that found as follows :—

Take the case of a wire carrying heat to an infinite block of metal whose surface is

Fie. 5.

!

a ee

plane, and remark that the isothermals in the block would be hemispherical surface
(fig. 5) having for their common centre the point where the axis of the wire enters
the ball, and suppose the flow of heat to be steady.
Let
K = conductivity of the wire,
i .s is ball,
a = radius of the wire,

beh ies j)eaballll:

THE THERMAL CONDUCTIVITY OF METALS. ialtyal

Then the quantity of heat that flows through any hemispherical surface distant 7
from the end of the wire is

Bea ee 2
Q=-hk Tp ot
and, since the flow is steady
ad dv
= ane 16) ad —
ie ( ap 2777 ) — 0
Hence
lv
Hoye
Gp Ci,

which gives

v= Cpr7!+ C,.

For r = a let v = V, and for 7 = b let v = @.

Hence
V-¢O _ 6b — Va
v= ab one
=i Cor
whence
Ho al WS © op
piled inca ake ead, 2
and
Wea
Q = 27k Re ab,
Ajso
g=(v,- We

where V, is the temperature at the hot end of the wire, and / the length of the wire.

Since V is the temperature of the wire just where it enters the ball, and 6 the
temperature at the centre of the ball, V — @ is certainly much greater than the
error, a superior limit to the magnitude of which we wish to ascertain. The heat
which flows through the wire must be equal to that which flows into the ball ;
therefore

T ‘K passe
(v, nlp V ) a wt ork ni Say ab,
whence
Kea (Gita)
a K (b—a
=-(V-0+409-V))< ee
and, therefore,
@ K (b — a)
BW ip tb
Mia’ ay Danaapraossa)i
te 0

V4

(p22) MR. J. H. GRAY ON A METHOD OF DETERMINING

In this case V, = 100° C, 0 = 15°C, and, since the copper of the wire and ball
were the same, K/k= 1; b = 27 millims., a= 1 millim.
Take 7 = 8 centims. ; then,

then V— 6 =) 85 Sen

Therefore 1°3° C. is greater than the extreme possible error made with the copper
wire, that is 1°3 in 85, or about 1°5 per cent.

Several attempts were made to obtain a direct test of this by applying a thermo-
electric junction to the wire just at the point where it entered the ball. Owing,
however, to the large mass of the ball which had to be heated, it was found most
difficult to solder the thin wires of the thermo-electric junction at the required place,
and, after several unsuccessful attempts, it was given up, as the indirect proof supplied
by using different lengths of wire seemed quite satisfactory.

3. The thermometer in the ball may not indicate the average temperature.

This also would be tested by using different lengths of wire, and, as will be seen,
the results show that there was no substantial variation.

4. Lag in the thermometer which measures the rise in temperature of the ball.
Here again different lengths will be a test. Also, in case that the water round the
bulb of the thermometer caused the lag, mercury was substituted, but no difference in
the result was obtained.

5. The solder at the ends did not cause any difference of value for different
lengths.

The method of conducting a test is as follows.

Take a length of not more than 8 centims. of the wire. As it is very easy to
obtain any diameter, it will be convenient to have a hole bored in the bottom of the
heating box, just below the thermometer, of diameter rather more than 2 millims., and
depth 3 or 4 millims. The heating box must be brazed together, otherwise it is apt
to fall to pieces when the wire is being soldered in. The latter process can be done
with ordinary solder.

The mass of copper in the box being considerable, it is rather a troublesome matter
to solder the wire into it, as the whole box has to be heated. For this reason a
soldering iron cannot be used. The box is most easily heated by a blow-pipe flame
and the wire then inserted. The extra solder is then cleared off, so as to give a
definite point from which to measure the length. After this end is fixed, the other
end is soldered in a similar manner to the copper ball, and in the latter case fusible
solder melting at about 100° C. will do quite well.

THE THERMAL CONDUCTIVITY OF METALS. 173

It was, however, found that the method of soldering just described, and used in
this investigation, was very troublesome, and required some practice. If new
apparatus were being made, it would certainly be much more convenient to make an
alteration in this respect.

The following plan would make the soldering of the wire a very easy process,
instead of, as described, a difficult one. Six copper plugs, each of the shape shown
in sectional elevation and plan in fig. 6, might be made, 8 miilims. in length,

and 1 centim. diameter, so as to screw into a corresponding hole in the bottom of the
heating box ; and six similar plugs might be made for the ball. In each of the plugs
the central hole might be made of a different diameter, varying from 2 to 4 millims.
In this way, wires of different diameters could very easily be soldered into the
suitable plugs, which could then be screwed, first the one end into the ball, then the
other end into the box. The two side holes shown in fig. 6 are for the purpose of
facilitating the screwing in of the plugs. By screwing into the ball first, the possi-
bility of twisting the wire is avoided. It is advisable not to use wire of diameter
much less than 2 millims., for, in wires of less diameter, the length required to give a
readable rise of temperature per minute becomes inconveniently small, unless the
calorimeter ball is made very small.

The calorimeter ball most frequently used in the present work was turned from
the solid, and is 5°5 centims. in diameter. This was found to be a very convenient
size for the metals of high conductivity—for example, gold, silver, and copper.
Any length from 4 to 8 centims. of wires of these metals may be used without
making it difficult to read the rise in temperature per minute. It is not advisable
to use lengths shorter than 4 centims., as there is then a danger of the water-
jacket being too near the heating-box, but it is better to use a smaller ball, say
of 4 centims. diameter, for metals of lower conductivity, For metals having con-
ductivities between 1:0 and 0°7 C.G.S. units, the large ball was found to be quite
convenient ; for lower values the smaller ball was used. The object aimed at was
to arrange the dimensions so as to enable an experiment to be finished in less than
half an hour from the time that one end was made hot by the boiling water.

After the wire has been soldered in, the box is placed in the screen L (fig. 2), and
fixed by any convenient means, so that the wire hangs vertical, and the asbestos
cover is put over the box. The cardboard tube, having been made of suitable
length, and slit along its length, is now slipped round the wire, and, after a little
cotton is loosely packed in, the slit is closed up by means of a strip of gummed paper.

174 MR. J. H. GRAY ON A METHOD OF DETERMINING

The wire is now completely enclosed in this tube, and loosely surrounded by cotton
wool,

The thermometer is placed in the hole in the ball, and a little water put in to fill
up the hole. The water-jacket may then be raised so as to surround the ball, and
the top of the water-jacket must be covered with two or three sheets of paper, holes
haviug been cut in these, so as to admit the wire and thermometer.

It was found best to make these preparations a few hours before the actual test
was begun, so as to allow the system to take up a permanent temperature. When it
has been ascertained that this temperature has been reached, a reading is taken from
the thermometer in the ball. The thermometer used was most carefully made and
calibrated for the tests by Mr. Orro Mtttisr, of Glasgow. The whole length of the
stem is 15 centims., and it is marked off to read twentieths of a degree from 9° to —
20° C. Each division is a half millimetre, so it is perfectly easy to read to one-
fortieth of one degree.

Before beginning the test, the water-jacket is lowered, and a vessel containing ice
and water raised so as to cover a part of the ball. By this means the temperature of
the ball is lowered by 6° or 7° below that of the air. While this is being done, the
boiling water is poured into the box, so as to nearly fill it, and the Bunsen lamp lit.
The water soon begins to boil rapidly, and the thermometer (which is 12 centims.
long and reads from 95° to 105° C.) indicates a constant temperature, usually 97° or
98° C. When the temperature of the ball has been lowered 6° or 7°, the ice and
water are taken away, and the ball is carefully dried with a soft cloth. The water-
jacket is again placed so as to surround the ball and the cover put on as before, the
circulation of water in the jacket having been started.

It is now only necessary to take readings of both thermometers every half minute.
The temperature of the hot water will be practically constant, but it is advisable
to take the readings in case of alteration. The calorimeter thermometer may be read
till it reaches 20° C.

It will be convenient to explain here the reason for cooling the ball 6° or 7° before
starting. In the preceding remarks no notice was taken of the fact that there will
be radiation to or from the surface of the ball unless the latter is at the same tempe-
ture as its surroundings. It would be impossible to allow for this by calculation, as
the surface is altered before every test by being heated while the wire is being
soldered into the ball. For the purpose of getting rid of the necessity of allowing
for this radiation, the ball is cooled down.

Let Q, =the quantity of heat which flows along the wire in unit time when the
_ hot end is at T° and the cool end at above the temperature t of the air and water-
jacket, and let Q, = the quantity when the cool end is & below that of the air.

Then, assuming that the conductivity does not change very much through 26°, and
that «, the loss by radiation in unit time when the ball is 6° above the air tempera-

THE THERMAL CONDUCTIVITY OF METALS. 175

ture; equal to the gain by absorption in unit time when the ball is @ below the
air temperature, we have |
_ KA

> Oh SL Ce ae
and
KA
Q=— [(T-(—A]+2
Therefore
; + Q, KA,
g a= — (TT — 2).

It is seen by the last equation that the effect of radiation to or from the surface of
the ball is completely eliminated since the coefficient of emission is numerically equal
to the coefficient of absorption for the same difference of temperatures. It therefore
fortunately does not matter how the surface of the ball becomes changed, so long as
it remains the same during the half hour of the experiment. As a matter of fact,
during the soldering process the surface becomes very much tarnished.

Table I. gives a specimen experiment taken at random fiom my laboratory book.

Fripay, 23rd March, 1894.—Pure Silver Wire (annealed). Length = 6°59 centims.
Diameter = 202 centim. Temperature of Air = 14°3° C.

| {
Te II. I. II.
Reading taken every Temperature of | Reading takenevery| Temperature of
half-minute. hot end. | halt-minute. hot end.
| I
mc: aC: OE mc:
10°3 98:2 14°75 98°3
10°5 98:2 14:9 98°4.
10°75 98:2 151 98°6
10°95 98°38 15°25 98:5
1115 98:2 15°45 98°6
11°35 98-2 | 156 98-4:
11°55 98:3 15°75 98-4.
11°75 93°3 15-9 98°6
| 11:95 98-2 16:05 98°5
| 12:15 98°3 16:25 98°6
12°35 98:2 16°4 98°6
12°55 98°3 16°55 98°6
12°75 98°5 16°7 98°6
12-815 98°35 16°85 98°6
31 98-4. 17:0 986
13:3 | 98-3 17-15 98:6
13°5 | 98-4 17:3 98°6
13°65 | SiO 17°45 98°6
13°85 5 98-4 17:6 98°6
14:05 | 984 We 98°7
14:25 98-4 17°86 | 98°6
144 98-4 | 18:0 98°6
14:6 98°3 |

176 MR. J. H. GRAY ON A METHOD OF DETERMINING

The numbers in column I. are put on a curve, as shown in diagram II. From this
curve the rise in temperature in half a minute is read off for «° above the temperature
of the air, and this is added to the rise for «° below the temperature of the air, where
« is any value from 0 to 5 or 6. In this way as many as 10 or 15 values are
obtained. If the curve were quite regular, each of these values would be the same,
since they each represent the rise in temperature per minute for the same difference
of temperature, but they are found to vary by about 1 or 2 per cent. But, by taking
the mean of 10 or 15 values, it will be seen that the result obtained must be very
near the correct value for the rise between the given temperatures. It is then only
necessary to multiply this rise in temperature by the thermal capacity, C, of the ball
to find the quantity of heat that has passed along the wire in one minute, and the
conductivity can be calculated from the formula

s Cal
~ ar? (T —#) 60
where 7 is the radius of the wire.

In order to obtain an accurate determination of the thermal capacity of the ball, I
took it to Dublin, where the capacity was most carefully determined for me, during
the time I was there, by Dr. Joun Joty, F.R.S., by his most ingenious steam
calorimeter method.* I have to thank Dr. Joty for the trouble to which he put
himself in making the determination.

As the most important thing in testing the method is to show that with different
lengths the resulting determination of the conductivity remains practically the same,
these series of tests and the results will be given first.

The wire first used was what was called six years ago high electrical conductivity
copper. The diameter was 2°1 millims., density 8°85, volume specific (electrical)
resistance, 1834 in electromagnetic units. This wire was almost exclusively used,
but in the course of the work tests were made of wire got from Messrs. GLOVER and
Co. in the end of the year 1890. Messrs. Glover’s wire was found to have con-
siderably higher conductivity, both electrically and thermally, than the first-
mentioned wire, which for convenience will be called the laboratory copper, as it was
what was used for all the electrical work in the laboratory. Taking the laboratory
wire as 100 per cent. conductivity (thermally and electrically), it was found that
Messrs. GLOVER’S wire was 106°6 per cent. electrical, and 108 per cent. thermal con-
ductivity.

These results will be referred to further on (p. 180). They are merely mentioned
here to show that the best conducting wire was not used for the exhaustive tests.

Table II. shows the record of series of experiments made on laboratory copper wire.
The wire was soldered into the heating box and ball as described ; an experiment
was made and the length measured carefully. The ball was then heated by a blow-

* J. Jony, ‘Roy. Soe. Proc.,’ vol. 41, p. 352, 1886,

THE THERMAL CONDUCTIVITY OF METALS. WC

pipe flame to allow the wire to be taken out. A short piece was then cut off and the
shortened wire again soldered into the ball.

TaBLeE I].—Showing rise of Temperature of Calorimeter Ball with time.

Diameter of wire = ‘210 centim. Temperature readings taken every half-minute.
Length Length Length Length Length
=6°31 centims. =5'87 centims. =} (O}, =4°39 centims. =4-01 centims.
| Temp. reading at | Temp. reading at| Temp. reading at| Temp. reading at | Temp. reading at
| every half-minute. | every half-minute. | every half-minute. | every half-minute. | every half-minute.
BC: =r °C. °C. mac!
6-45 6:25 7-0 6°65 735
6°65 645 0:25 6°95 a7
6 85 67 75 72 8:0
7:05 69 775 745 83
7:25 71 8:0 77 86
745 73 8:2 80 8:95
7-65 75 8-4. 8:25 9°25
7°85 775 8°65 8:5 9:55
8-05 095 8°85 875 9°85
8:25 8-2 all 9:05 10°15
8-45 | 8-4 9°35 9°3 10°40
8°65 | 86 9°55 9-6 10°75
8°85 | 88 9°8 9°85 11:05
9-05 9-0 10-0 10-1 11°36
9-2 9-2 10-2 10°35 11-65
9-4 94 | 10-4 10°6 11-9
9°55 9-6 10°65 108 12:2
9°75 9°8 10°85 10:05 125
9°95 10-0 11:05 | 11:3 12°75
1071 10°15 11-25 115 13:0
| 103 10°35 11-45 | 11°75 13°25
10°45 10°55 | 11°65 | 12:0 13:5
10°65 10°75 | 12-1 | 12:25 138
10:85 109 | 123 12-45 14.05
10°35 1 12°5 | 12:7 143
1115 | 11°25 | 12-7 12:95 14°55
113 | 11-45 12:9 | 13:15 148
11°45 11:65 | 13:05 13°35 15-1
116 118 | 13°25 13°56 15°35
11:3 12-0 138 156
11-95 | 12°15 140 15°85
12-1 12:35 14-25 16-1
12-25 12°55 | 14-45 168
12-4 | 16°55
126 | 168
12°75 |
12-9
3-05
al OY ees : ae
Temp. of air 9°85 C.| Temp. of air 9°11 C.| Temp. of air 10°-0 C.) Temp. of air 10°35 C., Temp. of air 12°3 C.
| Temp. of hot water | Temp. of hot water | Temp. of hot water | Temp. of hot water | Temp. of hot water
97°°3 C. | SOIC: 97°-0 C. 96°4° C. 96°°7 C.

|

MDCCCXCV.— A. Die

Diagram I.

MR. J. H. GRAY ON A METHOD OF DETERMINING

er

lela

orig he
LL

Z
e

BEERS ae |

ie \
HEHE SSS
ST SN
Ree oe ean
| eee Na

eepnubpnias prinehesy

eA

erasers
reed
PACTS 4S

ay

(SERA aS aa ee eae

Time in Half-Minutes.

24 26 28 30 52 34 36 38 40 42 44 46 478 50 52 54 56 58 60 62 Gt 66

22

10 l2 14 16 18 20

4 6 6.

2

THE THERMAL CONDUCTIVITY OF METALS. 179

The temperature of the hot water varied not more than half a degree during an
experiment, and the value given in each column of the preceding Table is the mean
throughout the time. The columns of temperatures were, immediately after an
experiment, put on a curve with time as abscissze. The effect of radiation to and
from the calorimeter ball is fairly well marked. At the point corresponding to the
temperature of the air in each curve there is an increase of curvature, caused by the
fact that the radiation has changed from negative to positive.

In order to find the flow of heat, the rise of temperature per minute was read from
the curve ata temperature « below that of the air, and this was added to the rise
for ° above that of the air. « varied from 0° to 4° or 5°. By this means from ten
to fifteen readings were got, and the mean of these gave the rise at the temperature
of the air.

For example, for the length 6°31 centims. in the first column of Table L, the rise
thus obtained from the curve, Diagram I, was ‘3605 in one minute. The capacity
of the ball and of the part of the thermometer with the water in the hole was found
to be 68°9.

There
68°9 x 3605 x 6:31
~ o@ x (105)? x 87-45 x 60
= °883 C.G:S. unit.

This value is not corrected for the error given by the approximate formula already
mentioned.
Error

~ ‘69° in this case.

This makes the difference of temperature less by ‘7°, and when this correction is
made we get for the conductivity ‘889 C.G.S. unit. The conductivity as calculated
from five different lengths becomes, after the correction is made—

Length in centims. | Conductivity.
6°31 “889
587 893
5°23 ‘890
459 ‘887
4-015 883

The greatest difference between these values is a little over 1 per cent. Taking
2A 2

180 MR. J. H. GRAY ON A METHOD OF DETERMINING

their mean, we get for the thermal conductivity of the laboratory ccpper wire
8884 O.G.S. unit. This value is the mean conductivity between the temperatures
97- C. and 10° €.

The following Table gives the resuits of a series of tests on another portion of the

same wire :—
Length in centims. Conductivity.
6:11 888
571 “883
4°80 “892
4°43 *889

The mean of these values is °8880, being 3'; per cent. less than that obtained from
the preceding series.
Taking Anastrom’s formula,

K = 1°027 (1 — :00214¢),

and finding K for 53°, which is the mean of 97° and 10°, we get K = ‘9208 C.GS.
unit.

The close agreement in the values obtained with different lengths shows that the
errors already mentioned as possible are practically eliminated. ANGsTROm’s value is
4°5 per cent. greater thau *8884, but, as has been mentioned (p. 176), the conductivity
of the laboratory copper wire is 8 per cent. less than that of GLoveER’s wire afterwards
tested. In a previous paper, ANGsTROM gives ‘91 as the value for 513° C.

In a paper read before the Royal Society last year, Dr. R. W. Stewart, using the
Forbes method, but substituting a single thermo-electric junction for the thermometers,
gives the values for copper and iron, At the temperature 53° C. he gets for copper
K = 1-067, which is 10 per cent. higher than the value obtained for any specimen of
copper tested in the present investigation.

The conductivity of the wire obtained from Messrs. GLovER and Son was found to
be 9594 C.G.8. This was the best conducting copper tested by the present method.
The specific electrical resistance was 1730 in absolute units.

To test separately the effect of any alterations, separate experiments were made.

I. Instead of enclosing the whole length of the wire (laboratory copper) in a tube,
only a part was enclosed.

The paper tube was shortened by 2 or 3 millims. each time, and the conductivity
of the same length of wire was determined after each shortening of the tube. The
result found was, that the shortening (which was, of course, done from the cool end of
the wire) had practically no effect on the value so long as it was arranged that there
were no draughts of cold air. If for no other reason, the paper tube is necessary to

THE THERMAL CONDUCTIVITY OF METALS. 181

prevent draughts, as the latter make a determination impossible. It was found that
the paper tube could be shortened as much as to leave the lower half of the wire
exposed without any appreciable diminution of the value obtained. When it was
shortened much further, the value began to diminish till, when the tube was removed
altogether, the value obtained was found to be fully 6 per cent. lower than when the
tube completely covered the wire. When the wire was bare it was found very
difficult to prevent draughts caused by the hot wire, and these draughts made the
readings of the thermometer very irregular.

In connection with this, it will be noted that there is a particular advantage
in having the calorimeter ball lower in position than the heating box, as the hot air
round the latter rises, and so does not affect the water-jacket. It has been suggested,
however, that a separate experiment should be made to test whether any heat reached
the ball otherwise than through the wire. For this purpose the ball was suspended
by silk threads, in such a way that its highest point was 4°4 centimetres from
the bottom of the heating box. The water jacket was placed round the ball, and the
sheets of paper put on the top of the jacket. The water in the heating box was kept
boiling for twenty-five minutes, and the temperature of the ball, as indicated by the
thermometer in it, was noted at intervals. No change in the thermometer reading
could be detected, although -45th of one degree can be read without difficulty on the
thermometer scale.

As a further test of the effect of the paper tube, the upper half length of the wire
which was being tested, was left unprotected: by any tube, while the lower half was
enclosed. The result was practically the same as if there had been no tube ai all.

In order to make certain that the thermometer in the hot water indicated the
temperature of the upper end of the wire, a thermo-electric junction was used. The
junction was made of very thin wires of copper and platinoid, and, after being wrapped
once round the hot end of the wire just at the end, was soldered there. The other
junction was fixed to a thermometer and immersed in water. The heating box was
then filled with water, which was kept boiling. The water in the vessel containing
the other junction was gradually heated up till there was no deflection in the mirror
galvanometer used. Both junctions must then be at the same temperature. When
there was no deflection in the galvanometer the thermometers were found to be
indicating the same temperatures.

Several qualities of copper were tested, the results of which are given below.

Copper wire, made by Messrs. Botton and Co., Cheadle. This wire was by
mistake sent away before its electrical conductivity was measured, and it cannot be
got again.

182 MR. J. H. GRAY ON A METHOD OF DETERMINING

Mean conductivity between

Length used (in centims.). 10° C. and 97° C

7:0 867
6:33 862
5-7 | 859
51 ‘858

The greatest variation here is 1 per cent., and the mean value is ‘8612.
Some specimens of copper wire were bought in a plumber’s shop, of quality used for
bell-hanging. .

|
Speci Diameter Specific resistance | Mean thermal
pel aes ted (in centims.). (electrical). | conductivity.
1 -200 5545 “3198
2 | 204 4701 3497
Conductivity of Laboratory wire 9-78 Lee Bhat
= =F or heat,

Conductivity of Specimen 1

= 2°86 for electricity.
Conductivity of Laboratory wire :
Conductivity of Specimen 2 AOE HOD INSEL
= 2°56 for electricity.
Conductivity of GLOVER’s wire
: = 1°08 for heat,

Conductivity of Laboratory wire

1:066 for electricity.

In all the wires tested it was found that if one metal was a better conductor for
electricity it was also better for heat. This has been noticed by several investigators,
notably Professor Tart, and WirpEMANN and Franz. Beyond this the present
results cannot go, as enough trials were not made to allow of comparison. Previous
experimenters have found that the ratio of electrical conductivities of two wires is
not exactly equal to the ratio of thermal conductivities. This is indeed to be
expected, if the coefficients already obtained for the alteration with temperature are
accurate. For example, in copper the coefficient of variation per degree for electrical
conductivity is very much greater than that found for thermal conductivity, so that,
even if the ratios were equal at one temperature, they must be unequal at all other
temperatures. In some of the wires tested the electrical and thermal ratios differed
by as much as 4 or 5 per cent.

Before the present investigation, the absolute values for the conductivity of the

THE THERMAL CONDUCTIVITY OF METALS. 183

more expensive metals had not been determined, although relative values had been
found by WIEDEMANN and FRANz.*

I am very much indebted to Messrs. Jonnson, Marrury, and Co. for their great
kindness in preparing and lending to me wires of gold, platinum, silver, and other
pure metals, of 2 millims. diameter, and of such a length as to enable me to measure
without difficulty. both the thermal and electrical conductivities.

Unfortunately, I cannot find a record of the value obtained for the electrical
conductivity of the gold wire, and it has been returned some time ago. As, however,
Messrs. Jonnson, Marruey, and Co. stated, when sending it, that it was as pure as
could be made, it will perhaps be sufficient for me to use the value that has already
been found for the electrical conductivity of gold as determined by other experi-
menters. :

The curves for the calculation of the conductivity of silver wire are shown in
Diagram II. The values for the different lengths are given below.

SILVER Wire.

Thermal conductivity im
Length. C.G.S. units between
15° C. and 98° C.

7°86 956
6°59 960
6°59 963
a6] 973

It will be observed that the second and third values, although for the same length,
differ by about 4} per cent. They are both given however, as they agree within the
limits of observational errors. The mean of these values is °9628.

As the curves for gold and platinum are very similar to those for copper and silver,
it may be enough to give the values obtained for their conductivities.

Gop Wire (not annealed), Diameter = ‘202 centim.

| . .
Hlectrical resistance as

determined by
Dr. MarruiessEen.

|
Thermal conductivity in |

C.G.S. unit.

7464 | 2188

|
1

Comparing these values with those for Messrs. GLovER’s copper, which was found
to be 959, we find that the thermal conductivity of gold is 78 per cent. and the
electrical conductivity 81°6 per cent. that of copper.

* © Annales de Chemie,’ vol. 41, p. 107, 1854.

Diagram IT.

184 MR. J. H. GRAY ON A METHOD OF DETERMINING

35] |

CHEE o

Eo al

RAE ae a
Yd HH eee
ne

ee
766

Bee
sc ann

{2

(2) Curwe foi
6-59 \c7s.

|

VieCurve

Curves for Silver Wire

‘epoibaquag einzpoisdway

Time in Half-Minutes.

THE THERMAL CONDUCTIVITY OF METALS. 185

Pratixum Wire (not annealed). Diameter = °202 centim.
: see :
Thermal conductivity. | Electrical resistance.

| hl
1861 | 9180 |

Here the thermal and electrical conductivities are each 19 per cent. of the
conductivity of copper.

The gold, platinum, and silver were afterwards carefully annealed by Messrs.
JoHNson, Matruey, and Co., and the conductivities again determined. In each of
the cases the alteration due to annealing was less than 1 per cent. both in electrical
and thermal conductivity.

The results for the different metals are therefore—

MEAN Conductivity between Temperatures 10° C. and 97° C.

{

| Diameter.

millims.

Copper—Specimen 1 =| 9594 | 2:00

Hf Dh name eee | “8884. 211

RU erie ere | 8612 | 3-09

| Very Ms ACS al as) eere| 3497 | 2°04

impure _ OR Oe ey leet meee eh | 3198 2-04:

DL Ver aera Mine | Spc les one cts 9628 | 2:02

Gold) (x qs ce ape ee eo | “7464. 2:00

IBlatingims ot «fo Serio ieee) ee Sl 1861 | 2:00

It is intended to use other liquids than boiling water to heat one end of the wire, and
in this way test the alteration of conductivity with temperature. Up to the present
time no alloys have been tested, but it is intended that tests should be made of some,
such as platinoid and German silver ; also iron, as pure as possible, might be tested.

Instead of boiling water, steam was used for some time in this investigation, and
was in some respects found to be more convenient. Fig. 7 is a sketch showing a
section through the middle of the apparatus.

The steam is generated in the vessel W, passes along the upper tube T in the
direction of the arrows, and blows directly on the end of the wire, afterwards passing
out through the outside copper tube P, and escaping by the outlet B.

The thermometer D indicates the temperature of the steam just when it strikes the
wire. It will be seen that the outer tube with the steam in it serves as a steam
jacket, and thus keeps the steam in the inner tube T at a high temperature. The
sloping bottom where the wire is fixed at A isso made to prevent water accumulating
there. To ensure that as much steam as will supply all the heat that the copper can
take up is impinging a A, it is only necessary to arrange that the steam emerges at
B as steam.

MDCCCXCV,—A. : 2B

186 MR. J. H. GRAY ON THE THERMAL CONDUCTIVITY OF METALS.

Fig. 7.

The outside tube need not be more than 4 centims. diameter, and may be round, but
the part where the wire is soldered in must be thickened and made as shown in the
sketch, so that there may be no risk of water gathering above the wire. The length
of the tube need not exceed 15 centims. This allows sufficient length for the tube to
be inserted into the screen, which prevents the heat of the lamp from altering the
temperature of the ball. The diameter of the inside tube may be 1°5 centims. With
this apparatus most satisfactory results were obtained.

When a metal is tested for the first time, it will be advisable to find its approxi-
mate thermal conductivity by comparing its electrical conductivity with copper. This
will give an idea as to which calorimeter ball to use, and what length of wire will: give
a convenient rise of temperature per minute. A test is then almost as simple as for
electrical conductivity. :

VI. Argon, a New Constituent of the Atmosphere.

By Lord Rayuricn, Sec. RS., and Professor WitttAM Ramsay, F.B.S.
Received and Read January 31, 1895.

“Modern discoveries have not been made by large collections of facts, with subsequent discussion,
separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an
hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition
are worked out, and then, and not till then, other facts are examined to see if their ulterior results are
found in Nature.” —De Morean, “ A Budget of Paradoxes,” ed. 1872, p. 55.

1. Density of Nitrogen from Various Sources.

Iy a former paper* it has been shown that nitrogen extracted from chemical
compounds is about one-half per cent. lighter than “atmospheric nitrogen.”

The mean numbers for the weights of gas contained in the globe used were as
follows :—

grams.
Hromepnitrichoxid ce eens ono OO
From nitrous oxide . .. . . 2°2990
From ammonium nitrite. . . . 2'2987

while for “ atmospheric” nitrogen there was found—
iByahomeopper, S920 ae cial O38
lany loon ure, WSO 6 5 1 6 A BIOO

‘By ferrous hydrate, 1894... -2°3102

At the suggestion of Professor THORPE, experiments were subsequently tried with
nitrogen liberated from wrea by the action of sodium hypobromite. The carbon and
hydrogen of the urea are supposed to be oxidized by the reaction to CO, and H,0,
the former of which would be retained by the large excess of alkali employed. It
was accordingly hoped that the gas would require no further purification than drying.
If it proved to be light, it would at any rate be free from the suspicion of containing
hydrogen.

* RayueicH, “On an Anomaly encountered in Determinations of the Density of Nitrogen Gas,”
‘Proc. Roy. Soc.,’ vol. 55, p. 340, 1894.

MDCCCXCV.—A. 2 BZ 27.6.95.

L388 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

The hypobromite was prepared from commercial materials in the proportions
recommended for the analysis of urea—100 grams. caustic soda, 250 cub. centims.
water, and 25 cub. centims. of bromine. For our purpose about one and a half times
the above quantities were required. The gas was liberated in a bottle of about
900 cub. centims. capacity, in which a vacuum was first established. The full quan-
tity of hypobromite solution was allowed to run in slowly, so that any dissolved gas
might be at once disengaged. The urea was then fed in, at first in a dilute condition,
but, as the pressure rose, in a 10 per cent. solution. The washing out of the
apparatus, being effected with gas in a highly rarefied state, made but a slight
demand upon the materials. The reaction was well under control, and the gas could
be liberated as slowly as desired.

In the first experiment, the gas was submitted to no other treatment than slow
passage through potash and phosphoric anhydride, but it soon became apparent that
the nitrogen was contaminated. ‘The “‘inert and inodorous” gas attacked vigorously
the mercury of the Tépler pump, and was described as smelling like a dead rat. As
to the weight, it proved to be in excess even of the weight of atmospheric nitrogen.

The corrosion of the mercury and the evil smell were in great degree obviated by
passing the gas over hot metals. For the fillings of June 6, 9, 13, the gas passed
through a short length of tube containing copper in the form of fine wire, heated by
a flat Bunsen burner, then through the furnace over red-hot iron, and back over
copper oxide. On June 19 the furnace tubes were omitted, the gas being treated
with the red-hot copper only. The results, reduced so as to correspond with those
above quoted, were—

Jwne @ » 5 © o 6 bo. BwoOrs
m Qo ee Te Ree ae ene Oe

SR IKDW pele uetaed Maal hy cous tac SmI O oi
CSO et eee eto Og or
Mean . W299 8i5

Without using heat it has not been found possible to prevent the corrosion of the
mercury. Even when no urea is employed, and air simply bubbled through the hypo-
bromite solution is allowed to pass with constant shaking over mercury contained in
a U tube, the surface of the metal was soon fouled. When hypochlorite was
substituted for hypobronute in the last experiment there was a decided improvement,
and it was thought desirable to try whether the gas prepared from hypochlorite and
urea would be pure on simple desiccation. A filling on June 25 gave as the weight
2°3243, showing an excess of 36 mgs., as compared with other chemical nitrogen, and
of about 25 mgs. as compared with atmospheric nitrogen. A test with alkaline
pyrogallate appeared to prove the absence from this gas of free oxygen, and only a
trace of carbon could be detected when a considerable quantity of the gas was passed
over red-hot cupric oxide into solution of baryta.

A NEW CONSTITUENT OF THE ATMOSPHERE. 189

Although the results relating to urea nitrogen are interesting for comparison with
that obtained from other nitrogen compounds, the original object was not attained on
account of the necessity of retaining the treatment with hot metals. We have found,
however, that nitrogen from ammonium nitrite may be prepared without the employ-
ment of hot tubes, whose weight agrees with that above quoted. It is true that the
gas smells slightly of ammonia, easily removable by sulphuric acid, and apparently
also of oxides of nitrogen. The solution of potassium nitrite and ammonium chloride
was heated in a water-bath, of which the temperature rose to the boiling-point only
towards the close of operations. In the earlier stages the temperature required
careful watching in order to prevent the decomposition taking place too rapidly. The
gas was washed with sulphuric acid, and after passing a Nessler test, was finally
treated with potash and phosphoric anhydride in the usual way. The following results
have been obtained :—

Dialysis. Saree niin amr 2p2983
5 9 22989
og he} 2°2990

Wieam-, 4 -5-=, Bx2oer

It will be seen that in spite of the slight nitrous smell there is no appreciable differ-
ence in the densities of gas prepared from ammonium nitrite with and without the
treatment by hot metals. The result is interesting, as showing that the agreement
of numbers obtained for chemical nitrogen does not depend upon the use of a red
heat in the process of purification.

The five results obtained in more or less distinct ways for chemical nitrogen stand
thus :—

IBrOmMUEnIETIChOXIGe mal UE 4) re cee Gy elite hale bras piseal nem, ie eS) (il
TOMI CLOUSNOMIC CII ese Coke Chia en rece hee ever eet Co. 9\()
From ammonium nitrite purified atared heat . . . . 2°2987
TOMEI C AEP aarEnESS esta Fee for Seren nee Rakes Mme ON)
From ammonium nitrite purified inthe cold. . . . . 2:2987

Meant ii ts, sees ea 2 2990

These numbers, as well as those above quoted for “atmospheric nitrogen,” are subject
to a correction (additive)* of -0006 for the shrinkage of the globe when exhausted.t If
they are then multiplied in the ratio of 2°3108 :1°2572, they will express the weights
of the gas in grams. per litre. Thus, as regards the mean numbers, we find as the
weight per litre under standard conditions of chemical nitrogen 1°2511, that of
atmospheric nitrogen being 1°2572.

[* In the Abstract of this paper (‘ Proc. Roy. Soc.,’ vol. 57, p. 265) the correction of ‘0006 was

erroneously treated as a deduction.—April, 1895.
+ Rayueien, “ On the Densities of the Principal Gases,” ‘ Proc. Roy. Soe.,’ vol. 53, p. 184, 1893.

190 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

It is of interest to compare the density of nitrogen obtained from chemical com-
pounds with that of oxygen. We have N,:O, = 2'2996 : 2°6276 = 0°87517 ; so that
if O, = 16, N, = 14:003. Thus, when the comparison is with chemical nitrogen,
the ratio is very nearly that of 16:14. But if “atmospheric nitrogen” be substituted,
the ratio of small integers is widely departed from. —

The determination by Stas of the atomic weight of nitrogen from synthesis of
silver nitrate is probably the most trustworthy, inasmuch as the atomic weight of
silver was determined with reference to oxygen with the greatest care, and oxygen is
assumed to have the atomic weight 16. If, as found by Stas, Ag NO,:Ag=1°57490:1,
and Ag:O = 107'930:16, then N:O = 14:049 : 16. .

To the above list may be added nitrogen, prepared in yet another manner, whose
weight has been determined subsequently to the isolation of the new dense constituent
of the atmosphere. In this case nitrogen was actually extracted from air by means
of magnesium. The nitrogen thus separated was then converted into ammonia by
action of water upon the magnesium nitride, and afterwards liberated in the free
state by means of calcium hypochlorite. The purification was conducted in the usual
way, and included passage over red-hot copper and copper oxide. The following was
the result :—

Globe empty, October 30, November 5. . . . . 2°82313
GlobesullOctober!s = cee eee Seg, 6 O2BO5
Weightiofsoas) <2 cia. cy eulir Goeiaee ty) epee OOS

It differs imappreciably from the mean of other results, viz., 2°2990, and is of
special interest as relating to gas which, at one stage of its history, formed part of
the atmosphere.

Another determination with a different apparatus of the density of “chemical ”
nitrogen from the same source, magnesium nitride, which had been prepared by
passing “ atmospheric ” nitrogen over ignited magnesium, may here be recorded. The
sample differed from that previously mentioned, inasmuch as it had not been
subjected to treatment with red-hot copper. After treating the nitride with water,
the resulting ammonia was distilled off, and collected im hydrochloric acid; the
solution was evaporated to dryness; the dry ammonium chloride was dissolved in
water, and its concentrated solution added to a freshly prepared solution of sodium
hypobromite. The nitrogen was collected in a gas-holder over water which had
previously been boiled, so as at all events partially to expel air. The nitrogen passed
into the vacuous globe through a solution of potassium hydroxide, and through two
drying-tubes, one containing soda-lime, and the other phosphoric anhydride.

At 18°38° C, and 754°4 mgs. pressure, 162°843 cub. centims. of this nitrogen
weighed 0°18963 gram. Hence :—

Weight of 1 litre at 0° C. and 760 millims. pressure . . . 1°2521 gram.

A NEW CONSTITUENT OF THE ATMOSPHERE. UL

The mean result of the weight of 1 litre of “chemical” nitrogen has been found
to equal 1:2511. It is therefore seen that “chemical” nitrogen, derived from
“atmospheric” nitrogen, without any exposure to red-hot copper, possesses the
usual density.

Experiments were also made, which had for their object to prove that the ammonia,
produced from the magnesium nitride, is identical with ordinary ammonia, and
contains no other compound of a basic character. For this purpose, the ammonia
was converted into ammonium chloride, and the percentage of chlorine determined
by titration with a solution of silver nitrate which had been standardized by titrating
a specimen of pure sublimed ammonium chloride. The silver solution was of such a
strength that 1 cubic centim. precipitated the chlorine from 0°001701 gram. of
ammonium chloride. ;

1. Ammonium chloride from orange-coloured sample of magnesium nitride.

01106 gram. required 43°10 cub. centims. of silver nitrate = 66°35 per cent. of
chlorine.

2. Ammonium chloride from blackish magnesium nitride.

0°1118 gram. required 43°6 cub. centims. of silver nitrate = 66°35 per cent. of
chlorine.

3. Ammonium chloride from nitride containing a large amount of unattacked
magnesium.

00630 gram. required 24°55 cub. centims. of silver nitrate = 66°30 per cent. of
chlorine.

Taking for the atomic weights of hydrogen, H = 1:0032, of nitrogen, N = 14:04,
and of chlorine, Cl = 35°46, the theoretical amount of chlorine in ammonium chloride
is 66°27 per cent.

From these results—that nitrogen prepared from magnesium nitride obtained by
passing “atmospheric” nitrogen over red-hot magnesium has the density of
“chemical” nitrogen, and that ammonium chloride prepared from magnesium nitride
contains practically the same percentage of chlorine as pure ammonium chloride—it
may be concluded that red-hot magnesium withdraws from “atmospheric” nitrogen
no substance other than nitrogen capable of forming a basic compound with hydrogen.

In a subsequent part of this paper, attention will again be called to this
statement. (See addendum p. 240.)

2. Reasons for Suspecting a hitherto Undiscovered Constituent in Arr.

When the discrepancy of weights was first encountered, attempts were naturally
made to explain it by contamination with known impurities. Of these the most
likely appeared to be hydrogen, present in the lighter gas, in spite of the passage over
red-hot cupric oxide. But, inasmuch as the intentional introduction of hydrogen
into the heavier gas, afterwards treated in the same way with cupric oxide, had no
effect upon its weight, this explanation had to be abandoned; and, finally, it became

192 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

clear that the difference could not be accounted for by the presence of any known
mpurity. At this stage it seemed not improbable that the hghtness of the gas
extracted from chemical compounds was to be explained by partial dissociation of
nitrogen molecules N, into detached atoms. In order to test this suggestion, both
kinds of gas were submitted to the action of the silent electric discharge, with the
result that both retained their weights unaltered. This was discouraging, and a
further experiment pointed still more markedly in the negative direction. The
chemical behaviour of nitrogen is such as to suggest that dissociated atoms would
possess a higher degree of activity, and that, even though they might be formed in
the first instance, their life would probably be short. On standing, they might be
expected to disappear, in partial analogy with the known behaviour of ozone. With
this idea in view, a sample of chemically-prepared nitrogen was stored for eight
months. But, at the end of this time, the density showed no sign of increase,
remaining exactly as at first.*

Regarding it as established that one or other of the gases must be a mixture,
containing, as the case might be, an ingredient much heavier or much lighter than
ordinary nitrogen, we had to consider the relative probabilities of the various possible
interpretations. Except upon the already discredited hypothesis of dissociation, it
was difficult to see how the gas of chemical origin could be a mixture. To suppose
this would be to admit two kinds of nitric acid, hardly reconcilable with the work of
Sras and others upon the atomic weight of that substance. The simplest explanation
in many respects was to admit the existence of a second ingredient in air from which
oxygen, moisture, and carbonic anhydride had already been removed. The pro-
portional amount required was not great. If the density of the supposed gas were
double that of nitrogen, one-half per cent. only by volume would be needed ; or, if the
density were but half as much again as that of nitrogen, then one per cent. would
still suffice. But in accepting this explanation, even provisionally, we had to face the
improbability that a gas surrounding us on all sides, and present in enormous
quantities, could have remained so long unsuspected.

The method of most universal application by which to test whether a gas is pure or
a mixture of components of different densities is that of diffusion, By this means
GRAHAM succeeded in effecting a partial separation of the nitrogen and oxygen of the
air, in spite of the comparatively small difference of densities. If the atmosphere
contain an unknown gas of anything like the density supposed, it should be possible
to prove the fact by operations conducted upon air which had undergone atmolysis.
If, for example, the parts least disposed to penetrate porous walls were retained, the
“nitrogen” derived from it by the usual processes should be heavier than that
derived in like manner from unprepared air. This experiment, although in view from
the first, was not executed until a later stage of the inquiry ({ 6), when results were

* Ray ecu, ‘ Proc. Roy. Soe.,’ vol. 55, p. 344, 1894.

A NEW CONSTITUENT OF THE ATMOSPHERE. 193

obtained sufficient of themselves to prove that the atmosphere contains a previously
unknown gas.

But although the method of diffusion was capable of deciding the main, or at any
rate the first question, it held out no prospect of isolating the new constituent of the
atmosphere, and we therefore turned our attention in the first instance to the con-
sideration of methods more strictly chemical. And here the question forced itself
upon us as to what really. was the evidence in favour of the prevalent doctrine that
the inert residue from air after withdrawal of oxygen, water, and carbonic anhydride,
is all of one kind.

The identification of “‘ phlogisticated air” with the constituent of nitric acid is due
to CAVENDISH, whose method consisted in operating with electric sparks upon a short
column of gas confined with potash over mercury at the upper end of an inverted
U-tube.* This tube (M) was only about ;/5 inch in diameter, and the column of
gas was usually about 1 inch in length. After describing some preliminary trials,
CAVENDISH proceeds :—“ I introduced into the tube a little soap-lees (potash), and then
let up some dephlogisticatedt and common air, mixed in the above mentioned
proportions which rising to the top of the tube M, divided the soap-lees into its two
legs. As fast as the air was diminished by the electric spark, I continued adding more
of the same kind, till no further diminution took place: after which a little pure dephlo-
gisticated air, and after that a little common air, were added, in order to see whether
the cessation of diminution was not owing to some imperfection in the proportion of
the two kinds of air to each other; but without effect. The soap-lees being then
poured out of the tube, and separated from the quicksilver, seemed to be perfectly
neutralised, and they did not at all discolour paper tinged with the juice of blue
flowers. Being evaporated to dryness, they left a small quantity of salt, which was
evidently nitre, as appeared by the manner in which paper, impregnated with a
solution of it, burned.”

Attempts to repeat CAVENDISH’S experiment in CAVENDISH’S manner have only
increased the admiration with which we regard this wonderful investigation.
Working on almost microscopical quantities of material, and by operations extending
over days and weeks, he thus established one of the most important facts in
chemistry. And what is still more to the purpose, he raises as distinctly as we

* “Wixperiments on Air,” ‘Phil. Trans.,’ vol. 75, p. 372, 1785.

[+ The explanation of combustion in CayenpisH’s day was still vague. It was generally imagined
that substances capable of burning contained an unknown principle, to which the name ‘ phlogiston’
was applied, and which escaped during combustion. Thus, metals and hydrogen and other gases were
said to be ‘ phlogisticated ’ if they were capable of burning in air. Oxygen being non-inflammable was
named ‘ dephlogisticated air,’ and nitrogen, because it was incapable of supporting combustion or life
was named by Priestipy ‘ phlogisticated air,’ although up till CaynnpisuH’s time it had not been made to
unite with oxygen.

The term used for oxygen by Cayenpisu is ‘ dephlogisticated air,’ and for nitrogen, ‘ phlogisticated
air.’—April, 1895.]

MDCCCXCV.—A. 6)

194 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

could do, and to a certain extent resolves, the question above suggested. . The
passage is so important that it will be desirable to quote it at full length.

“ As far as the experiments hitherto published extend, we scarcely know more of
the phlogisticated part of our atmosphere than that it is not diminished by lime-
water, caustic alkalies, or nitrous air; that it is unfit to support fire or maintain life
in animals; and that its specific gravity is not much less than that of common air ;
so that, though the nitrous acid, by being united to phlogiston, is converted into air
possessed of these properties, and consequently, though it was reasonable to suppose,
that part at least of the phlogisticated air of the atmosphere consists of this acid
united to phlogiston, yet it was fairly to be doubted whether the whole is of this
kind, or whether there are not in reality many different substances confounded
together by us under the name of phlogisticated air. I therefore made an experiment
to determine whether the whole of a given portion of the phlogisticated air of the
atmosphere could be reduced to nitrous acid, or whether there was not a part of a
different nature to the rest which would refuse to undergo that change. The fore-
going experiments indeed in some measure decided this point, as much the greatest
part of the air let up into the tube lost its elasticity; yet as some remained
unabsorbed it did not appear for certain whether that was of the same nature as the
rest or not. For this purpose I diminished a similar mixture of dephlogisticated and
common air, in the same manner as before, till it was reduced to a small part of its
original bulk. I then, in order to decompound as much as I could of the phlogisti-
cated air which remained in the tube, added some dephlogisticated air to it and
continued the spark until no further diminution took place. Having by these means
condensed as much as I could of the phlogisticated air, I let up some solution of liver
of sulphur to absorb the dephlogisticated air; after which only a small bubble of air
remained unabsorbed, which certamly was not more than y}9 of the bulk of the
phlogisticated air let up into the tube; so that, if there is any part of the phlogisti-
cated air of our atmosphere which differs from the rest, and cannot be reduced to
nitrous acid, we may safely conclude that it is not more than 73> part of the whole.”

Although CAVENDISH was satisfied with his result, and does not decide whether
the small residue was genuine, our experiments about to be related render it not
improbable that his residue was really of a different kind from the main bulk of the
“ phlogisticated air,” and contained the gas now called argon.

CAVENDISH gives data* from which it is possible to determine the rate of absorption
of the mixed gases in his experiment. The electrical machine used “was one of
Mr. NairNe’s patent machines, the cylinder of which is 123 inches long and 7 in
diameter. A conductor, 5 feet long and 6 inches in diameter, was adapted to it, and
the ball which received the spark was placed two or three inches from another ball,
fixed to the end of the conductor. Now, when the machine worked well, Mr. Gruprn
supposes he got about two or three hundred sparks a minute, and the diminution of

* ‘Phil. Trans.,’ vol. 78, p. 271, 1788.

A NEW CONSTITUENT OF THE ATMOSPHERE. 195

the air during the half hour which he continued working at a time varied in general
from 40 to 120 measures, but was usually greatest when there was most air in the
tube, provided the quantity was not so great as to prevent the spark from passing
readily.” The “ measure ” spoken of represents the volume of one grain of quicksilver,
or ‘0048 cub. centim., so that an absorption of one cub. centim. of mixed gas per hour
was about the most favourable rate. Of the mixed gas about two-fifths would be
nitrogen.

3. Methods of Causing Free Nitrogen to Combine.

The concord between the determinations of density of nitrogen obtained from
sources other than the atmosphere, having made it at least probable that some heavier
gas exists in the atmosphere, hitherto undetected, it became necessary to submit
atmospheric nitrogen to examination, with a view of isolating, if possible, the unknown
and overlooked constituent, or it might be constituents.

Nitrogen, however, is an element which does not easily enter into direct combination
with other elements ; but with certain elements, and under certain conditions, combi-
nation may be induced. The elements which have been directly united to nitrogen
are (a) boron, (b) silicon, (c) titanium, (d) lithium, (¢) strontium and barium,
(f) magnesium, (g) aluminium, (h) mercury, (2) manganese, (j) hydrogen, and
(k) oxygen, the last two by help of an electrical discharge.

(a.) Nitride of boron was prepared by W6HLER and DeviLiE* by heating amorphous
boron to a white heat in a current of nitrogen. Experiments were made to test
whether the reaction would take place in a tube of difficultly fusible glass ; but it was
found that the combination took place at a bright red heat to only a small extent,
and that the boron, which had been prepared by heating powdered boron oxide with
magnesium dust, was only superficially attacked. Boron is, therefore, not a convenient
absorbent for nitrogen. [M. Moissan informs us that the reputation it possesses is
due to the fact that early experiments were made with boron which had been
obtained by means of sodium, and which probably contained a boride of that metal.
—April, 1895. ]

(b.) Nitride of silicont also requires for its formation a white heat, and complete
union is difficult to bring about. Moreover, it is not easy to obtain large quantities
of silicon. This method was therefore not attempted.

(c.) Nitride of titanium is said to have been formed by DrviiLE and Caron,{ by
heating titanium to whiteness in a current of nitrogen. This process was not tried
by us. As titanium bas an unusual tendency to unite with nitrogen, it might,
perhaps, be worth while to set the element free in presence of atmospheric nitrogen,
with a view to the absorption of the nitrogen. This has, in effect, been already done

* © Annales de Chimie,’ (3), 52, p. 82.

+ Scuurzenpercur, ‘Comptes Rendus,’ 89, 644.

£ ‘ Annalen der Chemie u. Pharmacie,’ 101, 360.
DH Cnes

196 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

by WoxtER and DeEvILLE ;* they passed a mixture of the vapour of titanium chloride
and nitrogen over red-hot aluminium, and obtained a large yield of nitride. It is
possible that a mixture of the precipitated oxide of titanium with magnesium dust
might be an effective absorbing agent at a comparatively low temperature. [Since
writing the above we have been informed by M. Moissan that titanium, heated to
800°, burns brilliantly in a current of nitrogen. It might therefore be used with
advantage to remove nitrogen from air, inasmuch as we have found that it does not
combine with argon.—April, 1895.]

(d.), (e.) Lithium at a dull red heat absorbs nitrogen,t but the difficulty of
obtaining the metal in quantity precludes its application. On the other hand,
strontium and barium, prepared by electrolysing solutions of their chlorides in
contact with mercury, and subsequently removing the mercury by distillation, are
said by MAaQuENNE| to absorb nitrogen with readiness. Although we have not tried
these metals for removing nitrogen, still our experience with their amalgams has led
us to doubt their efficacy, for it is extremely difficult to free them from mercury by
distillation, and the product is a fused ingot, exposing very little surface to the action
of the gas. The process might, however, be worth a trial.

Barium is the efficient absorbent for nitrogen when a mixture of barium carbonate
and carbon is ignited in a current of nitrogen, yielding cyanide. Experiments have
shown, however, that the formation of cyanides takes place much more readily and
abundantly at a high temperature, a temperature not easily reached with laboratory
apphances. Should the process ever come to be worked on a large scale, the gas
rejected by the barium will undoubtedly prove a most convenient source of argon.

(f.) Nitride of magnesium was prepared by DevintLEe and Caron (loc. cit.) during
the distillation of impure magnesium. It has been more carefully investigated by
BRIEGLEB and GEUTHER,§ who obtained it by igniting metallic magnesium in a
current of nitrogen. It forms an orange-brown, friable substance, very porous, and
it is easily produced at a bright red heat. When magnesium, preferably in the form
of thin turnings, is heated in a combustion tube in a current of nitrogen, the tube is
attacked superficially, a coating of magnesium silicide being formed. As the temperature
rises to bright redness, the magnesium begins to glow brightly, and combustion takes
place, beginning at that end of the tube through which the gas is introduced. The
combustion proceeds regularly, the glow extending down the tube, until all the metal
has united with nitrogen. The heat developed by the combination is considerable,
and the glass softens; but by careful attention and regulation of the rate of the
current, the tube lasts out an operation. A piece of combustion tubing of the usual
length for organic analysis packed tightly with magnesium turnings, and containing

* © Annalen der Chemie u. Pharmacie,’ 73, 34.

+ Ovvrarp, ‘Comptes Rendus,’ 114, 120.

ft Otyrarp, ‘ Comptes Rendus,’ 114, 25, and 220.
§ ‘Annalen der Chemie u. Pharmacie,’ 123, 228.

A NEW CONSTITUENT OF THE ATMOSPHERE. 197

about 30 grams, absorbs between seven and eight litres of nitrogen. It is essential
that oxygen be excluded from the tube, otherwise a fusible substance is produced,
possibly nitrate, which blocks the tube. With the precaution of excluding oxygen,
the nitride is loose and porous, and can easily be removed from the tube with a rod ;
but it is not possible to use a tube twice, for the glass is generally softened and
deformed.

(g.) Nitride of aluminium has been investigated by Mauuer.* He obtained it in
erystals by heating the metal to whiteness in a carbon crucible. But aluminium
shows no tendency to unite with nitrogen at a red heat, and cannot be used as an
absorbent for the gas,

(h.) GERRESHEIM? states that he has induced combination between nitrogen and
mercury; but the affinity between these elements is of the slightest, for the
compound is explosive.

(z.) In addition to these, metallic manganese in a finely divided state has been
shown to absorb nitrogen at a not very elevated temperature, forming a nitride of the
formula Mn-N,.t

(j.) [A mixture of nitrogen with hydrogen, standing over acid, is absorbed at a
fair rate under the influence of electric sparks. But with an apparatus such as
that shown in fig. 1, the efficiency is but a fraction (perhaps 4) of that obtainable
when oxygen is substituted for hydrogen and alkali for acid.—April, 1895. |

4, Early Experiments on sparking Nitrogen with Oxygen in presence of Alkali.

Tn our earliest attempts to isolate the suspected gas by the method of CAVENDISH,
we used a RunMKoRFF coil of medium size actuated by a battery of five Grove cells.
The gases were contained in a test-tube A, fig. 1, standing over a large quantity of
weak alkali B, and the current was conveyed in wires insulated by U-shaped glass
tubes CC passing through the liquid round the mouth of the test tube. The inner
platinum ends DD of the wires were sealed into the glass insulating tubes, but
reliance was not placed upon these sealings. In order to secure tightness in spite
of cracks, mercury was placed in the bends. This disposition of the electrodes
complicates the apparatus somewhat and entails the use of a large depth of liquid in
order to render possible the withdrawal of the tubes, but it has the great advantage
of dispensing with sealing electrodes of platinum into the principal vessel, which
might give way and cause the loss of the experiment at the most inconvenient
moment. With the given battery and coil a somewhat short spark, or arc, of about
5 millims. was found to be more favourable than a longer one. When the mixed
gases were in the right proportion, the rate of absorption was about 30 cub. centims.

* © Journ. Chem. Soc.,’ 1876, vol. 2, p. 349.

+ ‘Annalen der Chemie u. Pharmacie,’ 195, 373.
¢ O: Preatineer, ‘Monatsh. f. Chemie,’ 15, 391.

198 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

per hour, or 30 times as fast as CAVENDISH could work with the electrical machine
of his day.

To take an example, one experiment of this kind started with 50 cub. centims. of air.
To this, oxygen was gradually added until, oxygen being in excess, there was no
perceptible contraction during an hour’s sparking. The remaining gas was then
transferred at the pneumatic trough to a small measuring vessel, sealed by mercury, ©

Fig. 1.

PMI

a

in which the volume was found to be 1:0 cub. centim. On treatment with alkaline
pyrogallate, the gas shrank to 32 cub. centim. That this small residue could not be
nitrogen was argued from the fact that it had withstood the prolonged action of the
spark, although mixed with oxygen in nearly the most favourable proportion.

The residue was then transferred to the test-tube with an addition of another
50 cub. centims. of air, and the whole worked up with oxygen as before. The residue
was now 2°2 cub. centims., and, after removal of oxygen, ‘76 cub. centim.

A NEW CONSTITUENT OF THE ATMOSPHERE. 199

Although it seemed almost impossible that these residues could be either nitrogen
or hydrogen, some anxiety was not unnatural, seeing that the final sparking took
place under somewhat abnormal conditions. The space was very restricted, and the
temperature (and with it the proportion of aqueous vapour) was unduly high. But
any doubts that were felt upon this score were removed by comparison experiments
in which the whole quantity of air operated on was very small. Thus, when a
mixture of 5 cub. centuns. of air with 7 cub. centims. of oxygen was sparked for one
hour and a quarter, the residue was 47 cub. centim., and, after removal of oxygen,
06 cub. centim. Several repetitions having given similar results, it became clear
that the final residue did not depend upon anything that might happen when sparks
passed through a greatly reduced volume, but was in proportion to the amount of air
operated upon.

No satisfactory examination of the residue which refused to be oxidised could be
made without the accumulation of a larger quantity. This, however, was difficult of
attainment at the time in question. The gas seemed to rebel against the law of
addition. It was thought that the cause probably lay in the solubility of the gas in
water, a suspicion since confirmed. At length, however, a sufficiency was collected
to allow of sparking in a specially constructed tube, when a comparison with the air
spectrum taken under similar conditions proved that, at any rate, the gas was not
nitrogen. At first scarcely a trace of the principal nitrogen lines could be seen, but
after standing over water for an hour or two these lines became apparent.

[The apparatus shown in fig. 1 has proved to be convenient for the purification of
small quantities of argon, and for determinations of the amount of argon present in
various samples of gas, e.g., in the gases expelled from solution in water. To set it
in action an alternating current is much to be preferred to a battery and break. At
the Royal Institution the primary of a small RunMKorFrF was fed from the 100-volt
alternating current supply, controlled by two large incandescent lamps in series with
the coil. With this arrangement the voltage at the terminals of the secondary,
available for starting the sparks, was about 2000, and could be raised to 4000 by
plugging out one of the lamps. With both lamps in use the rate of absorption of
mixed gases was 80 cub. centims. per hour, and this was about as much as could well
be carried out in a test-tube. Even with this amount of power it was found better
to abandon the sealings at D. No inconvenience arises from the open ends, if the
tubes are wide enough to ensure the liberation of any gas included over the mercury
when they are sunk below the liquid.

The power actually expended upon the coil is very small. When the apparatus is
at work the current taken is only 2°4 amperes. As regards the voltage, by far the
greater part is consumed in the lamps. ‘The efficient voltage at the terminals of the
primary coil is best found indirectly. Thus, if A be the current in amperes, V the
total voltage, V, the voltage at the terminals of the coil, V, that at the terminals of
the lamps, the watts used are*

* Ayrton and Sumpner, ‘ Proc. Roy. Soc.,’ vol. 49, p. 427, 1891.

— |

200 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

A : A
Wage S vain

In the present case a CARDEW voltmeter gave V = 904, V, = 88; and V,” in the
formula may be neglected. Thus,
| A

W= (V + V.)(V — V,.) =A(V — V,)

= 2°4 X 2°5 = 6:0 approximately.

The work consumed by the coil when the sparks are passing is, thus, less than 7$5 of
a horgse-power; but, in designing an apparatus, it must further be remembered that
in order to maintain the arc, a pretty high voltage is required at the terminals of the
secondary when ne current is passing in it.—April, 1895. }

5. Early Experiments on Withdrawal of Nitrogen from Air by means of Red-hot
Magnesium.

it having been proved that nitrogen, at a bright red heat, was easily absorbed
by magnesium, best in the form of turnings, an attempt was successfully made to
remove that gas from the residue left after eliminating oxygen from air by means of
red-hot copper.
Fig. 2.

The preliminary experiment was made in the following manner :—A combustion
tube, A, was filled with magnesium turnings, packed tightly by pushing them in with
arod. This tube was connected with a second piece of combustion tubing, B, by
means of thick-walled india-rubber tubing, carefully wired; B contained copper oxide,
and, in its turn, was connected with the tube CD, one-half of which contained soda-
lime, previously ignited to expel moisture, while the other half was filled with
phosphoric anhydride. E is a measuring vessel, and F is a gas-holder containing
‘atmospheric nitrogen.”

a

A NEW CONSTITUENT OF THE ATMOSPHERE. 201

In beginning an experiment, the tubes were heated with long-flame burners, and
pumped empty ; a little hydrogen was formed by the action of the moisture on the
metallic magnesium; it was oxidised by the copper oxide and absorbed by the
phosphoric pentoxide. A gauge attached to the SPRENGEL’s pump, connected with
the apparatus, showed when a vacuum had been reached. A quantity of nitrogen
was then measured in E, and admitted into contact with the red-hot magnesium.
Absorption took place, rapidly at first and then slowly, as shown by the gauge on the
SPRENGEL’s pump. A fresh quantity was then measured and admitted, and these
operations were repeated until no more could be absorbed. The system of tubes was
then pumped empty by means of the SPRENGEL’S pump, and the gas was collected.
The magnesium tube was then detached and replaced by another. The unabsorbed
gas was returned to the measuring-tube by a device shown in the figure (G) and the
absorption recommenced. After 1094 cub. centims. of gas had been thus treated,
there was left about 50 cub. centims. of gas, which resisted rapid absorption. It still
contained nitrogen, however, judging by the diminution of volume which it
experienced when allowed to stand in contact with red-hot magnesium. Its density
was, nevertheless, determined by weighing a small bulb of about 40 cub. centims.
capacity, first with air, and afterwards with the gas. The data are these :—

grm.
(a.) Weight of bulb and air — that of glass counterpoise . . 0°8094
- ,, alone — that of glass counterpoise. . . 0€°7588
m bi Aer eile Woe, sw OU auld gt ete 00506

(b.) Weight of bulb and gas — that of glass counterpoise . .. 0°8108
e » alone — that of glass counterpoise. . . 0°7588

a GSI | Mad tig ge IG owe aor ee ON coo) Om (an boa gees om OAA0)

Taking as the weight of a litre of air, 1°29347 grms., the mean of the latest
results, and of oxygen (= 16) 1°42961 grms.,* the density of the residual gas
is 14°88.

* The results on which this and the subsequent calculations are based are as follows (the weights
are those of 1 litre) :—

Air. Oxygen. Nitrogen. Hydrogen. |
PiBeenauor = 225, 1:29349 1438011 | 1:25647 0:08988
Won Jonny a cs 129383 142971 1:25819
TED UCL Mirra etnie| 1:29330 142910 1:25709 0:08985
IVAYERIGH); 5°. 5 1:29327 1:42952 1:25718 0:09001

REGNAULT’s numbers have an approximate correction applied to them by Crarrs. The mean of these
MUCCCXCV.— A. 2D

202 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

This result was encouraging, although weighted with the unavoidable error attach-
ing to the weighing of a very small amount. Still the fact remains that the supposed
nitrogen was heavier than air. It would hardly have been possible to make a mistake
of 2°7 milligrams.

It is right here to place on record the fact that this frst experiment was to a great
extent carried out by Mr. Percy Wixt1Ams, to whose skill in manipulation and great
care its success is due, and to whom we desire here to express our thanks.

Experiments were now begun on a larger scale, the apparatus employed being shown
in figs. 3 and 4.

A and B are large glass gas-holders of about 10 litres capacity. C is an arrange-
ment by which gas could be introduced at will into the gas-holder A, either by means
of an india-rubber tube slipped over the open end of the U-tube, or, as shown in the
figure, from a test-tube. The tube D was half filled with soda-lime (a), half with
phosphoric anhydride (b). Similarly, the tube E, which was kept at a red heat by
means of the long-flame burner, was filled half with very porous copper (a), reduced
from dusty oxide by heating in hydrogen, half with copper oxide in a granular form (0).
The next tube, F, contained granular soda-lime, while G contained magnesium turn-

numbers is taken, that of Recnavitr for nitrogen being omitted, as there is reason to believe that
his specimen was contaminated with hydrogen.

Air. | Oxygen. Nitrogen. Hydrogen.
| 142961 1:25749 0:08991
|

This ratio gives for air the composition by volume—

Oxyreny 7.) 10 an ene ee Oxo percents
INE Bho 6) 5 5 9 4 0 (AHO 5

a result verified by experiment.
It is, of course, to be understood that these densities of nitrogen refer to atmospheric nitrogen,
that is, to air from which oxygen, water vapour carbon dioxide, and ammonia have been removed.

A NEW CONSTITUENT OF THE ATMOSPHERE. 203

ings, also heated to bright redness by means of a long-flame burner. H contained
phosphoric anhydride, and I soda-lime. All joints were sealed, excepting those
connecting the hard-glass tubes E and G to the tubes next them.

The gas-holder A having been filled with nitrogen, prepared by passing air over red-
hot copper, and introduced at C, the gas was slowly passed through the system of
tubes into the gas-holder B, and back again. The magnesium in the tube G having
then ceased to absorb was quickly removed and replaced by a fresh tube. This tube
was of course full of air, and before the tube G was heated, the air was carried back
from B towards A by passing a little nitrogen from right to left. The oxygen in the
air was removed by the metallic copper, and the nitrogen passed into the gas-holder
A, to be returned in the opposite direction to B.

Fig. 4.

D (by

as

ly

In the course of about ten days most of the nitrogen had been absorbed. The
magnesium was not always completely exhausted ; usually the nitride presented the
appearance of a blackish- yellow mass, easily shaken out of the tube. It is needless to
say that the tube was always somewhat attacked, becoming black with a coating of
magnesium silicide. The nitride of magnesium, whether blackish or orange, if left
for a few hours exposed to moist air, was completely converted into white, dusty
hydroxide, and during exposure it gave off a strong odour of ammonia. If kept ina
stoppered bottle, however, it was quite stable.

It was then necessary, in order to continue the absorption, to carry on operations
on a smaller scale, with precautions to exclude atmospheric air as completely as
possible. There was at this stage a residue of 1500 cub. centims.

The apparatus was therefore altered to that shown in fig. 4, so as to make it possible
to withdraw all the gas out of the gas-holder A.

The left-hand exit led to the SPRENGEL’s pump; the compartment (a) of the
drying-tube B was filled with soda-lime, and (b) with phosphoric anhydride. C isa

2D2

204 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

tube into which the gas could be drawn from the gas-holder A. The stop-cock, as
shown, allows gas to pass through the horizontal tubes, and does not communicate
with A ; but a vertical groove allows it to be placed in communication either with the
gas-holder, or with the apparatus to the right. The compartment (a) of the second
drying-tube D contained soda-lime, and (b) phosphoric anhydride. The tube D com-
municated with a hard-glass tube E, heated over a long-flame burner ; it was partly
filled with metallic copper, and partly with copper oxide. This tube, as well as the
tube F filled with magnesium turnings, was connected to the drying-tube with india-
rubber. The gas then entered G, a graduated reservoir, and the arrangement H
permitted the removal or introduction of gas from or into the apparatus. The gas
was gradually transferred from the gas-holder to the tube C, and passed backwards
and forwards over the red-hot magnesium until only about 200 cub. centims. were
left. It was necessary to change the magnesium tube, which was made of smaller
size than formerly, several times during the operation. This was done by turning out
the long-flame burners and pumping off all gas in the horizontal tubes by means of
the SPRENGEL’S pump. ‘This gas was carefully collected. The magnesium tube was
then exchanged for a fresh one, and after air had been exhausted from the apparatus,
nitrogen was introduced from the reservoir. Any gas evolved from the magnesium
(and apparently there was always a trace of hydrogen, either occluded by the magne-
sium, or produced by the action of aqueous vapour on the metal) was oxidised by the
copper oxide. Had oxygen been present, it would have been absorbed by the metallic
copper, but the copper preserved its red appearance without alteration, whereas a little
copper oxide was reduced during the series of operations. The gas, which had been
removed by pumping, was reintroduced at H, and the absorption continued.

The volume of the gas was thus, as has been said, reduced to about 200 cub.
centims. It would have been advisable to take exact measurements, but, unfor-
tunately, some of the original nitrogen had been lost through leakage; and a natural
anxiety to see if there was any unknown gas led to pushing on operations as quickly
as possible.

The density of the gas was next determined. The bulb or globe in which the gas
was weighed was sealed to a two-way stop-cock, and the weight of distilled and
air-free water filling it at 17°15° was 162°654 grms., corresponding to a capacity of
162°843 cub. centims. The shrinkage on removing air completely was 0:0212 cub.
centim. Its weight, when empty, should therefore be increased by the weight of
that volume of air, which may be taken as 0°000026 grm. This correction, however,
is perhaps hardly worth applying in the present case.

The counterpoise was an exactly similar bulb of equal capacity, and weighing about
02 grm. heavier than the empty globe. The balance was a very sensitive one by
OERTLING, which easily registered one-tenth of a milligrm. By the process of
swinging, one-hundredth of a milligrm. could be determined with fair accuracy,

In weighing the empty globe, 0:2 grm. was placed on the same pan as that which

A NEW CONSTITUENT OF THE ATMOSPHERE. 205

hung from the end of the beam to which it was suspended, and the final weight was
adjusted by means of a rider, or by small weights on the other pan. This process
practically leads to weighing by substitution of gas for weights. The bulb was
always handled with gloves, to avoid moisture or grease from the fingers.

Three experiments, of which it is unnecessary to give details, were made to test
the degree of accuracy with which a gas could be weighed, the gas being dried air,
freed from carbon dioxide. The mean result gave for the weight of one litre of air
at 0° and 760 millims. pressure, 1°2935 grm. REGNAULT found 1:29340, a correction
having been applied by Crafts to allow for the estimated alteration of volume caused
by the contraction of his vacuous bulb. The mean result of determinations by several
observers is 1°29347 ; while one of us found 1°29327.

The globe was then filled with the carefully dried gas.

Temperature, 18°80°. Pressure, 759°3 millims.

Weight of 162°843 cub. centims. of gas 2. |. . . «021897 grm.
Weight of 1 litre gas at O° and 760 millims. . . . . 1°4386_,,
Density, that of air compared with O,=16, being 14'476 16°100 grms.

It is evident from these numbers that the dense constituent of the air was being
concentrated. As a check, the bulb was pumped empty and again weighed ; its
weight was 0'21903 srm. This makes the density 16°105.

It appeared advisable to continue to absorb nitrogen from this gas. The first tube
of magnesium removed a considerable quantity of gas; the nitride was converted
into ammonium chloride, and the sample contained 66°30 per cent. of chlorine,
showing, as has before been remarked, that if any of the heavier constituent of the
atmosphere had been absorbed, it formed no basic compound with hydrogen. The
second tube of magnesium was hardly attacked; most of the magnesium had melted,
and formed a layer at the lower part of the tube. That which was still left in the
body of the tube was black on the surface, but had evidently not been much attacked.
The ammonium chloride which it yielded weighed only 0:0035 grm.

The density of the remaining gas was then determined. But as its volume was
only a little over 100 cub. centims., the bulb, the capacity of which was 162 cub.
centims., had to be filled at reduced pressure. This was easily done by replacing the
pear-shaped reservoir of the mercury gas-holder by a straight tube, and noting the
level of the mercury in the gas-holder and in the tube which served as a mercury
reservoir against a graduated mirror-scale by help of a cathetomer at the moment of
closing the stop-cock of the density bulb.

The details of the experiment are these :—

Temperature, 19°12°C. Barometric pressure, 749°8 millims. (corr.).
Difference read on gas-holder and tube, 225°25 millims. (corr.).
Actual pressure, 524°55 millims.

206 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

Weight of 162°843 cub. centims. of gas . . . . . = 0'17913 grm.
Weight of 1 litre at 0° and 760 millims. pressure. . 1:7054 _,,
Density sow Ok Be Roan Bs 7, Sen POLO SG memos

This gas is accordingly at least 19 times as heavy as hydrogen.

A portion of the gas was then mixed with oxygen, and submitted to a rapid
discharge of sparks for four hours in presence of caustic potash. It contracted, and
on absorbing the excess of oxygen with pyrogallate of potassium the contraction
amounted to 15°4 per cent. of the original volume. The question then arises, if the
gas contain 15°4 per cent. of nitrogen, of density 14°014, and 84°6 per cent. of other
gas, and if the density of the mixture were 19°086, what would be the density of the
other gas? Calculation leads to the number 20:0.

A vacuum-tube was filled with a specimen of the gas of density 19°086, and it
could not be doubted that it contained nitrogen, the bands of which were distinctly
visible. It was probable, therefore, that the true density of the pure gas lay not far
from 20 times that of hydrogen. At the same time many lines were seen which
could not be recognized as belonging to the spectrum of any known substance.

Such were the preliminary experiments made with the aid of magnesium to
separate from atmospheric nitrogen its dense constituent. The methods adopted in
preparing large quantities will be subsequently described.

6. Proof of the Presence of Argon in Air, by means of Atmolysis.

?

It has already (§ 2) been suggested that if ‘atmospheric nitrogen” contains two
gases of different densities, it should be possible to obtain direct evidence of the fact
by the method of atmolysis. The present section contains an account of carefully
conducted experiments directed to this end.

The atmolyser was prepared (after GranHam) by combining a number of “ church-
warden” tobacco pipes. At first twelve pipes were used in three groups, each group
including four pipes connected in series. The three groups were then connected in
parallel, and placed in a large glass tube closed in such a way that a partial vacuum
could be maintained in the space outside the pipes by a water-pump. One end of
the combination of pipes was open to the atmosphere, or rather was connected with
the interior of an open bottle containing sticks of caustic alkali, the object being
mainly to dry the air. The other end of the combination was connected to a bottle
aspirator, initially full of water, and so arranged as to draw about two per cent. of
the air which entered the other end of the pipes. The gas collected was thus a very
small proportion of that which leaked through the pores of the pipes, and should be
relatively rich in the heavier constituents of the atmosphere. The flow of water
from the aspirator could not be maintained very constant, but the rate of two per
cent. was never much exceeded. ‘The necessary four litres took about sixteen hours
to collect.

A NEW CONSTITUENT OF THE ATMOSPHERE. 207

The air thus obtained was treated exactly as ordinary air had been treated in
determinations of the density of atmospheric nitrogen. Oxygen was removed by
red-hot copper followed by cupric oxide, ammonia by sulphuric acid, carbonic anhy-
dride and moisture by potash and phosphoric anhydride.

The following are the results :—

Globe empty July 10,14 . . . A) BLED
Globe full September 15 (twelve eee aah "50286
Wierohtiofgcast tae mae oa cea ne Ue eno S
Ordinary atmospheric nitrogen . . . . . 2°31016

Ditterencew ete ee oe et 00487
Globe empty September 17. . . ee os 45
Globe full September 18 (twelve Rae ah DIS)
Weight of gas. . . sia alse beh m Says
Ordinary atmospheric nitrogen . . . . . 2'31016

Witterences 1 ape gat ee ee OLS
Globe empty September 21 . . . 2 ne 2592320
Globe full September 20 (twelve bie) eee 51031
WEGENORGS er Shs Le Ue a PES)
Ordinary atmospheric nitrogen . . . . . 2°31016

Difteten ces) siti vd gente niece ee s00278
Globe empty September 21, October 30 . . 2°82306
Globe full September 22 (twelve pipes) . . 51140
Weight of gas. . . se agen ene seam 311 LOG
Ordinary atmospheric nitrogen . . . . . 2°31016

Ditterencem aa hn eee ee ett ie O

The mean excess of the four determinations is (00262 gram., or if we omit the first,
which depended upon a vacuum weighing of two months old, ‘00187 gram.

The gas from prepared air was thus in every case denser than from unprepared air,
and to an extent much beyond the possible errors of experiment. The excess was,
however, less than had been expected, and it was thought that the arrangement of
the pipes could be improved. ‘The final delivery of gas from each of the groups in
parallel being so small in comparison with the whole streams concerned, it seemed
possible that each group was not contributing its proper share, and even that there
might be a flow in the wrong direction at the delivery end of one or two of them. To

208 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

meet this objection, the arrangement in parallel had to be abandoned, and for the
remaining experiments eight pipes were connected in simple series. The porous
surface in operation was thus reduced, but this was partly compensated for by an
improved vacuum. ‘Two experiments were made under the new conditions :—

Globe empty, October 30, November 5 . . = 2°82313
Giobe full, November 8 (eight pipes) . . . 50930
Wreightiofigas) Nace ee ae . 2°31383
Ordinary atmospheric nitrogen . . . . . 2°31016

Difference. cl a es tee ee 008 bir
Globe empty, November 5,8... . . . 2°82355
Globe full, November 6 (eight pipes) . . . 51011
Wieiehtiol gas: 05. Si Gees ike etme oa
Ordinary atmospheric nitrogen . . . . . 2°31016

Difference: 4a ee, Eee eee OO R26

The excess being larger than before is doubtless due to the greater efficiency of
the atmolysing apparatus. It should be mentioned that the above recorded experi-
ments include all that have been tried, and the conclusion seems inevitable that
“ atmospheric-nitrogen ” is a mixture and not a simple body.

It was hoped that the concentration of the heavier constituent would be sufficient
to facilitate its preparation in a pure state by the use of prepared air in substitution
for ordinary air in the oxygen apparatus. The advance of 3} mg. on the 11 mg.,
by which atmospheric nitrogen is heavier than chemical nitrogen, is indeed not to be
despised, and the use of prepared air would be convenient if the diffusion apparatus
could be set up on a large scale and be made thoroughly self-acting.

7. Negative Experiments to Prove that Argon 1s not derived from Nitrogen or
From Chenucal Sources.

Although the evidence of the existence of argon in the atmosphere, derived from
the comparison of densities of atmospheric and chemical nitrogen and from the
diffusion experiments (§ 6), appeared overwhelming, we have thought it undesirable
to shrink from any labour that would tend to complete the verification. With this
object in view, an experiment was undertaken and carried to a conclusion on
November 13, in which 3 litres of chemical nitrogen, prepared from ammonium
nitrite, were treated with oxygen in precisely the manner in which atmospheric
nitrogen had been found to yield a residue of argon. In the course of operations an

A NEW CONSTITUENT OF THE ATMOSPHERE. 209

accident occurred, by which no gas could have been lost, but of such a nature that
from 100 to 200 cub. centims. of air must have entered the working vessel. The gas
remaining at the close of the large scale operations was worked up as usual with
battery and coil until the spectrum showed only slight traces of the nitrogen lines.
When cold, the residue measured 4 cub. centims. This was transferred, and after
treatment with alkaline pyrogallate to remove oxygen, measured 3°3 cub. centims.
If atmospheric nitrogen had been employed, the final residue should have been about
30 cub. centims. Of the 3°3 cub. centims. actually left, a part is accounted for by
the accident alluded to, and the result of the experiment is to show that argon is not
formed by sparking a mixture of oxygen and chemical nitrogen.

In a second experiment of the same kind 5660 cub. centims. of nitrogen from
ammonium nitrite were treated with oxygen in the large apparatus (fig. 7, § 8). The
final residue was 3°5 cub. centims.; and as evidenced by the spectrum, it consisted
mainly of argon.

The source of the residual argon is to be found in the water used for the
manipulation of the large quantities of gas (6 litres of nitrogen and 11 litres of
oxygen) employed. Unfortunately the gases had been collected by allowing them to
bubble up into aspirators charged with ordinary water, and they were displaced by
ordinary water. In order to obtain information with respect to the contamination
that may be acquired in this way, a parallel experiment was tried with carbonic
anhydride. Eleven litres of the gas, prepared from marble and hydrochloric acid
with ordinary precautions for the exclusion of air, were collected exactly as oxygen
was commonly collected. It was then transferred by displacement with water to a
gas pipette charged with a solution containing 100 grms. of caustic soda. The
residue which refused absorption measured as much as 110 cub. centims. In another
experiment where the water employed had been partially de-aerated, the residue left
amounted to 71 cub. centims., of which 26 cub. centims. were oxygen. The
quantities of dissolved gases thus extracted from water during the collection of
oxygen and nitrogen suffice to explain the residual argon of the negative experiments.

It may perhaps be objected that the impurity was contained in the carbonic
anhydride itself as it issued from the generating vessel, and was not derived from the
water in the gas-holder ; and indeed there seems to be a general impression that it is
difficult to obtain carbonic anhydride in a state of purity. To test this question,
18 litres of the gas, made in the same generator and from the same materials, were
passed directly into the absorption pipette. Under these conditions, the residue was
only 64 cub. centims., corresponding to 4 cub. centims. from-11 litres. The quantity
of gas employed was determined by decomposing the resulting sodium carbonate with
hydrochloric acid, allowance being made for a little carbonic anhydride contained in
the soda as taken from the stock bottle. It will be seen that there is no difficulty
in reducing the impurity to sjgoth, even when india-rubber connections are freely
used, and no extraordinary precautions are taken. The large amount of impurity

MDCCCXCV.—A, 25

210 LORD RAYLEIGIL AND PROFESSOR W. RAMSAY ON ARGON,

found in the gas when collected over water must therefore have been extracted from

the water.

A similar set of experiments was carried out with magnesium. The nitrogen, of
which three litres were used, was prepared by the action of bleaching-powder on
ammonium chloride. It was circulated in the usual apparatus over red-hot magnesium,
until its volume bad been reduced to about 100 cub. centims. An equal volume of
hydrogen was then added, owing to the impossibility of circulating a vacuum. The
circulation then proceeded until all absorption had apparently stopped. The remaining
gas was then passed over red-hot copper oxide into the SPRENGEL’s pump, and
collected. As it appeared still to contain hydrogen, which had escaped oxidation,
owing to its great rarefaction, it was passed over copper oxide for a second and a
third time. As there was still a residue, measuring 12°5 cub. centims., the gas was
left in contact with red-hot magnesium for several hours, and then pumped out ; its
volume was then 4°5 cub. centims. Absorption was, however, still proceeding, when
the experiment terminated, for at a low pressure, the rate is exceedingly slow. This
gas, after being sparked with oxygen contracted to 3:0 cub. centims., and on
examination was seen to consist mainly of argon. The amount of residue obtainable
from three litres of atmospheric nitrogen should have amounted to a large multiple
of this quantity.

In another experiment, 15 litres of nitrogen prepared from a mixture of ammonium
chloride and sodium nitrite by warming in a flask (some nitrogen having first: been
drawn off by a vacuum-pump, in order to expel all air from the flask and from the
contained liquid) were collected over water in a large gas-holder. The nitrogen was
not bubbled through the water, but was admitted from above, while the water escaped
below. This nitrogen was absorbed by red-hot magnesium, contained in tubes heated
in a combustion-furnace. The unabsorbed gas was circulated over red-hot magnesium
in a special small apparatus, by which its volume was reduced to 15 cub. centims.
As it was impracticable further to reduce the volume by means of magnesium, the
residual 15 cub. centims. were transferred to a tube, mixed with oxygen, and submitted
to sparking over caustic soda. The residue after absorption of oxygen, which
undoubtedly consisted of pure argon, amounted to 3°5 cub. centims. This is one-fortieth
of the quantity which would have been obtained from atmospheric nitrogen, and its
presence can be accounted for, we venture to think, first from the water in the
gas-holder, which had not been freed from dissolved gas by boiling in vacuo (it has
already been shown that a considerable gain may ensue from this source), and second,
from leakage of air which accidentally took place, owing to the breaking of a tube.
The leakage may have amounted to 200 cub. centims., but it could not be accurately
ascertained. Quantitative negative experiments of this nature are exceedingly
difficult, and require a long time to carry them to a successful conclusion.

A NEW CONSTITUENT OF THE ATMOSPHERE. 211

8. Separation of Argon on a Large Scale.

To separate nitrogen from “atmospheric nitrogen” on a large scale, by help of
magnesium, several devices were tried. It is not necessary to describe them all in
detail. Suffice it to say that an attempt was made to cause a store of “ atmospheric
nitrogen” to circulate by means of a fan, driven by a water-motor. The difficulty
encountered here was leakage at the bearing of the fan, and the introduced air
produced a cake which blocked the tube on coming into contact with the magnesium.
It might have been possible to remove oxygen by metallic copper; but instead of
thus complicating the apparatus, a water-injector was made use of to induce circula-
tion. Here also it is unnecessary to enter into details. For, though the plan worked
well, and although about 120 litres of “atmospheric nitrogen” were absorbed, the
yield of argon was not large, about 600 cub. centims. having been collected. This
loss was subsequently discovered to be due partially, at least, to the relatively high
solubility of argon in water. In order to propel the gas over magnesium, through a
long combustion-tube packed with turnings, a considerable water-pressure, involving
a large flow of water, was necessary. The gas was brought into intimate contact
with this water, and presuming that several thousand litres of water ran through the
injector, it is obyious that a not inconsiderable amount of argon must have been
dissolved. Its proportion was increasing at each circulation, and consequently its
partial pressure also increased. Hence, towards the end of the operation, at least,
there is every reason to believe that a serious loss had occurred.

It was next attempted to pass “atmospheric nitrogen” from a gas-holder first
through a combustion tube of the usual length packed with metallic copper reduced
from the oxide; then through a small U-tube containing a little water, which was
intended as an index of the rate of flow; the gas was then dried by passage through
tubes filled with soda-lime and phosphoric anhydride ; and it next passed through a
long iron tube (gas-pipe) packed with magnesium turnings, and heated to bright
reduess in a second combustion-furnace.

After the iron tube followed a second small U-tube containing water, intended to
indicate the rate at which the argon escaped into a small gas-holder placed to receive
it. The nitrogen was absorbed rapidly, and argon entered the small gas-holder, But
there was reason to suspect that the iron tube is permeable by argon at a red heat.
The first tube-full allowed very little argon to pass. After it had been removed and
replaced by a second, the same thing was noticed. The first tube was difficult to
clean ; the nitride of magnesium forms a cake on the interior of the tube, and it was
very difficult to remove it; moreover this rendered the filling of the tube very
troublesome, inasmuch as its interior was so rough that the magnesium turnings could
only with difficulty be forced down. However, the permeability to argon, if such be
the case, appeared to have decreased. The iron tube was coated internally with a
skin of magnesium nitride, which appeared to diminish its permeability to argon.

74 19)

212 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

After all the magnesium in the tube had been converted into nitride (and this was
easily known, because a bright glow proceeded gradually from one end of the tube to
the other) the argon remaining in the iron tube was ‘‘ washed” out by a current of
nitrogen; so that after a number of operations, the small gas-holder contained a
mixture of argon with a considerable quantity of nitrogen.

On the whole, the use of iron tubes is not to be recommended, owing to the diffi-
culty in cleaning them, and the possible loss through their permeability to argon.
There is no such risk of loss with glass tubes, but each operation requires a new tube,
and the cost of the glass is considerable if much nitrogen is to be absorbed. Tubes
of porcelain were tried ; but the glaze in the interior is destroyed by the action of the
red-hot magnesium, and the tubes crack on cooling.

By these processes 157 litres of “atmospheric nitrogen” were reduced in volume to
about 2°5 litres in all of a mixture of nitrogen and argon. This mixture was after-
wards circulated over red-hot magnesium, in order to remove the last portion of
nitrogen.

Fig. 5.
To wales, pump

To Sprengel's
JORG

As the apparatus employed for this purpose proved very convenient, a full deserip-
tion of its construction is here given. A diagram is shown in fig. 5, which sufficiently
explains the arrangement of the apparatus. A is the circulator. It consists of a sort
of SPRENGEL’s pump (a) to which a supply of mercury is admitted from a small

A NEW CONSTITUENT OF THE ATMOSPHERE. 213

reservoir (b). This mercury is delivered into a gas-separator (c), and the mercury
overflows into the reservoir (d). When its level rises, so that it blocks the tube (/),
it ascends in pellets or pistons into (e), a reservoir which is connected through (9)
with a water-pump. The mercury falls into (>), and again passes down the SPRENGEL
tube (a). No attention is, therefore, required, for the apparatus works quite auto-
matically. This form of apparatus was employed several years ago by Dr. CoLtts.

The gas is drawn from the gas-holder B, and passes through a tube C, which is
heated to redness by a long-flame burner, and which contains in one half metallic
copper, and in the other half copper oxide. This precaution is taken in order to remove
any oxygen which may possibly be present, and also any hydrogen or hydrocarbon.
In practice, it was never found that the copper became oxidised, or the oxide reduced.
It is, however, useful to guard against any possible contamination. The gas next
traversed a drying-tube D, the anterior portion containing ignited soda-lime, and the
posterior portion phosphoric anhydride. From this it passed a reservoir, D’, from
which it could be transferred, when all absorption had ceased, into the small gas-
holder. It then passed through E, a piece of combustion-tube, drawn out at both
ends, filled with magnesium turnings, and heated by a long-flame burner to redness.
Passing through a small bulb, provided with electrodes, it again entered the fall
tube. .

After the magnesium tube E had done its work, the stop-cocks were all closed, and
the gas was turned down, so that the burners might cool. The mixture of argon and
nitrogen remaining in the system of tubes was pumped out by a SPRENGEL’S pump
through F, collected in a large test-tube, and reintroduced into the gas-holder B
through the side-tube G, which requires no description. The magnesium tube was
then replaced by a fresh one; the system of tubes was exhausted of air; argon and
nitrogen were admitted from the gas-holder B; the copper-oxide tube and the
magnesium tube were again heated ; and the operation was repeated until absorption
ceased. It was easy to decide when this point had been reached, by making use of
the graduated cylinder H, from which water entered the gas-holder B. It was found
advisable to keep all the water employed in these operations, for it had become
saturated with argon. If gas was withdrawn from the gas-holder, its place was taken
by this saturated water.

The absorption of nitrogen proceeds very slowly towards the end of the operation,
and the diminution in volume of the gas is not greater than 4 or 5 cub. centims. per
hour. It is, therefore, somewhat difficult to judge of the end-point, as will be seen
when experiments on the density of this gas are described. The magnesium tube,
towards the end of the operations, was made so hot that the metal was melted in the
lower part of the tube, and sublimed in the upper part. The argon and residual
nitrogen had, therefore, been thoroughly mixed with gaseous magnesium during its
passage through the tube E.

To avoid possible contamination with air in the SPRENGEL’s pump, the last portion

214 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

of gas collected from. the system of tubes was not re-admitted to the gas-holder B, but
was separately stored.

The crude argon was collected in two operations. First, the quantity made by
absorption by magnesium in glass tubes with the water-pump circulator was purified.
Later, after a second supply had been prepared by absorption in iron tubes, the mixture
of argon and nitrogen was united with the first quantity and circulated by means of the
mercury circulator, in the gas-holder B. Attention will be drawn to the particular
sample of gas employed in describing further experiments made with the argon.

By means of magnesium, about 7 litres of nitrogen can be absorbed in an hour.
The changing of the tubes of magnesium, however, takes some time; consequently,
the largest amount absorbed in one day was nearly 30 litres.

At a later date a quantitative experiment was carried out on a large scale, the
amount of argon from 100 litres of “atmospheric”
been absorbed by magnesium, and the resulting argon measured at 12°. During the

nitrogen, measured at 20°, having

process of absorbing nitrogen in the combustion-furnace, however, one tube cracked,
and it is estimated that about 4 litres of nitrogen escaped before the crack was
noticed. With this deduction, and assuming that the nitrogen had been measured at
12°, 93°4 litres of atmospheric nitrogen were taken. The magnesium required for
absorption weighed 409 germs. The amount required by theory should have been
285 orms. ; but it must be remembered that in many cases the magnesium was by no
means wholly converted into nitride. The first operation yielded about 3 litres of a
mixture of nitrogen and argon, which was purified in the circulating apparatus. The
total residue, after absorption of the nitrogen, amounted to 921 cub. centims. The
yield is therefore 0°986 per cent.

At first no doubt the nitrogen gains a little argon from the water over which it
stands. But, later, when the argon forms the greater portion of the gaseous mixture,
its solubility in water must materially decrease its volume. It is difficult to estimate
the loss from this cause. The gas-holder, from which the final circulation took ‘place,
held three litres of water. Taking the solubility of argon as 4 per cent., this would
mean a loss of about 120 cub. centims. If this is not an over-estimate, the yield of
argon would be increased to 1040 cub. centims., or 1°11 per cent. The truth probably
lies between these two estimates.

It may be concluded, with probability, that the argon forms approximately 1 per
cent. of the “atmospheric” nitrogen.

The principal objection to the oxygen method of isolating argon, as hitherto
described, is the extreme slowness of the operation. An absorption of 30 cub.
centims. of mixed gas means the removal of but 12 cub. centims. of nitrogen. At
this rate 8 hours are required for the isolation of 1 cub. centim. of argon, supposed
to be present in the proportion of 1 per cent.

In extending the scale of operations we had the great advantage of the advice of

A NEW CONSTITUENT OF THE ATMOSPHERE, 215

Mr. Crookes, who a short time ago called attention to the flame rising from platinum
terminals, which convey a high tension alternating electric discharge, and pointed
out its dependence. upon combustion of the nitrogen and oxygen of the air.*
Mr. Crookes was kind enough to arrange an impromptu demonstration at his own
house with a small alternating current plant, in which it appeared that the absorp-
tion of mixed gas was at the rate of 500 cub. centims. per hour, or nearly 20 times
as fast as with the battery. The arrangement is similar to that first described by
SportiswoopE.t The primary of a RunmMKorrFr coil is connected directly with the
alternator, no break or condenser being required; so that, in fact, the coil acts
simply as a high potential transformer. When the arc is established the platinum
terminals may be separated much beyond the initial striking distance. /

The plant with which the large scale operations have been made consists of a
De Menritens alternator, kindly lent by Professor J. J. THomson, and a gas engine.
As transformer, one of SwinpurNe’s hedgehog pattern has been employed with
success, but the ratio of transformation (24:1) is scarcely sufficient. A higher
potential, although, perhaps, not more efficient, is more convenient. The striking
distance is greater, and the arc is not so liable to go out. Accordingly most of the
work to be described has been performed with transformers of the RuudMKoRFF type.

The apparatus has been varied greatly, and it cannot be regarded as having even
yet assumed a final form. But it will give a sufficient idea of the method if we
describe an experiment in which a tolerably good account was kept of the air and
oxygen employed. The working vessel was a glass flask, A (fig. 6), of about 1500 cub.
centims. capacity, and stood, neck downwards, over a large jar of alkali, B. As in
the small scale experiments, the leading-in wires were insulated by glass tubes, DD,
suitably bent and carried through the liquid up the neck. For the greater part of
the length iron wires were employed, but the internal extremities, EE, were of
platinum, doubled upon itself at the terminals from which the discharge escaped.
The glass protecting tubes must be carried up for some distance above the internal
level of the liquid, but it is desirable that the arc itself should not be much raised
above that level. A general idea of the disposition of the electrodes will be obtained
from fig. 6. To ensure gas tightness the bends were occupied by mercury. A tube,
C, for the supply or withdrawal of gas was carried in the same way through the
neck.

The RupnMKorrr employed in this operation was one of medium size. When the
mixture was rightly proportioned and the arc of full length, the rate of absorption
was about 700 cub. centims. per hour. A good deal of time is lost in starting, for,
especially when there is soda on the platinums, the arc is liable to go out if lengthened
prematurely. After seven days the total quantity of air let in amounted to 7925 cub.
centims., and of oxygen (prepared from chlorate of potash) 9137 cub. centims. On

* ‘Chemical News,’ vol. 65, p. 301, 1892.
+ “A Mode of Exciting an Induction-coil.”’ ‘Phil. Mag.,’ vol. 8, p. 390, 1879.

216 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

the eighth and ninth days oxygen alone was added, of which about 500 cub. centims,
was consumed, while there remained about 700 cub. centims in the flask. Hence the
proportion in which the air and oxygen combined was as 70:96. On the eighth day
there was about three hours’ work, and the absorption slackened off to about one
quarter of the previous rate. On the ninth day (September 8) the rate fell off still

Fig. 6.

more, and after three hours’ work became very slow. The progress towards removal
of nitrogen was examined from time to time with the spectroscope, the points being
approximated and connected with a small Leyden jar. At this stage the yellow
-nitrogen line was faint, but plainly visible. After about four hours’ more work, the
yellow line had disappeared, and for two hours there had been no visible contraction.
It will be seen that the removal of the last part of the nitrogen was very slow, mainly
on account of the large excess of oxygen present.

A NEW CONSTITUENT OF THE ATMOSPHERE. PANTS.

The final treatment of the residual 700 cub. centims. of gas was on the model of
the small scale operations already described (§ 4). By means of a pipette the gas was
gradually transferred to a large test-tube standing over alkali. Under the influence
of sparks (from battery and coil) passing all the while, the superfluous oxygen was
consumed with hydrogen fed in slowly from a voltameter. If the nitrogen had been
completely removed, and if there were no unknown ingredient in the atmosphere, the
volume under this treatment should have diminished without limit. But the con-
traction stopped at a volume of 65 cub. centims., and the volume was taken back-
wards and forwards through this as a minimum by alternate treatment with oxygen
and hydrogen added in small quantities, with prolonged intervals of sparking.
Whether the oxygen or the hydrogen were in excess could be determined at any
moment bya glance at the spectrum. At the minimum volume the gas was certainly
not hydrogen or oxygen. Was it nitrogen? On this point the testimony of the
spectroscope was equally decisive. No trace of the yellow nitrogen line could be seen
even with a wide slit and under the most favourable conditions.

When the gas stood for some days over water the nitrogen line again asserted
itself, and many hours of sparking with a little oxygen were required again to get rid of
it. As it was important to know what proportions of nitrogen could be made visible
in this way, a little air was added to gas that had been sparked for some time subse-
quently to the disappearance of nitrogen in its spectrum. It was found that about
14 per cent. was clearly, and about 3 per cent. was conspicuously, visible. About the
same numbers apply to the visibility of nitrogen in oxygen when sparked under these
conditions, that is, at atmospheric pressure, and with a jar in connection with the
secondary terminals.

When we attempt to increase the rate of absorption by the use of a more powerful
electric arc, further experimental difficulties present themselves. In the arrangement
already described, giving an absorption of 700 cub. centims. per hour, the upper part ~
of the flask becomes very hot. With a more powerful are the heat rises to such a
point that the flask is filled with steam and the operation comes to a standstill.

It is necessary to keep the vessel cool by either the external or internal application
of liquid to the upper surface upon which the hot gases from the are impinge. One
way of effecting this is to cause a small fountain of alkali to impinge on the top of
the flask, so as to wash the whole of the upper surface. This plan is very effective,
but it is open to the objection that a break-down would be disastrous, and it would
involve special arrangements to avoid losing the argon by solution in the large
quantity of alkali required. It is simpler in many respects to keep the vessel cool by
immersing it in a large body of water, and the inverted flask arrangement (fig. 6) has
been applied in this manner. But, on the whole, it appears to be preferable to limit
the application of the cooling water to the upper part of the external surface, building
up for this purpose a suitable wall of sheet lead cemented round the glass, The most

MDCCCXCV.—A. ZF

218 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

convenient apparatus for large-scale operations that has hitherto been tried is shown
in the accompanying figure (fig. 7).

The vessel A is a large globe of about 6 litres capacity, intended for demonstrating
the combustion of phosphorus in oxygen gas, and stands in an inclined position. It
is about half filled with a solution of caustic soda. The neck is fitted with a rubber
stopper, B, provided with four perforations. Two of these are fitted with tubes,
C, D, suitable for the supply or withdrawal of gas or liquid. The other two allow
the passage of the stout glass tubes, E, F, which contain the electrodes. For greater
security against leakage, the interior of these tubes is charged with water, held in
place by small corks, and the outer ends are cemented up. The electrodes are formed

“i

A }
% Soda solutt? Wy

of stout iron wires terminated by thick platinums, G, H, triply folded together, and
welded at the ends. The lead walls required to enclose the cooling water are
partially shown at I. For greater security the india-rubber cork is also drowned in
water, held in place with the aid of sheet-lead. The lower part of the globe is
occupied by about 3 litres of a 5 per cent. solution of caustic soda, the solution rising
to within about half-an-inch of the platinum terminals. With this apparatus an
absorption of 3 litres of mixed gas per hour can be attained,—about 3000 times the
rate at which CAVENDISH could work.

When it is desired to stop operations, the feed of air (or of chemical nitrogen in
blank experiments) is cut off, oxygen alone being supplied as long as any visible
absorption occurs. Thus at the close the gas space is occupied by argon and oxygen
with such nitrogen as cannot readily be taken up in a condition of so great dilution.

A NEW CONSTITUENT OF THE ATMOSPHERE, 219

The oxygen, being too much for convenient treatment with hydrogen, was usually
absorbed with copper and ammonia, and the residual gas was then worked over again
as already described in an apparatus constructed upon a smaller scale.

It is worthy of notice that with the removal of the nitrogen, the arc-discharge from
the dynamo changes greatly in appearance, bridging over more directly and in a nar-
rower band from one platinum to the other, and assuming a beautiful sky-blue colour,
instead of the greenish hue apparent so long as oxidation of nitrogen is in progress.

In all the large-scale experiments, an attempt was made to keep a reckoning of the
air and oxygen employed, in the hope of obtaining data as to the proportional
volume of argon in air, but various accidents too often interfered. In one successful
experiment (January, 1895), specially undertaken for the sake cf measurement, the
total air employed was 9250 cub. centims., and the oxygen consumed, manipulated
with the aid of partially de-aerated water, amounted to 10,820 cub. centims. The
oxygen contained in the air would be 1942 cub. centims. ; so that the quantities of
“atmospheric nitrogen” and of total oxygen which enter into combination would be
7308 cub. centims., and 12,762 cub. centims. respectively. This corresponds to
N + 1°75O0—the oxygen being decidedly in excess of the proportion required to form
nitrous acid—2HNO,, or H,0+N,+30. The argon ultimately found on absorption
of the excess of oxygen was 75'0 cub. centims., reduced to conditions similar to
those under which the air was measured, or a little more than 1 per cent. of the
‘atmospheric nitrogen” used. It is probable, however, that some of the argon was
lost by solution during the protracted operations required in order to get quit of the
last traces of nitrogen.

[In recent operations at the Royal Institution, where a public supply of alternating
current at 100 volts is available, the scale of the apparatus has been still further
‘increased.

The capacity of the working vessel is 20 litres, of which about one half is
occupied by a strong solution of caustic soda. The platinum terminals are very
massive, and the flame rising from them is prevented from impinging directly upon
the glass by a plate of platinum held over it and supported by a wire which passes
through the rubber cork. In the electrical arrangements we have had the advantage
of Mr. SwInBuRNE's advice. The transformers are two of the “hedgehog” pattern,
the thick wires being connected in parallel and the thin wires in series. In order to
control the current taken when the arc is short or the platinums actually in contact,
a choking-coil, provided with a moyable core of fine iron wires, is inserted in the
thick wire circuit. In normal working the current taken from the mains is about
22 amperes, so that some 24 h. p. is consumed. At the same time the actual
voltage at the platinum terminals is 1500. When the discharge ceases, the voltage
at the platinum rises to 3000,* which is the force actually available for re-starting
the discharge if momentarily stopped.

* A still higher voltage on open circuit would be preferable.

7, 0!

220 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

With this discharge, the rate of absorption of mixed gases is about 7 litres per hour.
When the argon has accumulated to a considerable extent, the rate falls off, and after
several days’ work, about 6 litres per hour becomes the maximum. In commencing
operations it is advisable to introduce, first, the oxygen necessary to combine with
the already included air, after which the feed of mixed gases should consist of about
11 parts of oxygen to 9 parts of air. The mixed gases may be contained in a large
gas-holder, and then, the feed being automatic, very little attention is required.
When it is desired to determine the rate of absorption, auxiliary gas-holders of glass,
graduated into litres, are called into play. If the rate is unsatisfactory, a determina-
tion may be made of the proportion of oxygen in the working vessel, and the
necessary gas, air, or oxygen, as the case may be, introduced directly.

In re-starting the arc after a period of intermission, it is desirable to cut off the
connection with the principal gas-holder. The gas (about two litres in amount)
ejected from the working vessel by the expansion is then retained in the auxiliary
holder, and no argon finds its way further back. The connection between the working
vessel and the auxiliary holder should be made without india-rubber, which is hable
to be attacked by the ozonized gases.

The apparatus has been kept in operation for fourteen hours continuously, and
there should be no difficulty in working day and night. An electric signal could
easily be arranged to give notice of the extinction of the arc, which sometimes occurs
unexpectedly ; or an automatic device for re-striking the arc could be contrived.—

April, 1895.]

9. Density of Argon prepared by means of Oxygen.

A first estimate of the density of argon prepared by the oxygen method was
founded upon the data recorded already respecting the volume present in air, on the
assumption that the accurately known densities of “atmospheric” and of chemical
nitrogen differ on account of the presence of argon in the former, and that during the
treatment with oxygen nothing is oxidised except nitrogen. Thus, if

D = density of chemical nitrogen,

De . atmospheric nitrogen,
Ca ¥ argon,
® = proportional volume of argou in atmospheric nitrogen,

the law of mixtures gives
ad+(1—e)D=D

or

d=D+(D'—D)a.

A NEW CONSTITUENT OF THE ATMOSPHERE. 221

In this formula D’—D and @ are both small, but they are known with fair
accuracy. From the data already given for the experiment of September 8th

whence, if on an arbitrary scale of reckoning D = 2-2990, D’ = 2°3102, we find
d = 3378. Thus if N, be 14, or O, be 16, the density of argon is 20°6.
Agein, from the January experiment,

75:0
7308

oo

whence, if N = 14, the density of argon is 20°6, as before. There can be little doubt,
however, that these numbers are too high, the true value of « being greater than is
supposed in the above calculations. :

A direct determination by weighing is desirable, but hitherto it has not been
feasible to collect by this means sufficient to fill the large globe (§ 1) employed for
other gases. A mixture of about 400 cub. centims. of argon with pure oxygen,
however, gave the weight 2°7315, 0°1045 in excess of the weight of oxygen, viz.,
2°6270. Thus, if « be the ratio of the volume of argon to the whole volume, the

number for argon will be
2°6270 + 0°1045/a.

The value of «, being involved only in the excess of weight above that of oxygen,
does not require to be known very accurately. Sufficiently concordant analyses by two
methods gave « = 01845; whence, for the weight of the gas we get 3°193; so that
if O = 16, the density of the gas would be 19°45. An allowance for residual nitrogen,
still visible in the gas before admixture of oxygen, raises this number to 19°7, which
may be taken as the density of pure argon resulting from this determination.*

10. Density of Argon Prepared by means of Magnesiui.t

It has already been stated that the density of the residual gas from the first and
preliminary attempt to separate oxygen and nitrogen from air by means of mag-
nesium was 19086, and allowing for contraction on sparking with oxygen the density
is calculable as 20°01. The following determinations of density were also made :—

(a.) After absorption in glass tubes, the water circulator having been used, and
subsequent circulation by means of mercury circulator until rate of contraction had

* [The proportion of nitrogen (4 or 5 per cent. of the volume) was estimated from the appearance of
the nitrogen lines in the spectrum, these being somewhat more easily visible than when 3 per cent.

of nitroger was introduced into pure argon (§ 8).—April, 1895. ]
+ See Addendum, p. 237.

222 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

become slow, 162°843 cub. centims., measured at 757°7 millims. (corr.) pressure, and
16°81° C., weighed 0°2683 grm. Hence,

Weight of 1 litre at 0° and 760 millms. . . . 1°7543 grms.
Density compared with hydrogen(O=16) . . 19°63 f

This gas was again circulated over red-hot magnesium for two days. Before
circulation it contained nitrogen as was evident from its spectrum ; after circulating,
nitrogen appeared to be absent, and absorption had completely stopped. The density
was again determined.

(b.) 162,843 cub. centims., measured at 745°4 millims. (corr.) pressure, and
17°25° C., weighed 0:2755 grm. Hence,

Weight of 1 litre at 0° and 760 millims. . . . 1°8206 grms.
Density compared with hydrogen (O = 16) . . 20°38 #

Several portions of this gas, having been withdrawn for various purposes, were
somewhat contaminated with air, owing to leakage, passage through the pump, &c.
All these portions were united in the gas-holder with the main stock, and circulated
for eight hours, during the last three of which no contraction occurred. The gas
removed from the system of tubes by the mercury-pump was not restored to the
gas-holder, but kept separate.

(c.) 162°843 cub. centims., measured at 758°1 millims. (corr.) pressure, and
17:09° C., weighed 0°27705 grm. Hence,

Weight of 1 litre at 0° and 760 millims. . . . 1°8124 grms.
Density compared with hydrogen (O= 16) . . 20°28 3

The contents of the gas-holder were subsequently increased by a mixture of
nitrogen and argon from 87 litres of atmospheric nitrogen, and after circulating,
density was determined. The absorption was however not complete.

(d.) 162°843 cub. centims., measured at 767°6 millims. (corr.) pressure, and
16°31° C., weighed 0°2703 grm. Hence,

Weight of 1 litre at 0° and 760 millims. . . . . 1°742 grms.
Density compared with hydrogen(O=16). . . 19°49 _,,

The gas was further circulated, until all absorption had ceased. This took about
six hours. Density was again determined.

(e.) 162°843 cub. centims. measured at 767°7 millims. (corr.) pressure, and 15:00°C.,
weighed 0°2773 grm. Hence,

Weight of 1 litre at 0° and 760 millims. . . . 17784 grms.
Density compared with hydrogen (O=16) . . 19°90 2B

A NEW CONSTITUENT OF THE ATMOSPHERE. 223

(f) A second determination was carried out, without further circulation.
162°843 cub. centims. measured at 769:0 millims. (corr.) pressure, and 16:00° C.,
weighed 0°2757 grm. Hence,

Weight of 1 litre at 0° and 760 millims. . . . 1°7713 germs.
Density compared with hydrogen(O = 16). . . 19°82 .

(g.) After various experiments had been made with the same sample of gas, it was
again circulated until all absorption ceased. A vacuum-tube was filled with it, and
showed no trace of nitrogen.

The density was again determined :—

162°843 cub. centims. measured at 750 millims. (corr.) pressure, and at 15°62° C.,
weighed 0°26915 orm.

Weight of 1 litre at 0° and 760 millims. . . . 1'7707 grms.
Density compared with hydrogen (O= 16). . . 19°82 -

These comprise all the determinations of density made. It should be stated that
there was some uncertainty discovered later about the weight of the vacuous globe in
(b) and (c). Rejecting these weighings, the mean of (e), (f), and (g) is 19°88. The
density may be taken as 19°9, with approximate accuracy.

It is better to leave these results without comment at this point, and to return
to them later.

11. Spectrum of Argon.

Vacuum tubes were filled with argon prepared by means of magnesium at various
stages in this work, and an examination of these tubes has been undertaken by
Mr. Crookes, to whom we wish to express our cordial thanks for his kindness in
affording us helpful information with regard to its spectrum. The first tube was
filled with the early preparation of density 19°09, which obviously contained some
nitrogen. A photograph of the spectrum was taken, and compared with a photograph
of the spectrum of nitrogen, and it was at once evident that a spectrum different from
that of nitrogen had been registered.

Since that time many other samples have been examined.

The spectrum of argon, seen in a vacuum tube of about 3 millims. pressure, consists
of a great number of lines, distributed over almost the whole visible field. Two lines
are specially characteristic ; they are less refrangible than the red lines of hydrogen or
lithium, and serve well to identify the gas when examined in this way. Mr. Crooxss,
who gives a full account of the spectrum in a separate communication, has kindly
furnished us with the accurate wave-lengths of these lines as well as of some others
next to be described ; they are respectively 696°56 and 705°64 X 107° millim.

Besides these red lines, a bright yellow line, more refrangible than the sodium line,

224 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

occurs at 603°84. A group of five bright green lines occurs next, besides a number of
less intensity. Of this group of five, the second, which is perhaps the most brilliant,
has the wave-length 56100. There is next a blue, or blue-violet, line of wave-length
470°2 and last, in the less easily visible part of the spectrum, there are five strong
violet lines, of which the fourth, which is the most brilliant, has the wave-
length 420°0.

Unfortunately, the red lines, which are not to be mistaken for those of any other
substance, are only to be seen at atmospheric pressure when a very powerful jar-
discharge is passed through argon. The spectrum, seen under these conditions, has
been examined by Professor ScousteR. ‘he most characteristic lines are perhaps
those in the neighbourhood of F, and are very easily seen if there be not too much
nitrogen, in spite of the presence of some oxygen and water-vapour. The approximate
waye-lengths are :—

ASE 5 a BAN RORIYES,
(A86:07)" oe ee DY
A84-71 . . . . . Not quite so strong.
AGO 32) re ee Strona?
476°50 |
473°53 . . . . Fairly strong characteristic triplet.
472°56 |

It is necessary to anticipate Mr. CrooksEs’s communication, and to state that when
the current is passed from the induction-coil in one direction, that end of the capillary
tube next the positive pole appears of a redder, and that next the negative of a bluer
hue. There are, in effect, two spectra, which Mr, Crooxess has succeeded in separat-
ing to a considerable extent. Mr. E. C. C. Baty,* who has noticed a similar phe-
nomenon, attributes it to the presence of two gases. The conclusion would follow that
what we have termed “ argon ” is in reality a mixture of two gases which have as yet
not been separated. This conclusion, if true, is of great importance, and experiments
are now in progress to test it by the use of other physical methods. . The full bearing
of this possibility will appear later.

A comparison was made of the spectrum seen in a vacuum tube with the spectrum
in a “plenum” tube, 7z.e., one filled at atmospheric pressure. Both spectra were
thrown into a field at the same time. It was evident that they were identical,
although the relative strengths of the lines were not always the same. The seventeen
most striking lines were absolutely coincident.

The presence of a small quantity of nitrogen interferes greatly with the argon
spectrum. But we have found that in a tube with platinum electrodes, after the

* *Proe. Phys. Soc.,’ 1893, p. 147. He says: ‘‘ When an electric current is passed through a mixture
of two gases, one is separated from the other, and appears in the negative glow.”

A NEW CONSTITUENT OF THE ATMOSPHERE. 225

discharge has been passed for four hours, the spectrum of nitrogen disappears, and
the argon spectrum manifests itself in full purity. A specially constructed tube, with
magnesium electrodes, which we hoped would yield good results, removed all traces
of nitrogen it is true, but hydrogen was evolved from the magnesium, and showed its
characteristic lines very strongly. However, these are easily identified. The gas
evolved on heating magnesium in vacuo, as proved by a separate experiment, consists
entirely of hydrogen.

Mr. Crookes has proved the identity of the chief lines of the spectrum of gas
separated from air-nitrogen by aid of magnesium with that remaining after sparking
air-nitrogen with oxygen, in presence of caustic soda solution.

Professor ScousteR has also found the principal lines identical in the spectra of
the two gases, when taken from the jar discharge at atmospheric pressure.

12. Solubility of Argon in Water.

The tendency of the gas to disappear when manipulated over water in small
quantities having suggested that it might be more than usually soluble in that liquid,
special experiments were tried to determine the degree of solubility.

The most satisfactory measures relating to the gas isolated by means of oxygen
were those of September 28. The sample contained a trace of oxygen, and (as
judged by the spectrum) a residue of about 2 per cent. of nitrogen. The procedure
and the calculations followed pretty closely the course marked out by BunsEn,* and
it is scarcely necessary to record the details. The quantity of gas operated upon was
about 4 cub. centims., of which about 14 cub. centims. were absorbed. The final
result for the solubility was 3°94 per 100 of water at 12° C., about 24 times that of
nitrogen. Similar results have been obtained with argon prepared by means of
magnesium. Ata temperature of 13°9°, 131 arbitrary measures of water absorbed
5°3 of argon. This corresponds to a solubility in distilled water, previously freed
from dissolved gas by boiling 7m vacuo for a quarter of an hour, and admitted to the
tube containing argon without contact with air, of 4:05 cub. centims. of argon per
100 of water.

The fact that the gas is more soluble than nitrogen would lead us to expect it in
increased proportion in the dissolved gases of rain water. Experiment has confirmed
this anticipation. Some difficulty was at first experienced in collecting a sufficiency
for the weighings in the large globe of nearly 2 litres capacity. Attempts at
extraction by means of a Topler pump without heat were not very successful. It was
necessary to operate upon large quantities of water, and then the pressure of the
liquid itself acted as an obstacle to the liberation of gas from all except the upper
layers, Tapping the vessel with a stick of wood promotes the liberation of gas in a

* “Gasometry,’ p. 141.
MDCCOXCV.—A. hE

226 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

remarkable manner, but to make this method effective, some means of circulating the
water would have to be introduced.

The extraction of the gases by heat proved to be more manageable. Although a
large quantity of water has to be brought to or near 100° C., a prolonged boiling is
not necessary, as it is not a question of collecting the whole of the gas contained in
the water. The apparatus employed, which worked very well after a little experience,
will be understood from the accompanying figure. The boiler A was constructed

Fig. 8.

aqnq7 ‘odi0g

from an old oil-can, and was heated by an ordinary ring Bunsen burner. For the
supply and removal of water, two co-axial tubes of thin brass, and more than four feet
in length, were applied upon the regenerative principle. The outgoing water flowed
in the inner tube BC, continued from C to D by a prolongation of composition
tubing. The inflowing water from a rain-water cistern was delivered into a glass
tube at E, and passed through a brass connecting tube FG into the narrow annular
space between the two principal tubes GH. The neck of the can was fitted with an
india-rubber cork and delivery-tube, by means of which the gases were collected in

A NEW CONSTITUENT OF THE ATMOSPHERE. 227

the ordinary way. Any carbonic anhydride was removed by alkali before passage
into the glass aspirating bottles used as gas-holders.

The convenient working of this apparatus depends very much upon the mainten-
ance of a suitable relation between the heat and the supply of water. It is desirable
that the water in the can should actually boil, but without a great development of
steam ; otherwise not only is there a waste of heat, and thus a smaller yield of gas,
but the inverted flask used for the collection of the gas becomes inconveniently hot and
charged with steam. It was found desirable to guard against this by the application
of a slow stream of water to the external surface of the flask. -When the supply of
water is once adjusted, nearly half a litre of gas per hour can be collected with very
little attention.

The gas, of which about four litres are required for each operation, was treated
with red-hot copper, cupric oxide, sulphuric acid, potash, and finally phosphoric anhy-
dride, exactly as atmospheric nitrogen was treated in former weighings. The weights
found, corresponding to those recorded in §1, were on two occasions, 2°3221 and
2°3227, showing an excess of 24 milliorms. above the weight of true nitrogen. Since
the corresponding excess for atmospheric nitrogen is 11 milligrms., we conclude
that the water-nitrogen is relatively twice as rich in argon.

Unless some still better process can be found, it may be desirable to collect the
gases ejected from boilers, or from large supply pipes which run over an elevation,
with a view to the preparation of argon upon a large scale.

The above experiments relate to rain water. As regards spring water, it is known
that many thermal springs emit considerable quantities of gas, hitherto regarded as
nitrogen. The question early occurred to us as to what proportion, if any, of the
new gas was contained therein. A notable example of a nitrogen spring is that at
Bath, examined by Davupeny in 1833. With the permission of the authorities of
Bath, Dr. ArTHUR RicHARDSON was kind enough to collect for us about 10 litres of
the gases discharged from the King’s Spring. A rough analysis on reception showed
that it contained scarcely any oxygen and but little carbonic anhydride. Two
determinations of density were made, the gas being treated in all respects as air,
prepared by diffusion and unprepared, were treated for the isolation of atmospheric
nitrogen. The results were :—

@October2OPe ae) 2 ee ee Pee oe SONS
IN\Owemilbere 7 5 65.6 6 6 ¢ 6 oo of wo - BSOHSY
Meanie: ee va che ney eae een css (KD,

The weight of the “nitrogen” from the Bath gas is thus about halfway between
that of chemical and “atmospheric” nitrogen, suggesting that the proportion of
argon is Jess than in air, instead of greater as had been expected.

Dy (CY

228 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

13. Behaviour at Low Temperatures.

A single experiment was made with an early sample of gas, of density 19°1,
which certainly contained a considerable amount of nitrogen. On compressing it in a
pressure apparatus to between 80 and 100 atmospheres pressure, and cooling to
— 90° by means of boiling nitrous oxide, no appearance of liquefaction could be
observed. As the critical pressure was not likely to be so high as the pressure to
which it had been exposed, the non-liquefaction was ascribed to insufficient cooling.

This supposition turned out to be correct. For, on sending a sample to Professor
OLSZEWSKI, the author of most of the accurate measurements of the constants of
gases at low temperatures, he was kind enough to submit it to examination. His
results are published elsewhere ; but, for convenience of reference, his tables, showing
vapour-pressures, and giving a comparison between the constants of argon and those
of other gases, are here reproduced.

‘VV APOUR-PRESSURES.

| | | ]
| ae | Pressure. Temperature. | Pressure. Temperature. | Pressure.
| : | cs | ae oe f i =
| — 186-9 740°5 millims. — 136-2 | 27:3 atms. — 1294 | 35°8 atms.
|
Pies 139'1 23:7 atms, | — 1351] 290 ,, —1286 | 3280 ,,
| 1383 25:3 55 — 1344 HS} on — 121-0 | BOO 5,
| | | |
| Critical | | ong a el . Pens Col
Gast | ornare | Critical | Boiling- Freezing- | Freezing Density | of liquid olour of
P pressure. | point. point. pressure. | of gas. | at boiling- liquid.
| BEE | point.
| :
| atms. 6 > | millims. | |
Hydrogen, H, . . .| Below | 20:0 ? ? || 1 P Colourless
| —220:0° |
Nitrogen, N,. . . .|—146:0) 35:0 —1944 —214:0 60) 7 |) 4 0;885e 3
Carbon monoxide, CO | —139°5 35°5 — 190-0 | —207-0 100 era ? 3
Argon yAT elroy fale be | al 210 ne o0;695i 186,95 89:65 ae | 19:9 | About és
| | cd |
Oxygen, O, . . .{—1188 | 50°8 --182°7 ? ? Ks) 1124 Bluish
Nitric oxide, NO > 6) Ger) cilky —153°6 | —167°0 133 eeerlomes| Pp | Colourless |
Methane, CH, Pes — S38 549 | —1640 | —185°8 | 80 | 8 0°415 _
| | | |

14. The ratio of the Specific Heats of Argon.*

In order to decide regarding the elementary or compound nature of argon,
experiments were made on the velocity of sound in it. It will be remembered that
from the velocity of sound, the ratio of the specific heat at constant pressure to that
at constant volume can be deduced by means of the equation

* See Addendum, p. 239.

A NEW CONSTITUENT OF THE ATMOSPHERE. 229
SS AL, If e C,
nh =o = ak at) — ?

where 7 is the frequency, \ is the wave-length of sound, v its velocity, e the
isothermal elasticity, d the density, (1 + at) the temperature-correction, C, the
specific heat at constant pressure, and C, that at constant volume. In comparing
two gases at the same temperature, each of which obeys Bovte’s law with sufficient
approximation and in using the same sound, many of these factors disappear, and the
ratio of specific heats of one gas may be deduced from that of the other, if known,
by the simple proportion
NAG 2 NEG 8 BPE} S aa,

where for example \ and d refer to air, of which the ratio is 1°408, according to
the mean of observations by ROnTGEN (1°4053), WULLNER (1°4053), Kayser (1°4106),
and JAMIN and RicHaRD (1°41).

The apparatus employed, although in principle the same as that usually employed,
differed somewhat from the ordinary pattern, inasmuch as the tube was a narrow one,
of 2 millims. bore, and the vibrator consisted of a glass rod, sealed into one end of
the tube, so that about 15 centims. projected outside the tube, while 15 centims. was
contained in the tube. By rubbing the projecting part longitudinally with a rag wet
with alcohol, vibrations of exceedingly high pitch of the gas contained in the tube
took place, causing waves which registered their nodes by the usual device of
lycopodium powder. The temperature was that of the atmosphere and varied little
from 17°5°; the pressure was also atmospheric, and varied only one millim. during
the experiments. Much of the success of these experiments depends on so adjusting
the length of the tube as to secure a good echo, else the wave-heaps are indistinct.
But this is easily secured by attaching to its open end a piece of thick-walled india-
rubber tubing, which can be closed by a clip at a spot which is found experimentally
to produce good heaps at the nodes.

The accuracy of this instrument has frequently been tested ; but fresh experiments
were made with air, carbon dioxide, and hydrogen, so as to make certain that
reasonably reliable results were obtainable. Of these an account is here given.

| | | | |
| Number of observations. Half-wave-length. |
Gas in tube. |— - | Ratio 4 :

| | £7) |

| I, | II. | I, II. | |

| | | |

Air. 3 2 19°60 19°59 1-408 Assumed |
CO;. 3 1511 Oo | 1:276 Found
125 ee 3 73°6 50 | 1376 Found

To compare these results with those of previous observers, the following numbers

230 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

were obtained for carbon dioxide :—Cazin, 1:291; ROnTGEN, 1°305; De Luccut,
1:292; MULLER, 1:265; WULLNER, 1°311; DuLonc, 1°339; Masson, 1:°274; Rec-
NAULT, 1°268; AMAGAT, 1:299 ; and JAMIN and RicHaRD, 1:29. It appears just to
reject DuLone’s number, which deviates so markedly from the rest; the mean of
those remaining is 1°288, which is in sufficient agreement with that given above.
For the ratio of the specific heats of hydrogen, we have :—Cazin, 1:410; RontcEn,
1°385 ; Dutone, 1'407; Masson, 1°401; REeGNAULT, 1°400; and Jamin and RicHarp,
1:410. The mean of these numbers is 1°402. This number appears to differ con-
siderably from the one given above. But it must be noted, first, that the wave-
length which should have been found is 74°5, a number differing but little from that
actually found ; second, that the waves were long and that the nodes were somewhat
difficult to place exactly ; and third, that the atomic weight of hydrogen has been
taken as unity, whereas it is more likely to be 1°01, if oxygen, as was done, be taken
as 16. The atomic weight 1°01 raises the found value of the ratio to 1°399, a number
differing but little from the mean value found by other observers.

Having thus established the trustworthiness of the method, we proceed to describe
our experiments with argon.

Five series of measurements were made with the sample of gas of density 19°82.
It will be remembered that a previous determination with the same gas gave as its
density 19°90. The mean of these two numbers was therefore taken as correct,
viz., 19°86.

The individual measurements are :—

| ih | IL. | Ws) jf? | V. Mean. |
| bi i | |
| millims.
| 18:16 1814 1802 | 1804 18:03 18:08
| |

for the half-wave-length. Calculating the ratio of the specific heats, the number
1°644 is obtained.

The narrowness of the tube employed in these experiments might perhaps raise a
doubt regarding the accuracy of the measurements, for it is conceivable that in
so narrow a tube the viscosity of the gas might affect the results. We therefore
repeated the experiments, using a tube of 8 millims. internal diameter.

The mean of eleven readings with air, at 18°, gave a half-wave-length of
34°62 millims. With argon in the same tube, and at the same temperature, the
half-wave-length was, as a mean of six concordant readings, 31°64 millims. The
density of this sample of argon, which had been transferred from a water gas-holder
to a mercury gas-holder, was 19°82; and there is some reason to suspect the presence
of a trace of air, for it had been standing for some time.

The result, however, substantially proves that the ratio previously found was

A NEW CONSTITUENT OF THE ATMOSPHERE. 231

correct. In the wide tube, C,:C,::1°61:1. Hence the conclusion must be
accepted that the ratio of specific heats is practically 1°66 : 1.

Tt will be noticed that this is the theoretical ratio for a monatomic gas, that is, a
gas in which all energy imparted to it at constant volume is expended in effecting
translational motion. The only other gas of which the ratio of specific heats has
been found to fulfil this condition is mercury at a high temperature.* The extreme
importance of these observations will be discussed later.

15. Attempts to induce Chemical Combination.

A great number of attempts were made to induce chemical combination with
the argon obtained by use of magnesium, but without any positive result. In such a
case as this, however, it is necessary to chronicle negative results, if for no other
reason but that of justifying its name, ‘“‘argon.” These will be detailed in order.

(a) Oxygen in Presence of Caustic Alkali.—This need not be further discussed
here; the method of preparing argon is based on its inactivity under such con-
ditions. |

(b) Hydrogen.—It has been mentioned that, in order to free argon from excess of
oxygen, hydrogen was admitted, and sparks passed to cause combination of hydrogen
and oxygen. Here again caustic alkali was present, and argon appeared to be
unaffected.

A separate experiment was, however, made in absence of water, though no special
pains was taken to dry the mixture of gases. The argon was admitted up to half an
atmosphere pressure into a bulb, through whose sides passed platinum wires, carrying
pointed poles of gas-carbon. Hydrogen was then admitted until atmospheric pressure
had been attained. Sparks were then passed for four hours by means of a large
induction coil, actuated by four storage cells. The gas was confined in a bulb closed
by two stop-cocks, and a small V-tube with bulbs was interposed, to act as a gauge,
so that if expansion or contraction had taken place, the escape or entry of gas would
be observable. The apparatus, after the passage of sparks, was allowed to cool to
the temperature of the atmosphere, and, on opening the stop-cock, the level of water
in the V-tube remained unaltered. It may therefore be concluded that, in all
probability, no combination has occurred ; or, that if it has, it was attended with no
change of volume.

(c) Chlorine.—Exactly similar experiments were performed with dry, and after-
wards with moist, chlorine. The chlorine had been stored over strong sulphuric acid
for the first experiment, and came in contact with dry argon. Three hours sparking
produced no change of volume. A drop of water was admitted into the bulb. After
four hours sparking, the volume of the gas, after cooling, was diminished by about

* Konpt and Warsure, ‘ Pogg. Ann.,’ 157, p. 353, 1876.

232 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

= CUD centim., due probably to the solution of a little chlorine in the small quantity
of water presents

, closed at one end, containing at
the closed end a small piece of phosphorus, was sealed to the mercury reservoir
containing argon; connected to the same reservoir was a mercury gauge and a
SPRENGEL’S pump. Atter removing all air from the tubes, argon was admitted to a
pressure of 600 millims. The middle portion of the combustion-tube was then heated
to bright redness, and the phosphorus was distilled slowly from back to front, so that
its vapour should come into contact with argon at a red heat. When the gas was hot,
the level of the gauge altered; but, on cooling, it returned to its original level,
showing that no contraction had taken place. The experiment was repeated several
times, the phosphorus being distilled through the red-hot tube from open to closed
end, and vice versé. In each case, on cooling, no change of pressure was remarked.
Hence it may be concluded that phosphorus at a red-heat is without action on argon.
It may be remarked parenthetically that no gaseous compound of phosphorus is
known, which does not possess a volume different from the sum of those of its
constituents. That no solid compound was formed is sufficiently proved by the
absence of contraction. The phosphorus was largely converted into the red modifica-
tion during the experiment.

(e) Sulphur.—An exactly similar experiment was performed with sulphur, again
with negative results. It may therefore be concluded that sulphur and argon are
without action on each other at a red heat. And again, no gaseous compound of
sulphur is known in which the volume of the compound is equal to the sum of those
of its constituents.

(f) Tellwriwm.—aAs this element has a great tendency to unite with heavy metals,
it was thought worth while to try its action. In this, and in the experiments to be
described, a different form was given to the apparatus. The gas was circulated over
the reagent employed, a tube containing it being placed in the circuit. The gas was
dried by passage over soda-lime and phosphoric anhydride ; it then passed over the
tellurium or other reagent, then through drying tubes, and then back to the gas-
holder. That combination did not occur was shown by the unchanged volume of gas
in the gas-holder ; and it was possible, by means of the graduated cylinder- which
admitted water to the gas-holder, to judge of as small an absorption as half a cubic
centimeter. The tellurium distilled readily in the gas, giving the usual yellow
vapours ; and it condensed, quite unchanged, as a black sublimate. The volume of
the gas, when all was cold, was unaltered.

(g) Sodium.—aA piece of sodium, weighing about half a gramme, was heated in argon.
It attacked the glass of the combustion tube, which it blackened, owing to liberation
of silicon ; but it distilled over in drops into the cold part of the tube. Again no
change of volume occurred, nor was the surface of the distilled sodium tarnished ; it
was brilliant, as it is when sodium is distilled in vacuo. It may probably also be

A NEW CONSTITUENT OF THE ATMOSPHERE. 233

concluded from this experiment that silicon, even while being liberated, is without
action on argon.

The action of compounds was then tried ; these chosen were such as lead to oxides
or sulphides. Inasmuch as the platinum-metals, which are among the most inert of
elements, are attacked by fused caustic soda, its action was investigated.

(h) Fused and Red-hot Caustic Soda.—The soda was prepared from sodium, in an
iron boat, by adding drops of water cautiously to a lump of the metal. When action
had ceased, the soda was melted, and the boat introduced into a piece of combustion-
tube placed in the circuit. After three hours circulation no contraction had occurred.
Hence caustic soda has no action on argon.

(7) Soda-lime at a red-heat.—Thinking that the want of porosity of fused caustic
soda might have hindered absorption, a precisely similar experiment was carried out
with soda-lime, a mixture which can be heated to bright redness without fusion.
Again no result took place after three hours heating.

(j) Fused Potassium Nitrate was tried under the impression that oxygen plus a
base might act where oxygen alone failed. The nitrate was fused, and kept at a
bright red heat for two hours, but again without any diminution in volume of the
argon. a

(k) Sodium Peroxide.—Yet another attempt was made to induce combination with
oxygen and a base, by heating sodium peroxide to redness in a current of argon for
over an hour, but also without effect. It is to be noticed that metals of the platinum
group would have entered into combination under such treatment.

(1) Persulphides of Sodium and Calciwm.—Soda-lime was heated to redness in
an open crucible, and some sulphur was added to the red-hot mass, the lid of the
crucible being then put on. Combination ensued, with formation of polysulphides
of sodium and calcium. This product was heated to redness for three hours in a
brisk current of argon, again with negative result. Again, metals of the platinum
group would have combined under such treatment.

(m) Some argon was shaken in a tube with nitro-hydrochloric acid. On addition
of potash, so as to neutralise the acid, and to absorb the free chlorine and nitrosyl
chloride, the volume of the gas was barely altered. The slight alteration was evidently
due to solubility in the aqueous liquid, and it may be concluded that no chemical
action took place.

(7x) Bromine-water was also without effect. The bromine vapour was removed
with potash. :

(0) A mixture of potassium permanganate and hydrochloric acid, involving the
presence of nascent chlorine, had no action, for on absorbing chlorine by means of
potash, no alteration in volume had occurred.

(p) Argon is not absorbed by platinum black. A current was passed over a pure
specimen of this substance ; as usual, however, it contained occluded oxygen. There
was no absorption in the cold. At 100°, no action took place; and on heating to

MDCCCXCV.—A. 2H

234 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

redness, by which the black was changed to sponge, still no evidence of absorption
was noticed. In all these experiments, absorption of half a cubic centimetre of argon
could have at once been detected.

We do not claim to have exhausted the possible reagents. But this much is
certain, that the gas deserves the name “argon,” for it is a most astonishingly indif-
ferent body, inasmuch as it is unattacked by elements of very opposite character,
ranging from sodium and magnesium on the one hand, to oxygen, chlorine, and
sulphur on the other. It will be interesting to see if fluorine also is without action,
but for the present that experiment must be postponed, on account of difficulties of
manipulation.

It will also be necessary to try whether the inability of argon to combine at
ordinary or at high temperatures is due to the instability of its possible compounds,
except when cold. Mercury vapour at 800° would present a similar instance of
passive behaviour.

16. General Conclusions.

It remains, finally, to discuss the probable nature of the gas or gases which we
have succeeded in separating from atmospheric air, and which has been provisionally
named argon.

That argon is present in the atmosphere, and is not manufactured during the
process of separation is amply proved by many lines of evidence. First, atmospheric
nitrogen has a high density, while chemical nitrogen is lighter. That chemical
nitrogen is a uniform substance is proved by the identity of properties of samples
prepared by several different processes, and from several different compounds. It
follows, therefore, that the cause of the high density of atmospheric nitrogen is due
to the admixture with heavier gas. If that gas possesses the density of 20 compared
with hydrogen as unity, atmospheric nitrogen should contain of it approximately
1 per cent. This is found to be the case, for on causing the nitrogen of the atmos-
phere to combine with oxygen in presence of alkali, the residue amounted to about
1 per cent.; and on removing nitrogen with magnesium the result is similar.

Second : This gas has been concentrated in the atmosphere by diffusion. It is true
that it cannot be freed from oxygen and nitrogen by diffusion, but the process of
diffusion increases relatively to nitrogen the amount of argon in that portion which
does not pass through the porous walls. That this is the case is proved by the
increase of density of that mixture of argon and nitrogen.

Third: On removing nitrogen from “atmospheric nitrogen” by means of magne-
sium, the density of the residue increases proportionately to the concentration of the
heavier constituent.

Fourth: As the solubility of argon in water is relatively high, it is to be expected
that the density of the mixture of argon and nitrogen, pumped out of water
along with oxygen should, after removal of the oxygen, exceed that of “atmos-
pheric nitrogen.” Experiment has shown that the density is considerably increased.

A NEW CONSTITUENT OF THE ATMOSPHERE. 235

Fifth: It is in the highest degree improbable that two processes, so different from
each other, should each manufacture the same product. The explanation is simple if
it be granted that these processes merely eliminate nitrogen from “ atmospheric
nitrogen.”

Sixth: If the newly discovered gas were not in the atmosphere, the discrepancies
in the density of “chemical” and “atmospheric” nitrogen would remain unexplained.

Seventh: It has been shown that pure nitrogen, prepared from its compounds,
leaves a negligible residue when caused to enter into combination with oxygen or
with magnesium.

There are other lines of argument which suggest themselves; but we think that it
will be acknowledged that those given above are sufficient to establish the existence
of argon in the atmosphere.

It is practically certain that the argon prepared by means of electric sparking with
- oxygen is identical with argon prepared by means of magnesium. The samples have
in common :—

First : Spectra which have been found by Mr. Crookes, Professor ScHuUSTER, and
ourselves to be practically identical.

Second: They have approximately the same density. The density of argon, pre-
pared by means of magnesium, was 19°9; that of argon, from sparking with oxygen,
about 19°7 ; these numbers are practically identical.

Third: Their solubility in water is the same.

That argon is an element, or a mixture of elements, may be inferred from the
observations of § 14. For Ciausius has shown that if K be the energy of translatory
motion of the molecules of a gas, and H their whole kinetic energy, then

Kee BCR = Oo)

H 2C, Q

CU, and C, denoting as usual the specific heat at constant pressure and at constant
volume respectively. Hence, if, as for mercury vapour and for argon (§ 14), the
ratio of specific heats C, : C, be 13, it follows that K = H, or that the whole kinetic
energy of the gas is accounted tor by the translatory motion of its molecules. In the
case of mercury the absence of interatomic energy is regarded as proof of the mon-
atomic character of the vapour, and the conclusion holds equally good for argon.

The only alternative is to suppose that if argon molecules are di- or polyatomic,
the atoms acquire no relative motion, even of rotation, a conclusion improbable in
itself and one postulating the sphericity of such complex groups of atoms.

Now a monatomic gas can be only an element, or a mixture of elements; and
hence it follows that argon is not of a compound nature.

According to AvoGaDRo, equal volumes of gases at the same temperature and
pressure, contain equal numbers of molecules. The molecule of hydrogen gas, the
density of which is taken as unity, is supposed to consist of two atoms. Its mole-

7 Wa,

236 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

cular weight is therefore 2. Argon is approximately 20 times as heavy as hydrogen,
that is, its molecular weight is 20 times as great as that of hydrogen, or 40. But its
molecule is monatomic, hence its atomic weight, or, if it be a mixture, the mean of
the atomic weights of the elements in that mixture, taken for the proportion in which
they are present, must be 40.

This conclusion rests on the assumption that all the molecules of argon are mon-
atomic. The result of the first experiment is, however, so nearly that required by
theory, that there is room for only a small number of molecules of a different
character. A study of the expansion of argon by heat is proposed, and would
doubtless throw light upon this question.

There is evidence both for and against the hypothesis that argon is a mixture: for,
owing to Mr. Crookes’s observations of the dual character of its spectrum ; against,
because of Professor OLszEwskI’s statement that it has a definite melting-point, a
definite boiling-point, and a definite critical temperature and pressure ; and because
on compressing the gas in presence of its liquid, pressure remains sensibly constant
until all gas has condensed to liquid. The latter experiments are the well-known
criteria of a pure substance ; the former is not known with certainty to be character-
istic of a mixture. The conclusions which follow are, however, so startling, that in
our future experimental work we shall endeavour to decide the question by other
means.

For the present, however, the balance of evidence seems to point to simplicity.
We have, therefore, to discuss the relations to other elements of an element of atomic
weight 40. We inclined for long to the view that argon was possibly one, or more
than one, of the elements which might be expected to follow fluorine in the periodic
classification of the elements—elements which should have an atomic weight between
19, that of fluorine, and 28, that of sodium. But this view is apparently put out of
court by the discovery of the monatomic nature of its molecules.

The series of elements possessing atomic weights near 40 are :—

C@hlovincee ieee ere oo
IROLASSIUM sy ye eee Ol!
Calcium: eee eee OO)
eEniebibt, Gag Ey on la A) Zuo),

There can be no doubt that potassium, calcium, and scandium follow legitimately
their predecessors in the vertical columns, lithium, beryllium, and boron, and that
they are in almost certain relation with rubidium, strontium, and (but not so
certainly) yttrium. If argon be a single element, then there is reason to doubt
whether the periodic classification of the elements is complete; whether, in fact,
elements may not exist which cannot be fitted among those of which it is composed.
On the other hand, if argon be a mixture of two elements, they might find place in
the eighth group, one after chlorine and one after bromine. Assuming 37 (the

A NEW CONSTITUENT OF THE ATMOSPHERE. 237

approximate mean between the atomic weights of chlorine and potassium) to be the
atomie weight of the lighter element, and 40 the mean atomic weight found, and
supposing that the second element has an atomic weight between those of bromine,
80, and rubidium, 85:5, viz., 82, the mixture should consist of 93°3 per cent. of the
lighter, and 6°7 per cent. of the heavier element. But it appears improbable that
such a high percentage as 6°7 of a heavier element should have escaped detection
during liquefaction.

If the atomic weight of the lighter element were 38, instead of 37, however, the
proportion of heavier element would be considerably reduced. Still, it is difficult te
account for its not having been detected, if present.

If it be supposed that argon belongs to the eighth group, then its properties would
fit fairly well with what might be anticipated. For the series, which contains

Sy Pu and Mi Ane and (Ole to walk

might be expected to end with an element of monatomic molecules, of no valency, we.,
incapable of forming a compound, or if forming one, being an octad ; and it would
form a possible transition to potassium, with its monovalence, on the other hand,
Such conceptions are, however, of a speculative nature; yet they may be perhaps
excused, if they in any way lead to experiments which tend to throw more light on
the anomalies of this curious element.

In conclusion, it need excite no astonishment that argon is so indifferent to reagents.
For mercury, although a monatomic element, forms compounds which are by no means
stable at a high temperature in the gaséous state ; and attempts to produce compounds
of argon may be likened to attempts to cause combination between mercury gas at
800° and other elements. As for the physical condition of argon, that of a gas, we
possess no knowledge why carbon, with its low atomic weight, should be a solid, while
nitrogen is a gas, except in so far as we ascribe molecular complexity to the former
and comparative molecular simplicity to the latter. Argon, with its comparatively
low density and its molecular simplicity, might well be expected to rank among the
gases. And its inertness, which has suggested its name, sufticiently explains why it
has not previously been discovered as a constituent of compound bodies.

We would suggest for this element, assuming provisionally that it is not a mixture,
the symbol A.

We have to record our thanks to Messrs. Gorpon, KrLuas, and MatrHews, and
especially to Mr. Percy WiuuiAms, for their assistance in the prosecution of this
research.

ADDENDUM (by Professor W. Ramsay).
March 20, 1895.

Further determinations of the density of argon prepared by means of magnesium
have been made. In each case the argon was circulated over magnesium for at least

238 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

two hours after ‘all absorption of nitrogen had stopped, as well as over red-hot
copper, copper oxide, soda-lime, and phosphoric anhydride. The gas also passed out
of the mercury gas-holder through phosphoric anhydride into the weighing globe.
The results are in complete accordance with previous determinations of density ; and
for convenience of reference the former numbers are included in the table which

follows.
Density of Argon.
se | | |
| | | | | Weight of | }
| Date. Volume. |Remperatntes Pressure. | Weight. | ae pie ee G2
| | millims. |
| |
cub. centims. | 5 | millims. erm.
(1) Nov. 26. . .| 162°843 15:00 Xda da 8°20) 17784. 19:904
(2) eee oe 162°843 16-00 Ip 2069,0 9 0:27 cari eel aealeg 19-823
(C)eDech22 racine 162843 15°62 | 7501 | 026915 | 1°7704 19°816
(4) Feb. 16... 162843 13:45 | geal Opmsiiey = Ih Tere BY 19:959
(GD) aie eae eae te 162:843 | 14°47 68:2, Fl NO2789)9 ge ler S42 19-969
b (Gy) py Zhe te 162°843 17°85 7644 | 027388 | 17810 19-932

The general mean is 19°900; or if Nos. (2) and (3) be rejected as suspiciously low,
the mean of the remaining four determinations is 19°941. The molecular weight may
therefore be taken as 39:9 without appreciable error.

The value of R in the gas-equation R = pv/T has also been determined between
— 89° and + 248°. For this purpose, a gas-thermometer was filled with argon, and
a direct comparison was made with a similar thermometer filled with hydrogen.

The method of using such a hydrogen-thermometer has already been described by
Ramsay and Suretps.* For the lowest temperature, the thermometer bulbs were
immersed in boiling nitrous oxide; for atmospheric temperature, in running water;
for temperatures near 100° in steam, and for the remaining temperatures, in the
vapours of chlorobenzene, aniline, and quinolene.

The results are collected in the following tables :—

Hyprocen Thermometer.

Temperature. Pressure. | Volume (corr.). | R.
| |

Ce millims. |
13:04 763°6 1-00036 2°6705 |
99°84. 992-6 100280 | 26697
130°62 1073°8 1:00364: 2°6701
185-46 1218-5 1:00518 2°6716 |
248-66 1385°1 100705 2°6737 |

— 87:92 497°3 0:99756 2°6804. |

QF QQ

* «Trans. Chem. Soc.,’ vol. 63, pp. 835, 836. It is to be noticed that the value of R is not involved
in using the hydrogen-thermometer ; its constancy alone is postulated.

A NEW CONSTITUENT OF THE ATMOSPHERE. 239

The value of R is thus practically constant, and this affords a proof that the four
last temperatures have been estimated with considerable accuracy.

Arcon Thermometer.

Temperature. Pressure. Volume (corr.). R.
| en millims. i

Series! I. 3. 1415 701-7 1:000396 2-44.46
14:27 | 699°7 1000401 2°4366
14-40 702°6 1:000404: 2:44.62
99-96 906°5 1:00280 24379
160-06 9048 1:00280 _ 24322
—87-92 455°6 | 099756 2°4.556

By mischance, air leaked into the bulb; it was therefore refilled.

Series II. .} 130°58 1060°0 10037 2°6363
185-46 1200°3 10052 2:6317

A bubble of argon leaked into the bulb, and the value of R increased.

Series II. . 12°05 760°9 1:00034. 2°6698
12°61 7613 1:00034 2°6728

248 °66 1384:0 | 1:0070 2°6717

248°66 1376:9 | 1:0070 2°6580

| 0:99756 26718

—87°92 495°7

1

It may be concluded from these numbers, that argon undergoes no molecular
change between — 88° and + 250°.

Further determinations of the wave-length of sound in argon have been made, the
wider tube having been used. In every case the argon was as carefully purified as
possible. In experiment (3) too much lycopodium dust was present in the tube ;
that is perhaps the cause of the low result. For completeness’ sake, the original
result in the narrow tube has also been given.

Half-wave-length. Temperature.

| Date. Density. 7 ; ee Ratio.

| In air. In argon. Air. Argon.

| °

heDecs Glee alee oe ite 19:92 19°59 18:08 175 17°5 1644
Jeeleb a eirw sites nies) 19°96 33°73 31-00 6:7 6:5 1-641
ieee Maalery okies Mert, eros IG Oz 34°19 31:31 7°22 8°64. 1-629

| Mins IS) 5 5 6 pe 0 19:94 | 3423 31°68 11:20 11:49 1659 |

The general mean of these numbers is 1643; if (3) be rejected, it is 1648. In
the last experiment every precaution was taken. The half-wave-length in air is
the mean of 11 readings, the highest of which was 34°67 and the lowest 34:00.
They run :—

240 LORD RAYLEIGH AND PROFESSOR W. RAMSAY ON ARGON,

34°67 ; 84:06 ; 34:27 ; 34:39; 34:00; 34:00; 34:13; 34:20; 34°20; 34:33; 34°33.
1252 110022 TOSSOXs LO Sis eOsOrelIsOy seW ese elie ele AS arn Gn mmleicca

With argon the mean is also that of 11 readings, of which the highest is 31°83,
and the lowest, 31°5. They are :—

Biles 3 Biles SG g silleyay Bsilesys) S sleg¢ Ss shilesh 3 Ghltsiess Biles s Bileso) 2 Bil-eC-
HIPS TIS ANS a Oe lly GMs eS 8 Files? 3 TilewH? 2 Wi -wl®,

If the atomic weight of argon is identical with its molecular weight, it must closely
approximate to 39°9. But if there were some molecules of A, present, mixed with a
much larger number of molecules of A,, then the atomic weight would be corres-
pondingly reduced. Taking an imaginary case, the question may be put :—What
percentage of molecules of A, would raise the density of A, from 19:0 to 19°99? A
density of 19°0 would imply an atomic weight of 38°0, and argon would fall into the
gap between chlorine and potassium. Calculation shows that in 10,000 molecules,
474 molecules of A, would have this result, the remaining 9526 molecules being
those of Aj.

Now if molecules of A, be present, it is reasonable to suppose that their number
would be increased by lowering the temperature, and diminished by heating the gas.
A larger change;of density should ensue on lowering than on raising the temperature,
however, as on the above supposition, there is not a large proportion of molecules of
A, present.

But it must be acknowledged that the constancy of the found value of R is not
favourable to this supposition.

A similar calculation is possible for the ratio of specific heats. Assuming the gas
to contain 5 per cent. of molecules of A,, and 95 per cent. of molecules of A, the
value of y, the ratio of specific heats, would be 1°648. All that can be said on this
point is, that the found ratio approximates to this number ; but whether the results
are to be trusted to indicate a unit in the second decimal appears to me doubtful.

The question must therefore for the present remain open.

ADDENDUM.
April 9.

It appears worth while to chronicle an experiment of which an accident prevented
the completion. It may be legitimately asked, Does magnesium not absorb any
argon, or any part of what we term argon? To decide this question, about
500 grms. of magnesium nitride, mixed with metallic magnesium which had

?

remained unacted on, during extraction of nitrogen from “ air-nitrogen,” was placed

in a flask, to which a reservoir full of dilute hydrochloric acid was connected. The

A NEW CONSTITUENT OF THE ATMOSPHERE. 241

flask was coupled with a tube full of red-hot copper oxide, intended to oxidise the
hydrogen which would be evolved by the action of the hydrochloric acid on the
metallic magnesium. To the end of the copper-oxide tube a gas-holder was attached,
so as to collect any evolved gas; and the system was attached to a vacuum-pump, in
order to exhaust the apparatus before commencing the experiment, as well as to
collect all gas which should be evolved, and remain in the flask.

On admitting hydrochloric acid to the flask of magnesium nitride a violent
reaction took place, and fumes of ammonium chloride passed into the tube of copper
oxide. These gave, of course, free nitrogen. This had not been foreseen ; it would
have been well to retain these fumes by plugs of glass-wool, The result of the
experiment was that about 200 cub. centims. of gas were collected. After sparking
with oxygen in presence of caustic soda, the volume was reduced to 3 cub. centims.
of a gas which appeared to be argon.

MDCCCXCV,—A, 2)

VIL. On the Spectra of Argon.
By Wiui1aM Crookes, F.RS., &c.
Received January 26,—Read January 31, 1895.

[PLATE 3. |

THrovGH the kindness of Lord RayLercH and Professor Ramsay I have been enabled
to examine the spectrum of this gas in a very accurate spectroscope, and also to take
photographs of its spectra in a spectrograph fitted with a complete quartz train.
The results are both interesting and important, and entirely corroborate the con-
clusions arrived at by the discoverers of argon.

The results of my examination are given in a table of wave-lengths, which follows,
and on a map of the lines accurately drawn to scale, accompanying this paper (Plate 3).
The map is 40 feet long, and the probable error of position of any line on it is not
greater than 1 millimetre.

Argon resembles nitrogen in that it gives two distinct spectra according to the
strength of the induction current employed. But while the two spectra of nitrogen
are different in character, one showing fluted bands and the other sharp lines, both
the argon spectra consist of sharp lines. It is, however, very difficult to get argon
so free from nitrogen that it will not show the nitrogen flutings superposed on its own
special system of lines. I have used argon prepared by Lord Rayueicu, Professor
Ramsay, and myself, and, however free it was supposed to be from nitrogen, I
could always at first detect the nitrogen bands in its spectrum. ‘These, however,
disappear when the induction spark is passed through the tube for some time,
varying from a few minutes to a few hours. The vacuum tubes best adapted for
showing the spectra are of the ordinary Pliicker form having a capillary tube in the
middle. For photographing the higher rays which are cut off by glass I have used a
similar tube, “end on,” having a quartz window at one end. I have also used a
Pliicker tube made entirely of quartz worked before the oxy-hydrogen blow-pipe. I
have not yet succeeded in melting platinum or iridio-platinum wire terminals into
the quartz, as they melt too easily, but a very good spectrum is obtained by coating
the bulbs outside with tin foil, connected with the terminals of the induction coil.

The pressure of argon giving the greatest luminosity and most brilliant spectrum
is 3 millims. At this point the colour of the discharge is an orange-red, and
the spectrum is rich in red rays, two being especially prominent at wave-lengths 696°56
and 705°64. On passing the current the traces of nitrogen bands disappear, and
the argon spectrum is seen in a state of purity. At this pressure the platinum from
the poles spatters over the glass of the bulbs, owing to what I have called ‘“ electrical
MDCCCXCV.—A, 2a 27.6,95,

“ “

944 MR, W. CROOKES ON THE SPECTRA OF ARGON.

evaporation,’* and I think the residual nitrogen is occluded by the finely-divided
metal. Similar occlusions are frequently noticed by those who work much with
vacuum-tubes. -

If the pressure is further teal and 4 teen jax intercalated in the circuit, the
colour of the luminous discharge changes from red to a rich steel blue, and the
spectrum shows an almost entirely different set of lines. The two spectra, called for
brevity red and blue, are shown on the large map, the upper spectrum being that of
“blue” argon, and the lower one that of “red” argon. It is not easy to obtain the
blue colour and spectrum entirely free from the red. The red is easily got by using
a large coilt actuated with a current of 3 ampéres and 6 volts. There is then no
tendency for it to turn blue. The blue colour may be obtained with the same coil by
actuating it with a current of 3°84 ampéres and 11 volts, intercalating a jar of
50 square inches surface ; the make-and-break must be screwed up so as to vibrate
as rapidly as possible. With the small coil a very good blue colour can be obtained by
using three Grove'’s cells and a Leyden jar of 120 square inches surface, and a very
rapid make-and-break. It appears that an electromotive force of 27,600 volts is
required to bring out the red, and a higher E.M.F. and a very hot spark for the blue.
It is possible so to adjust the pressure of gas in the tube that a very slight alteration
of the strength of the current will cause the colour to change from red to blue, and
vice versd. I have occasionally had an argon tube in so sensitive a state, that
with the commutator turned one way the colour was red, and the other way
blue. Induction coils actuated by a continuous current are never symmetrical as
regards the polarity of the induced current, and any little irregularity in the metallic
terminals of the vacuum-tube also acts as a valve. The red glow is produced by the
positive spark and the blue by the negative spark.

I have taken photographs of the two spectra of argon partly superposed. In this
way their dissimilarity is readily seen.{ In the spectrum of the blue glow I have
counted 119 lines, and in that of the red glow 80 lines, making 199 in all. Of these
26 appear to be common to both spectra.

I have said that the residual nitrogen is removed by sparking the tube for some
time when platinum terminals are sealed in. This is not the ouly way of purifying
the argon. By the kindness of Professor Ramsay, I was allowed to take some vacuum
tubes to his laboratory and there exhaust and fill them with some of his purest argon.
On this occasion I simultaneously filled, exhausted, and sealed off two Pliicker tubes,
one having platinum and the other aluminium terminals. On testing the gas
immediately after they were sealed off, each tube showed the argon spectrum, con-

* “Roy. Soc. Proc.,’ vol. 50, p. 88, June, 1891.
+ The coil used has about 60 miles of secondary wire, and when fully charged gives a torrent of sparks
24 HGS: long. The smaller coil gives six-inch sparks when worked with six half-pint Grove’s cells.
¢ Photographs of the different spectra of argon, and other gaseous spectra for Conese were
nboiseiod on the screen.

MR. W. CROOKES ON THE SPECTRA OF ARGON. 245

taminated by a trace of nitrogen bands. The next day the tube with platinum
terminals was unchanged, but that having aluminium terminals showed the pure spec-
trum of argon, the faint nitrogen bands having entirely disappeared during the night.
After an hour's current and a few days’ rest the tube with platinum terminals likewise
gave a pure argon spectrum. When a mixture of argon with a very little nitrogen is
submitted to the induced current in a tube made of fused and blown quartz, with-
out inside metallic terminals, the nitrogen bands do not disappear from the argon
spectrum, but the spectra of argon and nitrogen continue to be seen simultaneously.

A yacuum-tube was filled with argon and kept on the pump while observations
were made on the spectrum of the gas as exhaustion proceeded. The large coil was
used with a current of 8°84 amperes and 11 volts, no jar being interposed. At a
pressure of 3 millims. the spectrum was that of the pure red glow. This persisted as
the exhaustion rose, until, at a pressure of about half a millimetre, flashes of blue
light made their appearance. At a quarter of a millimetre the colour of the ignited
gas was pure blue, and the spectrum showed no trace of the red glow.

A striking instance of a change of spectrum from nitrogen to argon was shown in
a tube filled with argon kindly sent me by Lord RayteicH. It had been prepared
from the atmosphere by sparking, and it was considered ‘to contain about 3 per cent.
of nitrogen. This argon was passed into an exhausted tube and then rarefied to a
pressure of 75 millims. and kept on the pump. At this pressure the nitrogen con-
ducted all the induction current, the spectrum showing nothing but the nitrogen
bands. The pump was slowly kept going and spectrum observations were con-
tinuously taken. When the pressure fell to about 3 millims. a change came over
the spectrum, the nitrogen bands disappeared, and the spectrum of argon took its
place, the only contamination being a little aqueous vapour, due to my not having
sufficiently dried the gas. I took photographs of the spectrum given by this tube in
the two stages, one showing the pure nitrogen bands and the other the argon lines,
each being compared with the spectrum of argon prepared by Professor Ramsay.
Observations have shown that the spectra given by argon, obtained by the sparking
method of Lord Ray.ercH and by the magnesium method of Professor Ramsay from
the atmosphere, are identical.

It was of interest to see how little argon could be detected in admixture with
nitrogen by corabined pumping and passage of the current. Some argon prepared
by myself,* having 60 to 70 per cent. of nitrogen with it, was put into a small tube
furnished with large platinum terminals. Exhaustion was carried to 3 millims., and

* When a current of 65 volts and 15 ampéres, alternating 130 times a second, is passed through the
primary of my large coil, an arching flame, consisting of burning nitrogen, issues from each of the
secondary poles, meeting in the middle. When once started, the poles can be drawn asunder till the
fiame bridges across 212 millims. When the terminals are more than 46 millims. apart, the flame will
not strike across. By enclosing this flame ir a reservoir over alkaline water and feeding it with air and
oxygen I can burn up a litre of air an hour. —

246 MR. W. CROOKES ON THE SPECTRA OF ARGON.

the tube was then sealed off. The spark from the large coil, actuated with a current
of 3°84 amperes and 11 volts, was then put on, and the spectrum examined con-
tinuously. At first it showed only the nitrogen bands; in about half an hour the
nitrogen began to fade and the argon lines appeared, and in a few minutes later the
tube was just short of non-conducting. The colour of the gas was rich steel blue,
and the spectrum was that of the blue argon glow. Here the small diameter of
the bulbs of the tube and the large platinum wires facilitated much spattering
” of the platinum; the pressure also was the one most
suitable for that phenomenon. To this I attribute the rapid occlusion of the
residual nitrogen.

An experiment was now made to see if the small quantity of argon normally present
in the atmosphere could be detected without previous concentration. Nitrogen was
prepared from the atmosphere by burning phosphorus, and was purified in the usual
manner. This gas, well dried over phosphoric anhydride, was passed into a vacuum
tube, the air washed out by two fillings and exhaustions, and the tube was finally
sealed off at a pressure of 52 millims. It was used for photographing the band
spectrum of nitrogen on several occasions, and altogether it was exposed to the
induction current from the large coil for eight hours before any change was noticed.
The last time I used it for photographing the nitrogen spectrum difficulty was
experienced in getting the spark to pass, so I increased the current and intercalated a
small jar. The colour immediately changed from the reddish-yellow of nitrogen to the
blue of argon, and on applying the spectroscope the lines of argon shone out with
scarcely any admixture of nitrogen bands.. With great difficulty, and by employing
a very small jar, I was able to take one photograph of this changed spectrum and
compare it with the spectrum of argon from Professor Ramsay, both being taken on
the same plate, but the tube soon became non-conducting, and I could not then force
a spark through except by employing a dangerously large current. Whenever a
flash passed it was of a deep blue colour. Assuming that the atmosphere contains
1 per cent. of argon, the 3 millims. of nitrogen originally in the tube would contain
0°03 millim. of argon. After the nitrogen had been occluded by the spattered
platinum this pressure of argon would be near the point of non-conduction,

or “electrical evaporation

In all cases, when argon has been obtained in this manner, the spectrum has Bean
that of the blue-glowing gas. Very little of the red rays can be seen. ‘The change
from red to blue is chiefly dependent on the strength and heat of the spark ; partly
also on the degree of exhaustion. Nitrogen, when present, conducts the current
easiest. As the exhaustion increases and the conductivity of the nitrogen diminishes,
that of the red-glowing argon rises, until, at a pressure of about 3 millims., its
conductivity is at the greatest, and the luminosity is best. Beyond that point the
conductivity of the red form seems to get less, and that of the blue form to increase,
till the vacuum approaches a fraction of a millimetre, when further pumping soon
renders it non-conducting. It is not improbable, and I understand that independent

MR. W. CROOKES ON THE SPECTRA OF ARGON. 2AT

observations have already led both the discoverers to the same conclusion, that the
gas argon is not a simple body, but is a mixture of at least two elements, one of
which glows red and the other blue, each having its distinctive spectrum. The
theory that it is a simple body has, however, support from the analogy of other gases.
Thus, nitrogen has two distinct spectra, one or the other being produced by varying
the pressure and intensity of the spark. I have made vacuum tubes containing
rarefied nitrogen, which show either the fluted band or the sharp line spectrum by
simply turning the screw of the make-and-break, exactly as the two spectra of argon
can be changed from one to the other.

The disappearance of the red glow and the appearance of the blue glow in argon as
the exhaustion increases also resembles the disappearance of the red line of hydrogen
when exhaustion is raised to a high point. PxLtcKer, who was the first to observe
this occurrence, says:* “ When RuamKorrr’s small induction coil was discharged
through a spectral tube enclosing hydrogen, which was gradually rarefied to the
highest tenuity to be reached by means of GEISSLER’s exhauster, finally the beautiful
red colour of the ignited gas became fainter, and passed gradually into an undetermined
violet. When analysed by the prism, He (the red, C, line) disappeared, while H8
(the green, F, line), though fainter, remained well defined. Accordingly, light of a
greater length of wave was the first extinguished.”

The line spectrum of nitrogen is not nearly so striking in brilliancy, number,
or sharpness of lines as are those of argon, and careful scrutiny fails to show
more than one or two apparent coincidences between lines in the two spectra.
Between the spectra of argon and the band spectrum of nitrogen there are two or
three close approximations of lines, but a projection on the screen of a magnified
image of the two spectra partly superposed shows that two at least of these are not
real coincidences.

I have looked for indications of lines in the argon spectra corresponding to the
corona line at 531°7, the aurora line at 557°1, and the helium line at 587°5, but have
failed to detect any line of argon sutfticiently near these positions to fall within the
limits of experimental error.

I have found no other spectrum-giving gas or vapour yield spectra at all like those
of argon, and the apparent coincidences in some of the lines, which on one or two
occasions are noticed, have been very few; and would probably disappear on using a
higher dispersion, Having once obtained a tube of argon giving the pure spectra, I
can make no alteration in it, except that which takes place on varying the spark or
increasing the exhaustion, when the two spectra change from one to the other. As
far, therefore, as spectrum work can decide, the verdict must be that Lord RayLEeIcH
and Professor Ramsay have added one, if not two, members to the family of
elementary bodies.

# On the Spectra of Ignited Gases and Vapours.” By Drs, Priicxer and Hurrrorr, ‘ Phil. Trans,,’
Part L., vol. 155, p. 21.

248

MR, W. CROOKES ON THE SPECTRA OF ARGON,

WILLIAM Crookes. January 24, 1895.

THE Two Spectra of Argon,

Blue. Red.
Wave-length. | Intensity. Wave-length. Intensity.
|
| 764-6 2
750°6 A
UBYP Tl 3
| 726°3 | 2
| 70564 | 10 H
| 696°56 9
| 684-2 | 2
| 675°4 6
666°4 6
662°8 4
640:7 9
637:7 2
630°2 4
628:1 2
623°2 4, |
621-0 6 |
617-3 6 617-73 6 | Coincident.
6143 2 |
612-0 6 |
609°9 4,
605:6 2 |
604:5 3
603°8 8 603°8 8 Coincident.
593°5 ]
592°6 4 592°6 4. Coincident.
590°9 6
588°7 6
585°8 4,
583°4 2
580°3 1
5771 2
5 74°6 6
568°3 2
565°] 9
561:0 9
556°7 2
555°7 10
552:0 ]
55071 2
549-65 8
545°6 6
54404. 2
542:1 4.
525°8 6
522:2 7
518°58 10 |
5165 9 |

MR. W. CROOKES ON THE SPECTRA OF ARGON.

THE Two Spectra of Argon—(continued).

Blue.

Red.

Waye-length.

Intensity.

514-0
506°5
501-2
500-7
496°55
493°8
487-9
484-75
480°50
476°30
473-45
47266

465°65
460°80

458°69
457-95
45435

450-95
| 447-83
| 442-65
449-95
439-95
437-65
436-90
434-85

433°35

429-90
427-70
427-20
426°60
4.25°95
42515
422-85
42010
419-80
419-15
418°30
416°45
415°95

413°15
| 410°50
| 407°25
404-40
403°30
401-30
39785
396°78

a i
DOHTHODSDODNOSO

i)
STMOMDOOOANWOG Wwo

—

Wr OO CO 00 Ow

Wave-length.

Intensity.

506°5
5012

4.96°55
493-8
487°9

470°12
462°95
459°45

451-40
450°95

43450
433°35
430°05

427-20
4.26°60
425°95
425°15

420°10 -

419-80
419-15
418°30
41645
415°95
415°65

404-40

Soe AS

co bo

S50) or

ws tO —& OO

—

=
AOFPMDOS

Coincident.
Coincident.

Coincident.
Coincident.
Coincident.

Coincident.

Coincident.

Coincident.
Coincident.
Coincident.
Coincident.

Coincident.
Coincident.
Coincident.
Coincident.
Coincident.
Coincident.

Coincident.

MDCCCXCY.—A,

249

250 MR. W. CROOKES ON THE SPECTRA OF ARGON,

THE Two Spectra of Areon—(continued).

Blue.

Wave-length.

Intensity.

394°85
39435
39318
392°85
892°75
391°50

389°20
38755
38718
386°85
38515
38455
383°55
382°75
380°95
380°35
379°95
378-08

377:05
376°60
373°85
372°98
371°80

361°75
360°50
358°70
358'03
357-50
356'65
356°40

356-00
355°82
355745
85475
35445
35343
35205
35192
351°35
350°88
349-00
347°57
346°35
338°80
309°27
308°48
306-47

Re 05 8 05 0 8D

=
ORF PBNONDRFOCND tc

=
BOW mb

_

2)

Oo b

10

a)

boro

=
DEORE HTORORWANE BID

Red.
Wave-length. Intensity.
39485 10
390°45 8
383°55 3
377-15 1
363-25 2
362°37 1
362°28 1
360°50 5
356°65 4
356:28 1
35545 6

Coincident.

Coincident.

Coincident.

Coincident.

Coincident.

MR. W. CROOKES ON THE SPECTRA OF ARGON. 251

THE Two Spectra of Argon—(continued).

Blue. Red.

Wave-length. Intensity. Wave-length. Intensity.

304:27
299-82
297-86
294-27
292-96
283-02
279-44
273-45
270°72
269-30
266-12
265-26
262-95
257-12
256-07
248-49
243-85
224-66

WN PWN ROWDY Ri HrEw

119 lines in the ‘ Blue” Spectrum.
80 lines in the ‘‘ Red” Spectrum.

199 total lines.
26 lines common to the two spectra.

Nore.—-In the spectroscope the lies of argon appear almost equally fine, but of
very different intensities. This difference of brightness is represented in the
accompanying map by a variation in the thickness of the lines, faint lines being
made narrow and strongly luminous lines being widened. In some cases two or
three strong lines are too close together to enable their intensities to be represented
in this way without overlapping. This is the case with lines 442°65 and 442°25,
with lines 420710, 419°80, and 419°15, and with lines 415°95 and 415°65. In these
cases I have indicated the centres of the strong lines by short projecting lines
beneath.

Phil. Trans., 1895, A, Plate 3.

Crookes.

TRE SPECTRA OH ARGON:

as e8uj0d'e t

‘yyoef ‘SHMOOUQ, WVITTL A,

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- | | |

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|

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0¢9 0F9 069 099 049 089 069 O02 O

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VIII. The Liquefaction and Solidification of Argon.
By Dr. K. Ouszewsk1, Professor of Chemistry in the University of Cracow.

Communicated by Professor W1tuiAM Ramsay, F.R.S.
Received January 28,—Read January 31, 1895.

Havine been furnished, by Professor RAamsay’s kindness, with a sample of the new
gas, argon, I have carried out experiments on its behaviour at low temperatures and
at high pressures, in order to contribute, at least in part, to the knowledge of the
properties of this interesting body.

The argon sent by Professor Ramsay amounted to 300 cub. centims. It was
contained in a hermetically-sealed glass bulb, so constructed that it could easily be
transterred, with no appreciable loss, into the carefully-dried and vacuous apparatus
in which the proposed experiments were to be performed. The argon with which I
was supplied had, according to Professor Ramsay’s statement, been dried with phos-
phoric anhydride ; its density was 19°9 (H = 1); and he thought that at the outside
it might contain | to 2 per cent. of nitrogen, although it showed no nitrogen spectrum
when examined in a PLUCKER’s tube.

Four series of experiments in all were carried out, two with the object of deter-
mining the critical temperature and pressure of argon, as well as of measuring its
vapour pressure at several other low temperatures, while two other series served to
determine its boiling- and freezing-points under atmospheric pressure, as well as its
density at its boiling-point.

A detailed description of these experiments will be given in another place: I shall
here give only a short description of the manner in which they were made.

For the first two experiments I made use of a CAILLETET’s apparatus. Its metallic
manometer had been previously compared with the readings of a mercury manometer.
As cooling agent I used liquid ethylene, boiling under diminished pressure. The
glass tube of CAiLLETET’S apparatus was so arranged that the portion immersed in
the liquid ethylene had comparatively thin walls (not exceeding 1 millim.), so as to
equalize the external and internal temperature as quickly as possible.

In both the other experiments the argon was contained in a buretie, closed at both

27.6.95

254 PROFESSOR K. OLSZEWSKI ON THE

ends with glass stop-cocks. By connecting the lower end of the burette with a
mercury reservoir, the argon was transferred into a narrow doubly bent glass tube
connected with the upper end of the burette, and in which the argon was liquefied, and

ot

to a mereury air pump

Mercury reservotr

clund up shiv ayy 07 5

Li quiet Oxygei

Argon to be liquefied.

its volume in the liquid state measured. In these two series of experiments liquid
oxygen, boiling under atmospheric or under diminished pressure, was employed as a
cooling agent. I made use of a hydrogen thermometer in all these experiments to
ineasure low temperatures.

Determination of the Critical Constants of Argon.

As soon as the temperature of the liquid ethylene had been lowered to — 128°6,
the argon easily condensed to a colourless liquid under a pressure of 38 atmospheres.
On slowly raising the temperature of the ethylene, the meniscus of the liquid argon
became less and less distinct, and finally vanished at the following temperatures and
corresponding pressures :—

LIQUEFACTION AND SOLIDIFICATION OF ARGON. 255

Tixperiment. | Temperature. Pressure.
| ° atmos.
| 1 Bie — — 121°2 50°6
2 — 121-6 | 50°6
3 » — 120°5 50°6
4A — 121°3 50°6
5 = 12145 50°6
| 6 — 1198 | 50°6
| 7 = 1s} | 50°6
|

In all seven determinations the critical pressure was found to be 50°6 atmospheres ;
but determinations of the critical temperature show slight differences. In experiments
Nos. 3 and 6 less liquid argon was present in the tube than in the other five; in
these the volume of liquid exceeded the volume of gas.

In determining the vapour pressures of argon, a tabular record of which is given
below, I noticed slight differences of pressure according as I produced more or less of
the liquid at the same temperature. This proved that the sample of argon contained
an inconsiderable admixture of another gas, more difficult to liquefy ; it is doubtless
the trace of nitrogen previously referred to. The mean of the seven estimations of
the critical temperature is —121°, and this may be taken as the critical temperature
of argon. .

At lower temperatures the following vapour-pressures were recorded :—

Experiment. | Temperature. Pressure. Experiment. | Temperature. Pressure.
° atmos. | | ° atmos.
8 —128°6 38:0 13 | —134:4 29°8
9 —129°6 30'8 | 14 | —135:1 29-0
10 | —129-4 30°8 | 15 | —136:2 27°3
11 | —129°3 39°8 16 —188°3 25°3
12 —129°6 308 | 17 | —139'1 23°7

In Experiments Nos. 9, 10, and 17 the quantity of liquefied argon was very small,
for it filled the tube only to a height of 3 to 5 millims., and in the other experiments
the column of liquid argon was 20 millims. or more.

Determination of the Boiling- and Freezing-Points.

Two hundred cub. centims. of liquid oxygen, prepared in my large apparatus,* was
poured into a glass vessel with quadruple walls, so as to isolate the liquid from

* ‘Bulletin International de Académie de Cracovie,’ June, 1890; also WispEMANN’S ‘ Beiblatter,’
yol, 15, p. 29,

256. PROFESSOR K. OLSZEWSKi ON THE

external heat. After the liquid oxygen had been thus poured under atmospheric
pressure, a great part of it evaporated, but there still remained about 70 cub. centims.,
boiling under atmospheric pressure. A calibrated tube, intended to receive the argon
to be liquefied, and the hydrogen thermometer were immersed in the boiling oxygen.
At this temperature (— 182°-7*) on admitting argon, no appearance of liquefaction
could be noticed, even when compressed by increasing the atmospheric pressure by a
quarter. This shows that its boiling-point lies below that of oxygen. But on
diminishing the temperature of the liquid oxygen below — 187°, the liquefaction of
the argon became manifest. When liquefaction had taken place, I carefully equalised
the pressure of the argon with that of the atmosphere, and regulated the temperature,
so that the state of balance was maintained for a long time. This process gives the
boiling-point of argon under atmospheric pressure. Four experiments gave the
numbers: — 186°7, — 186°°8, —187°0, and — 187°°3. The mean is — 186°9,
which I consider to be the boiling-pomt under atmospheric pressure (740°5 millims.).

The quantity of argon used for these experiments, reduced to normal temperature
and pressure, was 99°5 cub. centims.; the quantity of liquid corresponding to that
volume of gas was approximately 0-114 cub. centim. Hence the density of argon at
its boiling-point may be taken as approximately 1°5. Two other determinations of
the density of liquid argon, for which I employed still smaller quantities of the gas,
yielded rather smaller numbers. Owing to the small amount of argon used for these
experiments, the numbers given cannot lay claim to great exactness ; yet they prove
that the density of liquid argon at its boiling-point (— 187°) is much higher than
that of oxygen, which I have found, under similar conditions, to be 1:124.

By lowering the temperature of the oxygen to — 191° by slow exhaustion, the
argon froze to a crystalline mass, resembling ice; on further lowering temperature it
became white and opaque. When the temperature was raised it melted ; four obser-
vations which I made to determine its melting-point gave the numbers: — 189°-0,
— 190°6, — 189°°6, and — 189°°4. The mean of these numbers is — 189°°6; and
this may be accepted as the melting-point of argon.

In the following table I have given a comparison of physical constants, in which
those of argon are compared with these of other so-called permanent gases. The data
are from my previous work on the subject.

* T have re-determined the boiling-point of oxygen, using large quantities of oxygen, and a hydrogen
thermometer of much larger dimensions than previously. The registered temperature is 1°°3 lower than
that which I previously recorded,

LIQUEFACTION AND SOLIDIFICATION OF ARGON.

257

Cite || Gece ag | Pewee |Jeooemarel eerie cA lara i
Nae: tempera- ritica oiling | Freezing | Freezing) Density | o iquid Co! our 0
pee pressure.| point. point. j pressure.) of gas. Jat boiling} liquid.
ae point.
|
| Atmos ° oS millims.

| Hydrogen (H,) . .|{ Below. \ 200 | 2 2 2 10 ? | Colourless
| Nitrogen (N,) —146:0 30°0 | —1944 | —214:0 60 14-0 0°885 es
| Carbonic oxide (CO) —139'5 30°5 | —190-0 | —207°0 100 140 Fs 5
| Angon (Ay) —1210| 50:6 | —187-0| —1896| ? 19-9 (eee i
| Oxygen (O3) - —118'8 50'S | —182:7 P iP 16:0 1124 | Bluish
Nitric oxide (N O) . — 93° 71:2 | —153°6 | —167-0 138 15:0 P Colourless
Methane (CH,) . — 81:8 549 | —164-0 | —185°8 80 8-0 0:415 5

As can be seen from the foregoing table, argon belongs to the so-called ‘‘ permanent ”
gases, and, as regards difficulty in lquefying it, it occupies the fourth place, viz.,
between carbon monoxide and oxygen. Its behaviour on liquefaction places it nearest
to oxygen, but it differs entirely from oxygen in being solidifiable ; as is well known,
oxygen has not yet been made to assume a solid state

The high density of argon rendered it probable that its ee would take
place at a higher temperature than that at which oxygen liquefies. Its unexpectedly
low critical temperature and boiling-point seem to have some relation to its simple
molecular constitution.

Note on A CoMPARISON OF THE VAPOUR-PRESSURES OF ARGON WITH THOSE OF
OTHER SUBSTANCES.

By Witu1AM Ramsay and SvpNEY YOuNG.
Received February 7, 1895.

The vapour-pressures of a considerable number of substances have been determined
from low temperatures to the critical points, but as the critical pressure of argon is
somewhat high, the boiling-points of very few are available for comparison through the
whole range of equal pressures.

The critical pressure of benzene is so slightly below that of argon that the extra-
polation of the vapour-pressure curve through the few degrees necessary to afford a
comparison at the critical pressure of the new element is justifiable.

The other two substances chosen are ethyl alcohol and oxygen;
interesting, as its vapour-pressures, like those of argon, have been determined
by Professor OLSZEWSKI.

In the following table the boiling-points—on the absolute scale—of argon, benzene,

MDCCCKCV.—-A. 2.

the second is

258 PROFESSOR K. OLSZEWSKI ON THE

ethyl alcohol, and oxygen, are given at the pressures at which observations have been
made with the first of these substances.

Boittine-Points on Absolute Seale.

| |
| pee he | Argon. | Benzene. | Ethyl alcohol. Oxygen.
74.0°5 86-1 352°5 350-65 90°1

| 18010 133-9 507°8 4626 1361
19230 1347 512:5 465:8 137-4
20750 | 1368 518-0 469°6 139-0
22040 137-9 5293 | 72-7 140-2
99650 | 1386 ve || sO 141-4
27210 | 143-5 5383 483°7 145-0
98837 | «1444 543-0 | 487-0 1465
384.60 | 1520 565-9 503-1 153:7

| |

The ratios of the absolute temperatures of argon to each of the other substances
were calculated and plotted against the centigrade temperatures of the latter.
Straight lines were then drawn to pass as well as possible through the points, and the
following formule for the ratios were obtained :—

Argon

R’= 2351+ 0001155 ¢ (¢ = temperature centigrade of benzene).

Benzene
Argon
Ethyl Alcohol

Argon

R’ = '2164 + 0003765 ¢ (t= temperature centigrade of ethyl alcohol).

R’ = 9518+ 000522 (t+ 190) (t= temperature centigrade of oxygen).

Oxygen

The ratios calculated from the boiling-points and those given by the above formule
are compared in the following table :—

| Ratios.
Pressure | / |
an Argon/Benzene. Argon/ Alcohol. Argon/Oxygen.
millims. |— —— | ;
| From From | From | From From From
| boiling-points.| formula. | boiling-points.| formula. boiling-points.} formula.
| Zee SOS et | fh |
740°5 24.43 2443 2455) il 2456 el 9556 | "9555
18010 2637 2622 | "2894. | 2878 9838 9795
1923 2628 2628 "2892 | “2890 “9804 | “9802
| 20750 | 2641 2634. 2913 2904 ‘9842 | 9810
22040 | 2640 "2639 2917 2916 9836 | 9817
22650 | 2644. 2641 | 2924 "2921 9802 |. 9828 |
27210 | 2666 2657 | 2967 2957 “9896 9842
28880 | "2659 2663 2965 | 2970 ‘9857 9850
38460 | 2686 2689 3021 | “3030 9889 - 9887
| es " shies ie

LIQUEFACTION AND SOLIDIFICATION OF ARGON. 259

Assuming the boiling-points of benzene, alcohol, and oxygen to be correct, those of
argon could be calculated from them by multiplying the absolute temperatures of each
substance by the corresponding ratio at each pressure.

The observed and re-calculated absolute temperatures of argon and the differences
are given below :—

Pressure | Boiling-points (absolute) of argon.
millims. | Observed. | From benzene. A. From alcohol. | A. From oxygen. A.

| |

| | |

7405 | 86:1 86:1 0 | 86:1 0 86:1 0

18010 | 1339 1331 —0°8 133:°1 | —08 133:3 —0°6
19230 | 1347 134:7 0 1346 | Or 134-7 0
20750 | 1868 136-4 —0-4 | 136°4 —0:4 | 1364 —0°4
22040 | 137-9 137°8 —01 137:8 | =O | 137°6 —03
22650 | 13886 138°5 —O1 | 138°5 —01 138°9 +0°3
27210 | 1438°5 143-0 | —0:5 | 1430 —0'5 142°7 | —08
28880 144-4 144-6 +02 | 144°6 | +02 144°3 —O01
38460 15205) | 152:2 +0°2 | 152°4. | +0:4 152:0 | 0

The comparison would, of course, be more valuable if there were some observations
between 740 and 18,000 millims., but, so far as it goes, it will be seen that there is
a very fair agreement between the observed temperatures and those calculated from
the smoothed ratios.

It is hardly likely, though not impossible, that so good an agreement would be
obtained with a mixture or an impure substance. It is, at any rate, certain that a
distinct want of agreement would have shown that the argon was not a definite, pure
substance, and the results may be taken as affording additional confirmation of the
conclusion that argon is a definite, hitherto unknown constituent of the atmosphere,
and that it has been isolated in a state very closely approaching to purity.

Ph Ivy,

le 26m]

IX. The Latent Heat of Evaporation of Water.
By E. H. Grirrirss, A., Sidney Sussex College, Cambridge.

Communicated by R. T. GuazEBRook, F.R.S.
Received December 28, 1894,—Read January 17, 1895.

[Puares 4-6. |

CoNTENTS.
Section. 3 Page.
I. Introductory note thee LR Sia eat eo Eee Ca re CUE RUMMY OP 3 beam ee any Tue her Oy |
bieElistoricall ee. 52 js Sey ace ae A eee el Bids sits sane a en OOS
Ill. Description of the nedvedle Sah map inte Ce ciated SO teas Sees ee Ree. CO)
TV. Method of maintaining the walls of ie surrounding Shonnbee at a constant
Lemperaturens iT SIs e etsy Ma SO SHS. C7 Seo esd eS hiat tae Wik, AU ei eh Cl
VW. Description of the calorimeter and itscontents . . . ....... . . . 246
Wilenhe determina bOULOE 2gou4 he ik ih yeahs tea Tse ai nd es ae er bear da uD oy
Wilientheiheatisuppliedsbyathestirrin oper supe tatty. seit ier res Gee co)
\AD Hae a - Current ewes ee pee Be ee ES areg heer Ae
IX. Results of experiments in which the evupoeation was unetiotea i the passage of
a gas ; Aas ey PMR Sse RPE CLNL UTED Mee EERE & 298
X. The method finally adoptetl Le syee crit Sa OS
XI. Discussion of the results, together with a note iby ‘Dr. Tore Fr R. Sia wipe ea is. Fee eeOlO
Xai Dheidensibygol, waberavapoute. sii eep yee mele wags) ee aire ele eagle) ee me Or
Deratts or EXPyRIMENTS.
Appendix.
I. The stirring supply... . . bee Pon nest MOP?
II. The capacity for heat of the oalovietes ae ihe specific heat of ite oil 6 eh 8g POS
iP eehewesistancerof thevcoile 517.04 AUR eT ea OE SARA et) EOE” SBS
PLATES.
Plate.

4, The steel chamber and regulating apparatus.
5. The calorimeter.
6. The gas circuit, the electrical circuit, and the differential thermometers.

Section I.—Inrropuctrory NOotTE.

Ir is possible that I have in succeeding pages, when describing apparatus and

methods of observation, entered unnecessarily into matters of detail. In defence,
1.7.95.

262 MR. E. H. GRIFFITHS ON THE LATENT

I would urge that the accuracy of determinations of physical constants depends on
the amount of attention devoted to apparently trivial matters, and that in the
absence of full information, it is impossible to rightly estimate the value of the
results. Corrections are often rendered necessary by subsequent re-determinations
of the constants involved, and the application of such corrections is only possible
when the writer has given his data in full, Much valuable experimental work has
with lapse of time become useless, owing to the author's natural reluctance to over-
crowd his communication with details which may at the time very possibly appear
both unnecessary and trivial.

Although the experiments described in this paper were not commenced until
the Summer of last year (1894), the preparation of the apparatus and the
standardisation of the instruments has engaged my attention for a considerable
time. Nearly the whole of the Spring and Summer of 1893 were expended in
fruitless efforts to render the calorimeter and its connections absolutely air-tight, and
I found it impossible to secure perfection in this respect until in the Autumn of that
year I succeeded in obtaining an alloy, by means of which I was able to unite glass
and metal tubes in a satisfactory manner. The calorimeter and connections had then
to be practically reconstructed and some improvements added, which experience had
shown to be desirable.

My original intention was to conclude my investigations into the latent heat of
evaporation of water over the range 10° to 60° C. before publishing my results, and,
had it not been for two misfortunes, I think that I shouid have now completed the
necessary experiments. An accident to the apparatus early in September involved
a loss of about ten days, and also compelled a redetermination of the capacity for
heat of the calorimeter. A second mischance was a temporary break-down in my
health, which compelled me to be absent from my laboratory for some days, and on
resuming the work I was at first able to devote but little energy to it. During the
University Term my time is not my own, and hence, when October 13 found the
inquiry unfinished, I was compelled to relinquish all hopes of completing my original
scheme until the Long Vacation of 1895 should again provide me with the necessary
leisure.

I feel, however, that all the experimental ditticulties have been overcome, and I
regard the work as completed at certain temperatures. I do not propose to repeat
the observations at those temperatures, and therefore I see no necessity to defer the
publication of the results for another twelve months.

Again, the facts set forth in Section XI. appear to me to so strengthen the
conclusions to which my experiments have led me as to render any postponement
unnecessary.

I wish to express my sincere thanks to Mr. C. T. Heycock and Mr. F. H. NEVILLE
for many valuable suggestions, and also for their help with the experiments on
certain critical occasions.

HEAT OF EVAPORATION OF WATER. 2638

During the summer of 1893 I was assisted by Mr. G. M. Crarx, B.A., and
throughout 1894 by Mr. C. GREEN, Scholar of Sidney Sussex College, and I am glad
to have this opportunity of acknowledging my indebtedness to both those gentlemen.

As frequent references have to be given to two former papers, I denote them as
follows :-—

Paper J.” “ The Mechanical Equivalent of Heat,” ‘Phil. Trans.,’ vol. 184
(1893), A, pp. 361-504.

Paper A.” ‘The Influence of Temperature upon the Specific Heat of Aniline,”
‘Phil. Mag.,’ January, 1895.

Section I].—HuistTorIcAt.

The following is, I think, a fairly complete table of results published since the
year 1843 :—

TABLE I.
| | No. of |
| o. of |
|Temperature.| Observer. experi- | a aie Reference.
ments. | ; ’
|
| 0° Dimrerrcr. .| 20 | 595°52-598:84 | 5968 | ‘Wied. Ann,’ vol. 37, 1889
=F tm 42 1GH| Iie 6 ol PR | eS oe ‘Mémoir. de l’Acad.,’ vol. 21, 1847
63°-88° a baie | aes 5b Ae eal| Bs fe 45
| 99°88 » + -| 44. | 583:3-588:4 | 536-67 i dh fs
99°-81 FAVRE and 3 | 632°59-541°77 | 53577 | ‘Ann. de Chimie,’ vol. 37, 1853
SILBERMANN |
100° | ANDREWS . . 8 | 5308-543-4 535°9 | ‘Chem. Soc. Journ.,’ 1849
| 100° BERTHELOT . 3 535°2-537°2 5362 | ‘Comptes Rendus,’ vol. 85, 1877
100° SCHALL. . . No de tails given 5320 | ‘ Ber. d. Chem. Ges.,’ vol. 17, 1884
Pe lLOOSLG: Harrog and 5 523°61-525'87 | 524-60 | ‘Manchester Phil. Soc. Proc.,’
HArKER* | 1893-4.
119°-194° | Reenavtt. .| 73 | a Me ‘Mémoir. de l’Acad.,’ vol. 21, 1847
|
| \

The values obtained by WINKELMANN (‘ Wied. Ann.,’ vol. 9, 1880) are not included
in the above table, as they are not based on independent experiments, but deduced
from the observations of REGNAULT.

I do not propose to examine at length any of the above determinations except those

* Tt is right to add that Messrs. Hartoc and Harxer state that these are the results of ‘‘ Preliminary
Experiments,” and should not be regarded as giving their final conclusions. I do not, therefore, include
their work in my criticisms.

+ It must be remembered that all the above values of L (with the exception of Disrmrici’s) depend
upon some assumption as to the changes in the specific heat of water caused by changes in temperature,
for they are either deduced from “ the total heat of steam,” or depend upon the observation of the rise
or fall in temperature of a certain mass of water. Again, as the nature of the thermal unit adopted by
the observer is, in some cases, doubtful, an uncertainty of an order of about 1 per cent. is thus
introduced.

264 MR. E. H. GRIFFITHS ON THE LATENT

by Reenavtr and Diererici, for none of the other observers appear to me to have
devoted as much care and attention to the matter. In some cases, ¢.g., ANDREWS
and BERTHELOT, we have records of only a few observations evidently undertaken not
so much with the object of obtaining an accurate determination of the latent heat of
evaporation of water, but rather for purposes of comparison with other liquids. In
other cases there are not sufficient details as to the thermometry, the unit of heat
adopted, &c., to render a close criticism of any profit.

Again, DieTErRIct is the only observer who has made direct experiments at tempera-
ture 0° ©. REGNAULT’s observations extended from 63° to nearly 200° C., and he also
performed a number of experiments where the temperature of the vapour was between
— 2° and + 16°, although this last group must be regarded (and I think was regarded
by RecGnavtt himself) as of less value than his observations at higher temperatures.

The method employed by Dirrerici was in principle very similar te that adopted
by me and described in subsequent pages.*

The heat required for the evaporation was abstracted from water at 0° and the
amount of heat deduced from the quantity of ice formed. The advantages of such a
method (upon which [ shall more fully dwell when I describe my own work) are as
tollows :—

(1.) No change of temperature takes place, thus all difficulties connected with the
capacity for heat of the apparatus and its contents are avoided.

(2.) The observer is almost entirely independent of thermometry—an advantage
which, to my mind, it is almost impossible to overestimate.

DIETERICI’s experimental results, as stated in Table I. (supra), vary from 595°52 to
598°84, but it should be noticed that both these extremes occur in his Table I. He
afterwards made what he considered to be improvements in the apparatus, and the
extreme values of his last 13 experiments (see his Tables II., III., IV.) are 595-74 and
597°29. His mean result is 596°80, and I would particularly draw attention to his
last two experiments, where he very greatly increased the rapidity of evaporation by
suddenly opening the communication between his evaporating vessel and a condenser
containing sulphuric acid in which the pressure was reduced as far as possible by
means of a mercury pump. These two experiments give respectively 597°07 and
596°68, The agreement between the individual experiments throughout the whole
series leaves little to be desired, and, if it were not for one doubt, I would without
hesitation accept those results as conclusive; but I am afraid, for the following
reasons, that our knowledge is not yet sufficiently exact.

The quantities of heat were deduced by measuring the mass of mercury expelled
from the BuNSEN calorimeter during the formation of ice, and the results, therefore,

* My own experiments described in this paper were completed before the work of Dinrerici came to
my notice, and the close similarity between the general principles adopted by both of us is a matter of

chance, not of design. Had I previously perused his paper, I should have been saved much time and °

many preliminary experiments.

HEAT OF EVAPORATION OF WATER. 265

depend entirely on the constant which gives the relation between the quantity of
heat and the mass of expelled mercury. DieETERIct in this matter shifts the respon-
sibility on to other shoulders. His only reference to the subject is as follows :—

“Diese sind gemessen in mittleren Calorien, also in dem hundertsten Theile
derjenigen Wiirmemenge, welche ein Gramm Wasser von 0° auf 100° erwiirmt, und
zwar liegt der Berechnung der Mittelwerth der Beobachtungen von BuNSsEN,
ScHULLER und WartTHA und VELTEN,* zu Grunde dass einer mittleren Calorte
15°44 mg. Hg. entsprechen.”+

Now, Bunsen by assuming his own value of this constant obtained 80°025 as the
latent heat of fusion of ice, and the marked difference between this number and that
obtained by REGNAULT (79°24), requires explanation. This discrepancy is greater
than appears at first sight, for the ‘‘mean thermal unit” (over the range 100° to 0°)
adopted by BuNSEN is supposed to be greater than the “thermal unit at 15°”
adopted by REGNAULT during his researches into Latent Heat, and thus the divergence
would be increased if both were expressed in terms of the same thermal unit.

The doubt introduced by the above considerations is due to uncertainty regarding
the comparative magnitude of the different thermal units and does not affect the
value of Dirrericr’s experiments, although it renders his conclusions somewhat
uncertain.

There can be but little doubt that the mass of mercury expelled from a Bunsen
calorimeter by the subtraction of a definite thermal unit is a quantity that can be, and
doubtless will be, determined with accuracy, and if any correction on the conclusions
arrived at by BuNSEN, SCHULLER and WaRrHA, and VELTEN is found to be necessary,
it can be applied to the values of the latent heat of evaporation at 0° obtained by
DIeTERICI.

This case well illustrates a matter to which I have before endeavoured to call
attention,{ viz., that a mistake in thermometry is a fatal error in experimental
work. It is impossible to correct the conclusions arrived at by the investigator,
however our knowledge of thermometry may increase, since we should require to have
in our possession the actual thermometer used by the observer, together with a full
knowledge of the circumstances under which it was observed. As before remarked,
Drerericr’s results were independent of thermometry, hence their peculiar value.

ReeNav.t’s formula for the “ total heat of steam” has been so generally accepted,
and the experiments upon which he founded it are so justly considered as examples of
that singular skill and ability for which all his work is distinguished, that it is with
diffidence that I venture to offer criticisms on his methods or conclusions. I would
repeat that Recnautr himself evidently attached less importance to his determina-

* The actual values obtained by these observers were as follows:—Bunsen, 15°41; Scuutier and
Warraa, 15-442; Vuuren, 15°47 mg. ‘Wied. Ann.,’ vol. 33, 1888, p. 439.

+ ‘Wied. Ann.,’ vol. 37, 1889, p. 499.

t ‘Science Progress,’ April, 1894.

MDCCCXCV,.—A. 2M

266 MR. E. H. GRIFFITHS ON THE LATENT

tions at low temperatures than to those above 65°C. In Table IV. of his paper,
“Sur les chaleurs latentes de la vapeur aqueuse 4 saturation sous diverses pressions,”
are given the results of all his experiments below 63°, and in his introductory remarks
to this table (pp. 712-719) he clearly indicates his comparative want of contidence in
the results. *

A searching criticism of ReGNAULT’s work is given by WINKELMANN in ‘ Wied.
Ann.,’ vol. 9, 1880, and had the limits of this communication permitted it, I should have
liked to quote several pages of that paper, but I will content myself with giving a
short summary of his arguments.

I would first remark that WINKELMANN’s object was to explain the discrepancy
between what he terms the “theoretical density” of water vapour, and that which
results from “the mechanical theory of heat.” He assumes the former as 0°6225 ;
but does not give the data by which he obtains that number (I find that if we take
the molecular weight of H,O as 17°98, and the density of H as -06924 (air = 1), we
arrive at the same value). He then (assuming that J = 424) calculates the density
from the thermodynamic equation L = T/J (s’ — s) dP/dT, by substituting for L—

(a) the values resulting from Reanautt’s formula for the “ total heat,” viz.,

606°5 + ‘3056,
(>) the values of L given by the equation
L = 589°5 — 0'2972¢ ~~ 0:0032147¢? + 0°0000081478. . . . (W),

the last being a formula constructed by WINKELMANN, but based on REGNAULT’s
experiments at high temperatures.

WINKELMANN contends that not only does the use of (W) bring the values
obtained by the “mechanical theory” into greater harmony with the “ theoretical
value,” but also that the formula (W) is in closer agreement with RecNnau.t’s
experiments than is the formula given by REGNAULT himself.

True, the values obtained by WINKELMANN are always greater than 0°6225, but he
contends that it is impossible to imagine the real density as less than the “ theo-
retical,” although it is easy to see that it may be greater.

* “ Jai cherché a obtenirla chaleur latente de la vapeur d’eau a saturation aux basses températures
par une autre méthode qui me permettra, j’espére, d’obtenir cette donnée avec beancoup d’exactitude et
contre laquelle on ne peut pas élever les objections que nous avons faites contre le premier procédé.
Mais cette méthode, que j’ai décrite 4 la fin de mon Mémoire sur l’hygrométrie (‘ Annales de Chimie et
de Physique,’ 3° série, tome 15, p. 227), exige la connaissance de plusieurs données sur lesquelles il reste
encore beaucoup Cincertitude. On a besoin notamment de connaitre la capacité calorifique de l’air et la
quantité de chaleur que l’air absorbe pendant sa dilatation. II m’a paru nécessaire de déterminer ces
deux éléments par de nouvelles expériences, et c’est seulement Jorsyue celles-ci seront terminées que je
pourrai calculer les déterminations de la chaleur latente de Ja vapeur d’eau,” p. 722.

HEAT OF EVAPORATION OF WATER. 267

When I give the results of my experiments, I think that I shall be able to show
that WINKELMANN in his desire to lower the value of L at low temperatures has
considerably overshot the mark, and that in deducing the values at, or near, 0° from
experiments above 65° he has carried the method of extrapolation beyond due
bounds. At present, however, J will only consider his reasons, with which I agree in
the main, for rejecting REGNAULT’s determinations at lower temperatures.

(1) There is no doubt that Reanavtt’s formula does not give the mean result of
his experiments at low temperatures. In all, he performed twenty-two experiments
at temperatures below 65° (Table IV., ‘Mémoir. de l’Acad.,’ xxi., 1847), and the
mean value given by these twenty-two experiments differs from that given by his
formula by_1°8.

(2) The experiments above referred to were performed in a different manner from
those at the higher temperatures. The water to be evaporated was placed in a
spiral within the calorimeter, and the pressure reduced until the water boiled, the
vapour being condensed in a vessel surrounded by ice. Recnavir deduced the
temperature of the water when evaporating by observing the pressure of the vapour
in the condenser—hence, as REGNAULT himself says, ‘‘ It is probable that the elastic
force observed on the barometric manometer is decidedly less than the mean pressure
at which the vapour is distilled,” and thus the evaporation is taking place under a
greater pressure and at a higher temperature than that given by his Table IV.

Again, the temperature of the saturated vapour is sensibly beneath the tempera-
ture of the calorimeter, and so lowers the temperature of the calorimeter more than
would be done by the evaporation alone.

In the case of other liquids, REGNAULT made a correction for the heat abstracted
by the vapour while passing out of the calorimeter, but he did not apply this correc-
tion in the case of water. It is true that no special arrangements were made to
warm the vapour to the calorimetric temperature (as was done by coils with the
vapours of other liquids), but there can be no doubt that the vapour must have
abstracted heat from the walls of the calorimeter.

Let & be the specific heat of the vapour, ¢ the temperature at which evaporation
takes place, t, and ¢, the initial and final temperatures of the calorimeter, then the
heat per unit mass absorbed should be £ {3(¢,-+¢,) —t}; at the same time this is
not a correction that can be applied with certainty.

(3) At these low temperatures a small difference in the pressure of the vapour
corresponds to a considerable ditference in temperature; thus, if the temperature of
the water is deduced from the pressure in the receiver, the error may be considerable.*
The effect of all these errors would be to make the value of L given by REGNAUL1’s
experiments too great.

The above criticisms do not apply to the experiments at the higher temperatures.

* For example, a difference of 0°4 millim. at 4° would correspond to a difference of 1°C,

2M 2

268 MR. E. H. GRIFFITHS ON THE LATENT

I think the preceding summary fairly represents the remarks of WINKELMANN on
the determinations at low temperatures.*

I will now add some remarks of my own.

REGNAULT was compelled to limit the duration of these experiments as much as
possible, otherwise his correction for the loss or gain by radiation, etc. (which was at
best but a somewhat uncertain one) became large as compared with the other
magnitudes to be measured. The average length of an experiment was about five
minutes, though in one or two extreme cases it extended to 11 minutes; in this
time he evaporated about 5°3 grams of water, and thus he was compelled to reduce
the pressure in the condenser very considerably below the pressure of saturated
vapour at the temperature of the calorimeter. He was, therefore, unable to diminish
the sources of error (subsequently dwelt upon by WINKELMANN) in the manner he
might have done had he not been thus limited in time. REGNAULT, referring to the
difference between the pressure in the condenser and in the calorimeter, writes as
follows : “‘ La différence entre les deux tensions doit méme étre assez grande; car
pour que l’expérience se fasse dans des conditions favorables d’exactitude ; il faut que
la distillation soit assez rapide, afin que la correction e ne soit jamais qu’une fraction
trés-petite de ¢) — 4.”

Again, another matter of importance is the thermometry. On p. 692 (ibid.) he
says: ‘‘ Les thermométres 4 mercure des calorimétres ont étés gradués avec le plus
grand soin, un degré centigrade occupe sur la tige du thermométre

du calorimétreC. . . . . 18°°7620; par suite 1° vaut 0°:053283.
= On ¢ = » 5 LA EROS I ODESSA.

93

Il est facile d’apprécier avec certitude le dixiéme des divisions, c’est-A-dire 345 de
deoré centigrade dans les lunettes horizontales avec lesquelles on observe les
thermométres.”

The only other reference is on p. 707, where he remarks that he reduced the
readings from the mercury to the air scale by means of the table given on p. 239 of
his paper ‘‘ De la mesure des Températures.”{ I have searched the paper throughout
for some indication as to the thermometers actually used, in the hope that I might
be able to identify them with some one of those of whose comparison with the air
thermometer he gave an account in another paper; but the above are the only
references to the thermometry that I have been able to find. Had a direct com-
parison between these thermometers and the air thermometer been made, it is most
probable that Recnautt would have mentioned it; we may, therefore, assume that,

* Had not RecNauLT measured the temperature of the evaporating water by means of the vapour
pressure in the condenser, the above objections would lose their force.

+ ‘Mémoir. de l’Acad.,’ vol. 21, 1847, p. 716.

t ‘ Mémoir. de l'Institut,’ vol. 21, p. 220

HEAT OF EVAPORATION OF WATER. 269

knowing the nature of the glass, he simply reduced them to the air scale by the table
above referred to.

Throughout the low temperature determinations the temperature of the calorimeter
fell during an experiment through about 5°°6 (in the greatest case 5°°761), and thus
an error of 0°01 in his thermometry would cause a difference of more than 1 in 600
in the results. At higher temperatures, however, the average rise in the temperature
of the calorimeter exceeded 12° and thus the effect of any such thermometric error
would be considerably reduced.

Again, the observations of the change in temperature of the calorimeter at low
temperatures were always taken on a falling thermometer. I have in a previous
paper (J., p. 442) expressed my disbelief in the value of any observations of mercury
thermometers when their temperature is falling. I am not alone in this opinion,*
and it has been confirmed by subsequent experience. I am sure that inaccuracies of
a much larger order than 0°01 would have presented themselves from this cause
alone, and the great divergences observable amongst REGNAULT’S individual experi-
ments at low temperatures is I have no doubt partly attributable to this cause.t In
all his experiments at higher temperatures, however, his thermometers were rising
and the discrepancies between individual observations were much less marked.

_ It will be noticed that the various sources of error which have been enumerated
either disappear or are much diminished at the higher temperatures.

Again, the ever-recurring difficulty with regard to the specific heat of water
presents itself. The correction is not so simple as has been assumed by those who
have merely applied ReGNAULT’s own formula for the specific heat of water to the
expression for the total heat of steam, for the correction would have to be applied
during the reduction of each separate experiment, as the quantity of heat absorbed
by the calorimeter and contents when warming or cooling through a degree of
temperature would vary according to the mean temperature of the range and the
resulting correction would, I believe, be greater than is usually supposed.

There appears to be but little doubt that ReG@NAuLt’s expression for the changes
in the specific heat of water is inaccurate. As far as I know, RowLanp (1877),
Bartout and StRAccrati (1889), and myself (1892) are the only observers who have
seriously attacked this difficulty since the time of ReGNAULT, and all agree in one
conclusion, viz., that the specific heat of water diminishes as the temperature rises to
20°, and the methods of experiment employed by these observers were so entirely
different that their agreement in this matter carries great weight. We cannot,
therefore, accept without question REGNAULT’s conclusions as to the changes at
higher temperatures. The magnitude of the correction involved may be illustrated,
as pointed out by DirrTericr himself, by the following example. If we assume

* Scuusrer and Gannon, Communication to the Royal Society, Nov. 22, 1894.

+ The comparatively slow rate of stirring would also tend to make the temperature measurements
uucertain.

270 MR. E. H. GRIFFITHS ON THE LATENT

Row.anv’s value for the specific heat of water at 15° C., the difference between the
thermal unit at 15° C. and “the mean thermal unit” over the range 100° to 0°,
amounts (if we accept Drererict’s interpretation of REGNAULT’s values) to nearly
13 per cent.,* and would reduce the value of L at 0°, as given by Ruanautt’s formula
(viz., 606°5), below the value found by Drererictr (598°8).+

The tacit assumption amongst physicists that the discrepancies arising from doubts
as to the value of the thermal unit are so trivial that they may be disregarded is, as
shown by the above example, much to be regretted, and the many efforts to deduce
specific volumes, etc., from the equation J = L/T (s’ — s) dp/dT, shows how frequently
this difficulty is ignored. It is strange that, although so much attention has been
devoted, during recent years, to the exact determination of various physical units, so
little has been done with regard to this extremely important fundamental constant.

The experimental difficulties are not so great as to prevent all progress, and
I venture to appeal to the Royal Society to consider this matter ; indeed, I would
go so far as to express my personal belief that the method of measuring small
differences of temperature indicated in a paper read before the Physical Society
last October removes many of the difficulties which have hitherto barred the way.

It is, I think, evident that we are not justified in concluding that our knowledge
of the value of the latent heat of evaporation of water at low temperatures is sufficient.
It has been already shown that the effect of most of the causes of error above
enumerated diminishes at higher temperatures; and a study of Reenavtt’s Tables I.
to IIT. will confirm the conclusion that we may regard the results at those tempera-
tures as of greater accuracy. Even at higher temperatures, however, the difficulties
with regard to the measurement of differences of temperature and of the capacity for
heat of water present themselves.

I can find no record of experiments by any observer at temperatures between 16°
and 65° C.

The above considerations are, I think, sufficient to indicate the necessity of a
re-determination of the latent heat of evaperation of water, at all events at low
temperatures.

Section IIJ].—Derscrierion or THE METHOD.

I was anxious, if possible, to devise a method of such a nature that my results would
not be appreciably affected by
(1) errors in thermometry,
(2) changes in the specific heat of water,
(3) the capacity for heat of the calorimeter,
(4) loss or gain of heat by radiation, &c.,
* At the end of this paper I give figures which lead to the conclusion that the difference between the

‘* mean thermal unit’? and the “thermal unit at 15°”
+ Dreterict, ‘ Wied. Ann.,’ vol. 37, 1889, p. 506.

is less than is usually assumed.

HEAT OF EVAPORATION OF WATER. 271

and if these points are borne in mind they may serve to explain some of the con-
trivances which might otherwise appear uncalled for.

If the vessel in which the evaporation is taking place is kept at a constant tem-
perature, we are independent of the capacity for heat of it and its contents; we also
dispense with the measurements of changes of temperature. Thus, if matters be so
arranged that the loss and gain of heat throughout an experiment are balanced, many
frnitful causes of error are avoided. Of course, the actual temperature of the calori-
meter during evaporation must be determined, but a small error here is of little con-
sequence. The change in the value of L (when L is the latent heat of evaporation of
water) is small as compared with the changes in #. In fact, an accuracy of an order
of ;'5 of a degree would be sufficient when determining the actual elevation.

The heat was supplied to the calorimeter by means of a wire whose ends were kept
at a constant potential difference. The thermal balance could be maintained in one
of two ways,

(1) If the heat supply was too great, the electric current could be temporarily
stopped : or, the rate of evaporation of the water increased. (The latter was
the method that I generally adopted.)

(2) If the cooling was too rapid, the only mode of maintaining the balance was (in
the apparatus about to be described) to reduce the rate of evaporation.

The water to be evaporated was placed in a small silver flask, connected with which
was a spiral coil of silver tubing 18 feet in length. Both flask and spiral were within
the calorimeter, and the water-vapour, after passing through the spiral, emerged from
the apparatus at the temperature of the calorimeter. Surrounding the flask, and
between it and the spiral, a coil of platinum silver wire was arranged, and flask,
spiral and coil were entirely immersed, in aniline during my preliminary experiments,
subsequently in a certain oil of which an account will be given later.

The calorimeter (which was filled to the roof with the aniline or oil, and the equality
of temperature maintained by rapid stirring) was suspended by glass tubes within a
steel chamber, whose walls were maintained at a constant temperature. So long,
therefore, as the calorimeter and the surrounding walls were at equal temperatures,
there was no loss or gain by radiation, &c. If during an experiment the temperature
of the surrounding walls changed, the method of experiment involved a corresponding
change in the temperature of the calorimeter, and, therefore, some loss or gain of heat
would be experienced. The apparatus was so designed that any such change in
temperature was extremely small (in no case amounting to 7p), yet, in order to
estimate the loss or gain, it was necessary to know approximately the capacity for
heat of the calorimeter and contents.

Small differences between the temperature of the calorimeter and the surrounding
walls would, during an experiment, be of no consequence, provided that the oscillations
were of such a nature that the mean temperature of the calorimeter was that of the

272 MR. E. H. GRIFFITHS ON THE LATENT

surrounding space, and I think I shall be able to show that this condition was
fulfilled.

In addition to the heat supplied by the electric current there is also a supply due
to the work done by the stirrer. It was in the estimation of this “ stirring supply ”
that I found my greatest difficulties, and I regard that portion of my determinations
with the least confidence. Fortunately the heat thus generated was only about 797
of the heat supplied by the current, and thus any small error in that portion of the
work becomes of little account.

Of the accuracy with which the electrical supply could be measured, there is no
question, and I have but one remark to make on this portion of the subject, viz., that
even if the values of the E.M.F. of my Clark cells, or the absolute resistance of the
box-coils given by the standardisations performed during my determinations of J, are
in any way inaccurate, such errors would eliminate, since the value of J was
determined by means of the same standards as those by which the quantity of heat
developed in these experiments was determined. Hence, by assuming my former
value of J, I get the comparison in terms of a thermal unit at 15° C., independently
of the numerical value of J assumed in the reductions.

One further correction remains to be noticed. I have spoken of the temperature
of the calorimeter as oscillating about the exterior temperature, and it might happen
that at the close of an experiment this difference was not the same as that at the
commencement—if any such difference existed. The magnitude of this correction
depended, of course, on the ability of the observer to maintain the thermal balance.
In these experiments the correction was extremely small, and in any case could
be determined with great accuracy.

Having indicated the nature of the observations I will proceed to state the relation
between the various sources of loss, or gain of heat.

Let Q, be the thermal units per second due to the electrical supply.
» Qs »» »» 2 x mechanical supply.
,, 2g be the total heat supply during an experiment from any other causes.

Then, if M be the mass of water evaporated, L the latent heat of evaporation
at temperature @, and if the electrical supply is maintained for a time ¢t,, and the
mechanical for a time f,,

ML = Q4, Qi to 2G i ye ee eS

Now the D.P. at the ends of the coil was always some integral multiple of the D.P.
of a Clark cell.

Let e be the D.P. of a Clark cell, x the number of cells, and R, the resistance of
the coil at the temperature 6,, then

pr

en

Q. a Roe : : : sks . . . . . . (2).

HEAT OF EVAPORATION OF WATER. 273

If the calorimeter at the commencement and end of an experiment was at exactly
the same temperature as the surrounding walls, then if their temperature was
unchanged, the term q would vanish; but although this term throughout these
experiments was of small dimensions, it could not be entirely ignored.

Let @ and 6”, be the temperature of the surrounding walls at the beginning
and end of an experiment; suppose the calorimeter temperature (6,) to exceed the
surrounding temperature by d’ at the commencement and d” at the end of an
experiment. Then fall in temperature of calorimeter

=(0),+ a’) —(0 +a’).
Hence the heat given out by the calorimeter in consequence of this fall in tempera-
ture is
Co, (0 + @’) — (0% + dD},

where C,, is the capacity for heat of calorimeter and contents at the temperature 0).

If we neglect any small loss by radiation, &c., due to the differences @’ and d”
between the temperature of the calorimeter and the surrounding walls, we may
conclude that the whole of the heat thus evolved by the calorimeter was expended iu
the evaporation of water, hence

pes Ch (UO) Pode ee. ee)
Hence
ML = ae + Q, X t + Oy, (0% — 0%) + (@ — a"). (A)

Tn order to convey an idea of the relative importance of the terms in equation (4)
I will here give the approximate mean value of each term resulting from the experi-
ments described in succeeding pages.

TABLE II.
Qete. Qs bse =q.
When
G =Venigsd 2. 2 5 6 « 2150 19:2 +16
G = Beachy . og 5c 2305 32°9 +12
Ge ander — ome ene 1752 32°9 ae 19)

* This apparently clumsy method of representing the quantity of heat evolved or taken up by the
calorimeter was adopted because, as the method of experiment involved separate determinations of
6", 0", d' and d’, the actual temperature of the calorimeter at any time could only be obtained in this
manner.

MDCCCXCYV,—A. 2N

274 MR. E. H. GRIFFITHS ON THE LATENT |

Although, of course, I had, when commencing these experiments, no exact know-
ledge as to the comparative values of the terms, some preliminary observations
enabled me to form a rough estimation of their magnitudes and consequently of the
degree of attention which should be devoted to their accurate measurement.

Section [1V.—THE MernHop or MAINTAINING THE SPACE SURROUNDING THE
CALORIMETER AT A CONSTANT TEMPERATURE.

I have, in Paper J., given an account of the apparatus employed for this purpose,
and full details and plates will be found on pp. 374-378 (cbid.).

In order, however, to give a general idea of the arrangements, and to save the
reader the trouble of reference, I will here quote the brief description given in the
abstract of that paper :—‘ The calorimeter was suspended within an air-tight steel
chamber. The walls and floor of this chamber were double, and the space between
them filled with mercury. The whole structure was placed in a tank containing about
20 gallons of water, and was supported in such a manner that there were about
three inches of water both above and beneath it. The mercury was connected by a
tube with a gas regulator of a novel form, which controlled the supply of gas to a large
number of jets. Above these jets was placed a flat silver tube, through which tap-
water was continually flowing into the tank, all parts of which were maintained at an
equal temperature by the rapid rotation of a large screw. Thus, the calorimeter may
be regarded as suspended within a chamber placed in the bulb of a large thermometer
—the mercury in that bulb weighing 70 Ibs. A change of 1° C. in the temperature
of the tank-water caused the mercury in the tubes of the regulating apparatus to rise
about 300 millims. Special arrangements were made by which it was possible to set
the apparatus so that the walls surrounding the calorimeter could be maintained for
any length of time at any required temperature, from that of the tap-water (in summer
about 13° C., in winter 3° C.) up to 40° C. or 50° C.”

I think the above summary, together with the section on Plate 4, will convey a
sufficient idea of the apparatus.

Since 1892, I have made certain improvements, which I will briefly describe.

During my J. experiments the range of temperature was from about 14° C. to 26° C.
In subsequent experiments when I have required to use the apparatus at higher
temperatures, it was found that the oscillations in temperature became serious, in some
cases amounting to 35° C. This was due to the temperature lag of the large mass of
mercury, so that when the gas was lowered by the action of the regulator the resulting
in-flow of cold water lowered the tank temperature before the mercury had contracted
sufficiently to again heat the in-flow. In Paper A. I have described as follows the
arrangements made to meet this difficulty :—‘ As now arranged, when working above
temperatures about 20° C., a small motor acts as a heart, and, the tap-water being
shut off, pumps the tank-water itself round through the silver tube placed above the

HEAT OF EVAPORATION OF WATER. 275

gas-jets. The water, by passing through the pump, &c., is slightly cooled; thus, the
work of the regulator is confined to simply supplying the heat lost by convection,
radiation, &c., and it performs this task admirably. As an illustration, | may mention
that, in the series of over 50 experiments treated of in this communication, on only one
oceasion did the temperature of the steel! chamber change by as much as 75° C.
throughout the duration of an experiment. On the solitary occasion that a change
amounting to nearly 45° C. was observed, the cause was found in the caking of the
lime through which the gas was passed on its way to the regulator, and, in
consequence, the experiment was discarded before working out its results.”

On account of the use of the differential thermometers (see Section V.) employed
in the present investigation, it was essential that any changes in the temperature of
the steel chamber should be measured with greater accuracy than was necessary in
my previous work, for now such changes influenced the temperature measurements,
whereas on former occasions they only affected the loss by radiation, ete. An open
range mercury thermometer placed in mercury in the hole E (Plate 4) gave the
temperature of the walls surrounding the calorimeter and changes in the mean stem
temperature had to be guarded against for the reason above given. The small motor
already referred to now served another purpose. A portion of the water raised by
the pump, instead of returning to the tank through the silver tube passed into a coil
of about 20 feet of ‘‘ compo. ” tubing inserted in the tank, was then forced up a glass
tube surrounding the stem of the thermometer, and passing out at the top, returned
to the tank. Thus the stem-temperature was kept constant throughout an experi-
ment, the regularity of the flow being secured by an overflow system. True, the
water near the top of the glass tube would be slightly cooler than the tank water
when working at high temperatures, but this was of no consequence, as the chief
use of the thermometer was to detect differences during an experiment. Two
thermometers labelled A and II. were used. Although an accuracy of an order of
zo CU. would have been sufficient in actual elevation, I compared these thermometers
every 05 C. of their ranges with two different Tonnelot thermometers, standardised
by the Bureau International des Poids et Mesures, and also with my own platinum
standard. The results of the separate comparisons (expressed on the nitrogen scale)
agreed within ‘005° C. |

The stems of both thermometers were graduated in millimetres. A (range 16° to
26° C.) having about 27 millims. per 1° C. and II. (range 28° to 53° C.) about 20
millims. per 1° C. A table was constructed for the whole range of temperature,
giving the value in degrees C. of (#) each millimetre of these thermometers in terms
of the air thermometer, and (b) in terms of the millimetres of the “mean bridge wire
scale” used by me for the determination of differences of temperature.

These thermometers were observed through a microscope fitted with a micrometer
scale so divided that it gave 10 divisions to the millimetre. There was no difficulty

2N2

276 MR. EH. H. GRIFFITHS ON THE LATENT

in estimating 3/5 of the micrometer divisions, and thus readings could be taken to

‘01 millim., that is to about ‘0004° C. on A and to about *0005° C. on No. II.

I do not, of course, claim that I could determine actual temperatures to this
closeness, by these or any other mercury thermometers, but, owing to the precautions
above described, I have no doubt but that changes in temperature of the order of
0°-001 C. (2.e., about *025 millim.) could be detected, especially as any movement was
extremely slow—in no case as much as 0°01 C. per hour. A constant vibration,
due to the pumping of the water up the surrounding tube, tended to prevent
“ sticking.”

A further improvement has been the addition of a gas pressure regulator. This
apparatus was designed for me by Mr. Horace Darwiy, and is the only satisfactory
instrument of the kind I have seen. It is most perfect in its action, and J am now
absolutely indifferent to changes of pressure in the mains.

With these additions, I think that the whole of this constant temperature portion
of the apparatus may be considered as nearly perfect. Only those who have watched
it actually at work can appreciate the certainty of its action; it can be set with
precision to any temperature between that of the tap-water and 64° (the highest
temperature at which I have actually tested it), and my only regret is that cir-
cumstances compel me to leave unused, for the greater portion of each year,
apparatus by means of which so many difficulties could be overcome.

Section V.—DESCRIPTION OF THE CALORIMETER AND ITS CONNECTIONS.

The calorimeter was made of brass and was of cylindrical form, 10 centims. in
diameter and 10 centims. in height.

It contained a silver flask, F (see Plate 5, fig. 1), in which the evaporation took
place ; a stirrer, of which the lower end only is shown at 8; a rack (shown in the
horizontal section, Plate 5, fig. 2) which carried a coil of platinum-silver wire, and
about 18 feet of silver tubing wound in a spiral—shown in section at p.p’. A
platinum thermometer also passed from the top to the bottom. With so many
objects crowded into so small a space, it is difficult to convey any clear idea of the
internal arrangements, therefore I will only attempt a brief description, and shall
rely chiefly on the sections given in Plate 5 to convey the necessary information.
The capacity of the flask, F, up to the side opening at d, was about 68 cub. centims.
Any vapour or gas passing from the flask into the spiral at d, after descending to the
bottom of the calorimeter, ascended throughout the whole length of the coil, and
thence up the tube e. This arrangement was adopted to diminish any chance of the
carrying of the liquid, or “priming,” by the flow of vapour or gas, as it appeared
improbable that particles of liquid would be carried up a gentle slope of 18 feet in
length.

HEAT OF EVAPORATION OF WATER. 277

Any inflow of gas came down the tube f, and passed directly into the bottom of
the flask at g.

The stirrer S had two paddles, reaching from top to bottom of the flask; the
blades and the central tube were of thin copper. Down this tube passed a steel.
shaft, which hung at the lower extremity within a hole in a sheet of brass projecting
from the side of the calorimeter. The bearings of the stirrer were entirely outside
the calorimeter, and the lower end did not touch the base, or bear on the surrounding
plate, whose only purpose was to check vibration. The paddles had a slight “ pitch,”
so as to throw the liquid upwards, as well as cause it to rotate. The exterior
bearings at the top of the glass tube S (fig. 3) were of the kind figured in Plate 2,
Paper J., and were certainly sufficiently air-tight to prevent any diffusion, even when
the stirrer was rotating rapidly, but, as the calorimeter was filled with a non-volatile
liquid, the air-tightness of this joint was of little consequence, especially as the tem-
perature of the calorimeter remained constant during the experiments and the air-
space above the liquid was small. The rubbing surfaces were very true and always
immersed in oil, thus the heat generated must in any case have been unimportant.
The greater portion of any heat developed in the external bearings would pass to the
brass tube, of which they formed a part, and, as the lower portion of this tube was
washed by the tank water, its temperature would in any case rise but little. Any
heat passing down the steel shaft (length 28 centims., diameter 0°35 centim.) would,
of course, be included in the “stirring correction,” but I should imagine that it was
in reality negligible, for about 4 inches of the glass tube down which it passed were
also washed by the tank water.

Further, slightly above the top of the calorimeter a section of ivory was inserted in
the stirring shaft, in order to diminish conduction as much as possible.

- The platinum-silver coil was wound on small ebonite tubes surrounding the narrow
brass pillars of the rack, whose section is shown at R (fig. 2). The method by which
the insulation of the rack was maintained, where the two brass pillars R, R, passed
through the top of the calorimeter, is shown by the section (Plate 5, fig. 4). _ It must
be remembered that these junctions had not only to be perfectly insulated, but that
they had also to be absolutely air-tight, over a considerable range of temperature (10° to
60° C.),* even to pressures of 1 atmosphere.

The platinum-silver coil was about 100 centims. in length, and so wound that it
was completely immersed when the depth of the liquid was 4 centims. ‘Two copper
wires (B. W.G., 21) were soldered to each of the pillars R, and R, where they projected
ubove the roof of the calorimeter at / and /’ (fig. 3), thus, in the steel lid, there were
four junctions similar to those above described (see Plate 6, fig. 3). The blocks of
ebonite forming the top slab of the junctions were, however, in this case, made
nearly five inches in length; they projected as far as the lid cf the tank, and

* The insulation of the whole circuit after all the apparatus was placed in position, was better than 1
could measure, z.¢., LO’ ohms,

278 MR. E. H. GRIFFITHS ON THE LATENT

thus all contact between the leads and tank-water was prevented. The calori-
meter was hung below the steel lid by five glass tubes, thus ten air-tight junctions
of glass to metal were required, in fact, four of these junctions were, in reality,
double ones, for the lower extremities of the narrow tubes e and f (Plate 5, fig. 1)
had not only to be fixed into the lid of the calorimeter, but also joined on to the
ends of the silver tubing. In like manner, where they passed through the steel
lid, they had to join also on to glass tubes leading to two glass taps immersed in
the outer tank. There were, therefore, practically fourteen such joints. I have
previously described an alloy by which I was enabled to make these joints absolutely
air-tight.* In order to show how carefully all these joints were tested, as well as
several others in the external connections by which communication with the mercury
pumps was established, I extract the following from Paper A. :—‘‘In the spring of
this year the intra-mural space was exhausted until the reading of the McLeod gauge
connected therewith was reduced to 11, indicating a pressure of about 0°12 millim,
The apparatus was then left untouched fora month, except that the temperature was
occasionally raised or lowered, and at the end of that time the reading of the gauge
was still less than 12. Dry air was then re-admitted to this space, and the silver
flask, with its connecting tubes (embracing about 50 feet of tubing with several joins),
tested in a similar manner. Those who have had to deal with low pressures will
understand that, when all was found satisfactory, a great difficulty had been sur-
mounted. I did not retain this vacuum during the experiments, as I felt that it
would subject the glass tubes, &c., to a continuous strain which the conditions of the
experiments rendered unnecessary. The labour had not been lost, however, for I was
able to count with confidence on the gas-tightness of the whole apparatus.”

Where the supporting glass tubes entered the calorimeter lid (as shown by the
plan, Plate 5, fig. 3), they were surrounded by metal tubes (shown by the outer ring”
in each case) nearly 1 centim. in length which had their lower extremities soldered to
the lid. The annular space between these and the glass tubes was filled with the
alloy and the joints on the top of the steel lid, from which the apparatus hung, were
of the same kind but slightly deeper. The tube 8 surrounded the stirrer shaft. The
platinum thermometer AB passed down T, and this tube was also used for inserting
or withdrawing the calorimeter liquid. The thermometer was wrapped with india-
rubber tape so that the annular space between it and the glass tube T was made
air-tight throughout the upper 4 inches.

Through h’ h communication was established between the exterior and the
silver flask. During my earlier experiments a thermometer stood in this tube
with its bulb nearly at the bottom of the fiask. It was of course possible to
render air-tight the connection between the thermometer stem and the top of
the tube h’, where the latter projected above the tank. This would not, however,
have been sufficient, for the flask contained a volatile liquid, and distillation would

* ‘Cambridge Phil. Soc. Proc.,’ 1893.

HEAT OF EVAPORATION OF WATER. 279

have taken place into and out of the annular space between the tube and
thermometer stem, according as the calorimeter was warmer or cooler than the
tank water. This thermometer had also to be frequently removed in order to
insert liquids into the flask, and therefore any junction at the bottom could not
be made a permanent one. The difficulty was surmounted as follows :--The
silver tube & (Plate 5, fig. 1), which passed up from the lid of the silver flask
was soldered to the calorimeter lid, above which it projected. A hollow brass rod
just fitting the glass tube, but with its lower end tapered, was, before fixing the glass
in place, held vertically with the tapering end filling the open end of the silver tube.
The annular space between the silver and surrounding brass tube was then filled
with the melted alloy, to above the top of the silver, and the glass tube lowered into
its final position. When the alloy hardened, the brass rod was loosened by lowering
into it a red-hot wire. The lower inch or so of the brass rod having been cut off was
then placed co-axially round the thermometer stem and made one with it by filling
the annular space between it and the stem with the same invaluable alloy. Thus, on
lowering the thermometer into its place, the brass tube almost exactly fitted into the
ring of alloy at the bottom of the glass tube. The fit was made good by prolonged
grinding with rotten stone—using the thermometer stem as a rotating shaft. The
result was a practically air-tight join at the calorimeter lid. It must be remembered
that as the air-tightness was secured by the cork at the upper end, this joint had not
to stand any pressure, but was only required to prevent diffusion.

I have, for two reasons, fully described this method of fixing the tube. (1) I
thereby overcame a difficulty which had perplexed me for a long time; (2) it was
necessary to explain the constriction at the lower end of the tube h, which im its turn
became a source of difficulty when I altered my method of experiment.

J and /, (fig. 3) are the insulating junctions for the rack on which the coil
was. wound.

The base of the calorimeter, which was not fixed until everything else was in
place, was heated until solder contained in the circular trough, of which a section is
snown at M (fig. 1), became fluid; the calorimeter was then pressed down upon it,
and, as soon as the solder commenced to harden, the calorimeter was set in cold
water. The base was thus soldered on without melting the alloy in the lid or
injuring the internal fittings.

The whole apparatus was a difficult and complicated one to construct, and I ewe
my sincere thanks to Mr. Tuomas for the ingenuity and patience he devoted to the
task. My brief description can convey but little idea of the many difficulties that
had to be surmounted between the conception and completion of this apparatus, and
I may mention that although commenced in February, 1893, it was not until the
spring of this year (1894) that the calorimeter could be regarded as completed.

280 MR. E. H. GRIFFITHS ON THE LATENT

Exterior Connections.

The upper end of the narrow glass entrance tube f (Plate 5, fig. 1) was, as before
stated, connected with a glass single-way tap, T; (Plate 6, fig. 1), which, on the
further side was connected with about 30 feet of thin-walled copper tubing immersed
in the tank water. Thus, all gas entering the silver flask through T; would be
at the temperature of the tank water, and (the calorimeter temperature being
identical with that of the tank) no heat would be added or subtracted when gas was
passed through the flask and spiral. T, was a four-way tap on the exit side, the
arms of the one passage through its core being at right angles to each other. The
tap is shown in fig. 1 (¢nfra). A is the tube leading from the flask and connected with e
(Plate 5, fig. 1). By rotating the core, A could be connected with B or D, or C
could be connected with B or D. ‘The glass tubes forming the outer case of both
taps T,; and T, were sealed at the lower extremity, and after a portion of the tube
above the core had been filled with mercury, these taps were perfectly air-tight.
The outer glass tube of each was about 6 inches long, thus the lower 4 inches were
below the surface of the tank water, and the upper parts of the tubes were packed
with cotton wool. The cores narrowed to a glass rod, which, passing through the
wool, projected above the tank lid, where a handle was attached ; thus the taps
could be opened or shut from the exterior of the whole apparatus. The position of
the taps is indicated in Plate 6, fig. 1.

Tube B (fig. infra) which communicated with the apparatus into which, during
my earlier experiments, the vapour was passed, extended under the surface of the
water to the walls of the tank, it then passed above a row of small gas jets, and thus
no condensation took place until the vapour arrived at the drying bulbs. At the close
of an experiment a movement of the tap connected C and B, and as C was connected
by a three-way tap (T,, Plate 6, fig. 1) with the dry air supply, any moist air
remaining in B or its continuation was swept into the receiving apparatus. On the
other hand, by connecting A and D before the commencement of an experiment the
vapour brought by the gas which had passed through the calorimeter was disposed of
without affecting the weight of the receiving apparatus attached to B. Thus an
experiment could be started at any moment by changing the connection at tap T,
from AD to AB, and that without altering in any way the conditions as to flow
of gas, rate of evaporation, &c.

Finally, I would remark that throughout the gas circuit, the yas only came into
contact with the following materials—glass, silver (only hard solder was used for all
the flask and tube connections), the glass-metal-joining alloy at the junctions, and the
drying agents. True, in my “exhaust” experiments with water the vapour had to
pass through about half-an-inch of thick rubber on the exit side, where connection was
made with the condenser, but when using other liquids, this joint can easily be
replaced by a glass one. When evaporating ether (with which I have made some

HEAT OF EVAPORATION OF WATER. 281

preliminary experiments), the grease on the cores of the glass taps was replaced by a
trace of phosphoric acid, which appeared to answer admirably. Thus, the apparatus
can be used without alteration for all volatile liquids which do not act on the metals,
a possibility I kept steadily in view when designing it.

Fig. 1.
Four way tap ly

[May 4, 1895.—At the meeting of the Physical Society on January 11, 1895,
Professor Ramsay exhibited an apparatus by means of which the comparative latent
heats of evaporation of different liquids could be determined. I had the pleasure of
seeing the apparatus at work, and from that time I abandoned all idea of extending
my own investigation to other liquids than water. The method adopted by Professor
Ramsay is so perfect, and at the same time so simple, that I feel that it would be
waste of time and energy to pursue my absolute determinations. I mention this
because many of the precautions described in the preceding sections were adopted
with the view of conducting experiments with various liquids, and (as I now discover)
might have been dispensed with.

Professor RaMsAY now informs me that, although certain practical difficulties in
the working of his apparatus have not as yet been entirely overcome, he has already
determined (approximately) the comparative latent heats of evaporation of a con-
siderable number of volatile compounds, and that the results will shortly be
published.

I venture, however, to call attention to the fact that the very perfection of
Professor RAMsAyY’s method increases the importance of an accurate knowledge of the
absolute latent heat of evaporation of water. |

MDCCCXCV.—A. 20

282 MR. E. H. GRIFFITHS ON THE LATENT

Section VI.—THEr DETERMINATION OF Sq.

I will now describe the method of obtaining the value of the various terms im
Equation I. (p. 272) by which the quantity of heat supplied during an experiment is
ascertained.

=q is the quantity whose accurate determination presented the greatest difficulty,
therefore the apparatus was so designed as to reduce this term to as small dimensions
as possible, and since many of the contrivances adapted to this end may, unless their
purpose is explained, appear unnecessary and cumbersome, [ commence with this term
in order to avoid repetitions.

Had it been possible to so arrange matters that the temperature of the calorimeter
at the beginning and end of an experiment should be absolutely unaltered, this term
(=q) would have vanished, and in my earlier experiments, during which I endeavoured
to determine the mass of water evaporated by passing the resulting vapour through
drying bulbs, this condition was practically fulfilled, since it was always possible to
stop an experiment at any time. I was compelled, for reasons which will be given
later, to abandon this method of estimating M, and to adopt a method in whicha
given mass of water was to be evaporated. The observer had, therefore, no choice as
to the time when the experiment should be completed, and as the thermal balance
could not be absolutely maintained throughout an experiment, it was impossible to
ensure the identity of the initial and final temperatures.

It was advisable, if possible, to so arrange matters (I.) that a small alteration in the
quantity of heat should produce a considerable change in temperature, so that small
differences in the thermal equilibrium might render themselves evident ; (II.) that the
oscillation in temperature might be reduced to as small dimensions as possible ; (III.)
that the difference, if any, between the initial and the final temperatures should be
accurately measured.

Although Nos. I. and II. appear contradictory, such is not the case, for the
important matter was to ensure the equality of the thermal, as distinct from the
temperature balance ; therefore, if small alterations in the former made themselves
readily evident by changes in the latter, and if the latter changes were kept small,
the desired end was attained.

Within the calorimeter there were two agencies at work—the cooling due to the
evaporation (which for convenience I shall henceforth venture to speak of as a “supply
of cold”), and a supply of heat due to the current; therefore, unless some means were
adopted of rapidly bringing the contents to a uniform temperature, the temperature
gradient from the hotter to the colder portions would be considerable. It was thus
necessary to completely fill the calorimeter with some liquid and to rapidly stir this
liquid.

Two objections to the use of water immediately presented themselves : (a) its great
capacity for heat (which would have caused changes in the thermal balance to have

HEAT OF EVAPORATION OF WATER. 283

buta small effect on the temperature) ; (b) its electric conductivity, which would have
necessitated the covering of the platinum-silver coil with some insulator.

I therefore gave my first attention to the selection of some more suitable liquid.
The ideal one ought to have small “ volume heat,”* and should be a perfect insulator,
and therefore I at first selected aniline. I determined its specific heat over a range
of from 15° to 52° C., and found that in some respects it suited my purposes admir-
ably. A full description of this work will be found in paper A.

Early in September I had, in consequence of an accident, to take the calorimeter to
pieces and withdraw the aniline. I was then alarmed by the darkening in colour
which it had undergone. In the discussion on the paper above referred to, Dr.
ARMSTRONG expressed his opinion that the change in constitution indicated by this
change in colour was not of a nature to render it likely that it would produce any
appreciable effect on the specific heat, as it was probably due to the formation of a
body whose properties were similar to those of aniline. I may add that Professor
Ramsay independently expressed an opinion to the same effect. My observations
show that no alteration in the specific heat of aniline had been indicated by the
change in colour referred to, and I am still of opinion that it may be regarded as a
liquid admirably adapted for calorimetric purposes, as it is but rarely that it would
be required for experiments extending over a period of months or years.

If I am able to carry out my investigations into the latent heat of evaporation of
water and other liquids according to the plan I have designed, it is probable that the
enquiry will occupy my leisure time for some years, and as the exact determination of
the capacity for heat of the calorimeter and contents throughout a large range of
temperature is a most laborious one, I was anxious to employ some liquid about the
constancy of whose composition I should have no anxiety.

At this time, Mr. THomas suggested to me that I should try a particular kind of
petroleum oil supposed to consist of hydrocarbons only. ‘This is a singularly limpid
oil, without colour, smell, or taste. I tested its insulating powers very severely over
a range of temperature 10° to 150° C., and although I placed two large electrodes
within a quarter of an inch of each other, and used a potential difference of 10 volts,
I could cause no permanent deflection in a high resistance galvanometer throughout
this range of temperature. Its specific gravity at 15° is °865, and, as I shall show
hereafter, its “volume heat” is smaller than that of aniline.t After several
experiments of different kinds, I came to the conclusion that this oil was a most
suitable liquid for my purpose.{

The replacement of aniline by oil necessitated a re-determination of the capacity

* IT propose to use the above term to denote the capacity for heat of any volume of a substance as
compared with the capacity for heat of an equal volume of water. The phrase has already been used in
a similar sense by Derxuy, ‘Chem. Soc. Journ.,’ 1893, p. 854.

+ This oil appears to me to be well adapted to many physical purposes.

t See note at end of this Section.

20 2

284 MR. HE. H. GRIFFITHS ON THE LATENT

for heat of the calorimeter and its contents throughout my range of temperature, and
as far as regards the purposes of the present enquiry, a great portion of my work on
aniline was rendered useless. The method employed during the aniline investigation
necessitated a repetition of the experiments with different masses of aniline and with
different electromotive forces. As, however, those experiments had given me a very
exact determination of the capacity for heat of the calorimeter itself throughout the
range of temperature 15° to 52° C., the whole of the labour had not to be gone
through again, for (the “water equivalent ” of the calorimeter being known) it was not
necessary, when using oil, to repeat the experiments with different masses.

In Appendix II., I give particulars of the method employed for determining the
capacity for heat of the calorimeter and contents at different temperatures.

The following table gives the results, and as the value of the specific heat of this
oil at different temperatures may be of use to other experimenters, I have also given
(in terms of a thermal unit at 15° C.) the capacity for heat (C,,) of calorimeter and
contents at temperature 6, (N scale), and the specific heat of the oil S,;. The mass of
oil (corrected to vacuo) = 474°02 grams.

TABLE III.
| a, Ow. S. -4830 + (0, — 20) x -00087, |
20 307°50 | -4830 -4830
| 30 312:38 | -4917 ‘4917
40 31779 | 5006 5004
50 323-14. 5092 5091

The tables in Appendix II. show that the numbers in Column III. are durect
experimental results, not “smoothed” in any way.

It is noticeable that the value of S, is a linear function of @, throughout the above
range, although the curvature of the line giving the capacity for heat of the
calorimeter is very marked.

Probably these results are correct to better than 1 in 1000 (see Appendix IT.), but,
as an inspection of Table II. will show, an order of accuracy of 1 in 10 would have
been sufficient. As, however, the accurate determination of C, and 8, involved (by
the method adopted) little more labour than an approximate determination, I thought
it advisable to ascertain the specific heat of the oil with accuracy.

Since Yq = C,, {(0 — 0”) + (dt —d”)} and C,, varied from 307 to 323, it is
obvious that if Sg was to be kept small, the changes in # and d must be very
limited, and that such changes must be measured with extreme care. Having
already described the manner in which the temperature of the surrounding walls was
kept constant, and the way in which any small variations in 4) were ascertained,
I now indicate the method of measuring the values of d’ and d” (ue., the initial and

HEAT OF EVAPORATION OF WATER. 285

final differences between the temperature of the calorimeter, 6,, and that of the
surrounding walls, 4,).

As differences of temperature had now to be dealt with, the use of differential
thermometers naturally suggested itself.

The following extract is taken from a full description of these thermometers given
in my Paper A. (see also Plate 6, fig. 2) :—

“Two platinum thermometers (labelled AB and CD) were constructed with great
care; four stout platinum leads passed down the stem of each, supported and
insulated in the usual manner by small disks of mica, and the resistance of all these
leads was made as equal as possible before attaching the coils. Great attention was
given to this matter, and it is probable that the leads in no case differed amongst
themselves by 1 in 10,000. The coils, consisting of a particularly pure sample
of platinum wire, were then attached, and several days were devoted to securing
their equality Their resistance in ice was about 18 ohms, thus ygoo of their
resistance could be directly determined on the box. The galvanometer swing was
about 500 for a change of ‘01 in the box; and such equality was secured that when
both thermometers were placed in ice (the necessary precautions being taken with
regard to exterior connections, &c.) no readable difference in the swing of the
galvanometer could be observed ; thus they differed by a quantity certainly less than
1 in 100,000. This equality, although not a necessity, was a great convenience.

“ Although cut from the same length of wire, and insulated in a precisely similar
manner, the coils did not possess exactly the same coefficients. The resistances in
steam and sulphur were repeatedly determined and checked by observations in the
vapour of aniline. Both thermometers were on several occasions heated to a red
heat, the hard glass tubes containing them becoming slightly bent in the process ;
but, since this annealing, no further change has been observable in them. The method
of completely standardising such instruments has been fully described by Professor
CALLENDAR and myself in ‘ Phil. ['rans.,’ 1891, A, and I need not, therefore, here
dwell upon it. The values of 6 differed slightly, viz, 1°513 and 1°511; but such a
difference, even if not allowed for, would, over the range 0° C. to 100° C., in no case
cause an error exceeding about 3,55 C. in elevation. These thermometers were so
connected that the compensating leads of AB were placed in series with the coil of
CD, and vice versd. Any heating of the stem of AB or CD, therefore, added an
equal resistance to each arm of the bridge; and, as the leads were everywhere bound
together, the indications were absolutely independent of all changes in temperature
except those of the bulbs.

“The two thermometers, with their leads connected as described, were placed at
opposite ends of a bridge-wire of platinum-silver. During the spring of this
year this wire was subjected to a most careful calibration by what was practically
Carey Fosrer’s method, and it proved to be more unequal than I had expected. It
was therefore re-calibrated by a different method in which a resistance-box was used

286 MR. £. H. GRIFFITHS ON THE LATENT

as a shunt, and the agreement between the results was satisfactory. The whole wire
was 80 centims. long and had a total resistance of about 0°4 ohm. For convenience,
and to avoid thermal effects, a similar wire connected with the galvanometer was laid
alongside it, and the sliding-piece was fitted with a screw so arranged that a small
turn of the serew-head made contact with both wires.

“The wire and contact maker were covered by a thick copper shield (the screw-
head projecting through a narrow slot) passing from end to end of the bridge. Thus
the temperature of the wire was kept uniform. By means of a vernier, the divisions
on the scale could be read to 3/5 millim., which with this wire and thermometers AB
and CD indicated at 50° C. a temperature difference of -600915° C. The temperature
coefficient of this wire was found to be (00029. The resistances of the different parts
of the wire were, after correction for the errors of individual coils, &c., merely expressed
in terms of the mean box ohm, the absolute value being of no consequence so long as
the fixed points were determined in terms of the same standard. The remaining two
arms of the bridge were constructed of german-silver. They were wound together,
boiled in paraflin, placed in a bottle, and I expended much care in finally adjusting
them until equal. Their resistance was about 5 ohms, and that of the galvanometer
about 8 ohms, which, assuming the resistance of the thermometers as about 20 ohms
each, would give nearly the maximum of sensitiveness. A single storage-cell was
always used, and a resistance of 40 ohms was placed in the battery circuit when the
thermometers were in ice. A table was then calculated which gave the resistance
necessary in the battery circuit when the thermometers were at any temperature in
order that C?R (where R is the thermometer resistance) should be constant. Thus
the rise in the temperature of the thermometer-coils due to current-heating was
always the same, and consequent errors were eliminated, a point to which I attach
considerable importance.

“The value of R, — R, in thermometer AB was 6°88815; therefore a difference of
1 ohm at 50° C. indicated a difference of 14°°5177 C., and as

dpt 2t — 100
ii = 1 — 8 i002 i,

the degree value of any bridge-reading at other temperatures can be deduced.

“There was no difficulty, in the arrangement above described, of reading with
certainty a difference of yo'99° C., and, as an illustration, | may mention the fact that
if the thermometers were placed in separate hypsometers side by side on the bench
and one of the hypsometers was then removed to the ground (about 3 feet below),
the difference in the bridge-wire reading thus caused slightly exceeded °4 millim.”

In the paper above referred to, further particulars are given regarding the
standardisation of these thermometers. During the experiments there described
they were used to determine the rate of rise in the temperature of the calorimeter,
whereas, in the work I am now describing, they were used chiefly as detectors of any

HEAT OF EVAPORATION OF WATER. 287

difference of temperature between the calorimeter and the surrounding walls, and I
therefore omit the details of the determination of their fixed points, &c., although I
must add some other facts which are of importance for the present purpose.

The bridge-wire scale was so fixed that the mark 60 centims.* fell exactly in the
middle. Had the bridge-wire been uniform therefore, and had the coefficients of the
two thermometers been always the same, then when both were at the same tempera-
ture the bridge-wire reading would necessarily have been always 60 centims. I
have stated that the thermometer resistances might be regarded as practically equal
when both were in ice. The bridge-wire reading, however, was found to be 598°35
millims., when AB and CD were both in ice. At first sight this appeared to indicate
a difference in the resistances of the two thermometers at 0°, but when the
calibration of the bridge was concluded, it gave 5984 millims. as the middle point of
the bridge and thus afforded independent proof of the truth of the calibration and
of the equality of the coils forming the other two arms of the bridge. Owing to the
slight difference above referred to in the coefficients of the two thermometers the
reading of the bridge null-point was found to be 601°4 millims. when both thermo-
meters were at 100°. Now (as described in Paper A.) the fixed points of these
thermometers in ice, steam, aniline, and sulphur-vapour, had been repeatedly
determined with extreme care. I have, since the conclusion of these experiments
(z.e., on November 4), again taken the values of Ry and R,—ice and steam. They
remain practically unchanged and are as follows :—

AB. CD.
Raine 41) 24558526 2.4°58333t
Rp oe 4 IAGRVALT 17°69720
R, — R,= 6°88815 6°88613

Thus the difference between AB and CD would, when in steam, exceed their
difference in ice by ‘00198 ohm. Now the value of 1 millim. of the bridge-wire at
reading 60 was 1:0020 times the mean bridge-wire millim., and the value of the
mean bridge millim. was ‘00062875 box ohm. Thus 1 millim. of bridge-wire at
60 = ‘0006300 box ohm. Hence the movement of the two thermometers from
ice to steam ought, according to the standardisation, to have caused a movement
of 42° millims. = 3°1 millims. On placing both thermometers in steam at 100° the

63
actual bridge-wire reading was found to have altered from 598°35 to 601°40, a

* The scale was marked from 20 to 100 centims.
+ Expressed after correction for individual coil errors, &c., in terms of my ‘ mean-box” ohm
(Paper J., p. 409). The absolute values being of no consequence, I have, in order to save arithmetic,

expressed the resistances of all my platinum thermometers in ‘‘ mean-box’”’ ohms.
yP

288 MR. E. H. GRIFFITHS ON THE LATENT

change of 3°05 millims.; thus, entirely independent methods agree in giving the
following formula as a sufficiently close approximation for the bridge-wire null-point
at any temperature @, viz.,

N.P. = 598°35 =F ‘030.

True, the coefficient of @ should be slightly larger, but I did not profess to read the
vernier to nearer than ‘05 millim. during the calibration of the wire, and therefore
any closer approximation would be useless.

As even a small difference between the average temperature of the calorimeter
and the surrounding walls would have some effect in experiments lasting more than
an hour, the agreement between the results obtained by the different methods above
described was extremely satisfactory. In addition [ carried out a series of observa-
tions with both thermometers strapped together and immersed in the rapidly-
stirred tank water, the temperature of which was gradually raised from 15° to 54°,
and the position of the bridge-wire null-point was found throughout that range to
be accurately given by the above formula.

The galvanometer was observed by means of a microscope fitted with a micrometer
eye-piece by Zeiss. The swing was very ‘dead beat” and very uniform for a
given D.P. The ;'oth of a division could be estimated without difficulty by anyone
accustomed to the instrument, and it was found more convenient to read and enter
swings with 75th of a division as unity rather than to express the fractions as decimals.
Thus a swing of 2°5 divisions was entered as 25. I mention this as otherwise
the swings given in the tables might appear curiously large. Occasionally the
swing due to a change of 1 millim. in the bridge-wire reading was observed, but as
the E.M.F. used was constant, and the galvanometer control-magnet was not
re-adjusted during these experiments, the swing for a given change was found
to remain practically constant when the temperature of the thermometers was
unchanged. As the resistance of two arms of the bridge altered when @ altered, the
swing varied slightly when @ changed, but the arrangement, above described, for
keeping C’R constant, diminished the extent of this change. A swing of 90 corre-
sponded to a change of 2 millims. in the bridge-wire reading when 6 = 40°, and the
swing at 30° was about 94.

The swing was of course obtained by reversing the battery connections and was
thus independent of thermal effects, changes in the position of the galvanometer
zero-point, &¢,

Now, as above stated, a change of 1 millim. of bridge-wire about the reading
60 centims. indicated a difference of ‘0006300 box ohm. If therefore the bridge-
wire reading was at the null-point a swing of 10 indicated a difference of § of
‘0006300 = -000140 ohm in the resistance of the two thermometers.

The following Table (calculated from the constants of the thermometers by means

HEAT OF EVAPORATION OF WATER. 289

of the formula on p. 286) gives the change in temperature (on the N scale) corre-
sponding to a change of 0°1 box ohm in thermometer AB*.

TABLE LV.
: = a i
| Temp. | AR (box ohms). | A pt. AO.
| |

| ° | ° °
| 20 | 0-1 | 14518 14387
| 30 | 01 14518 14430
| 40 | O-1 | 14518 14474

50 0-1 | 1-4518 14518

Now the value of the mean millimetre of the bridge-wire (at temperature 15°) was
00062875 box ohm, hence the following Table which (col. 2) gives the difference in
@ indicated by a difference of 1 mean bridge-wire millim. from the bridge-wire null-
point at the given temperature, and (col. 3) the difference in temperature indicated
by a swing of 10 when the contact-maker is on the null-point.

TABLE) Vic
] i }
| .

| ‘Temp. DOOD IE rence Ona meet |) “Noltorlswing of 10:
| _ baw.

o ° O°

20 0:009046 0-001865
| 30 0-009073 0:001930
| 40 0:009101 0-002022
| 50 0:009128 0-002074

Before an experiment, the contact-maker was set, with the aid of a magnifying
glass, to the exact null-point corresponding to the temperature at which the experi-
ment was to be conducted, and it was left untouched throughout the experiment.t

The initial and the tinal swing rarely exceeded 30 or 40, and could certainly be read
with a limit of error of 2, when only one observation was taken, and as, at these
times, three observations were meaned (they were, by the way, usually identical), the

* As AB was the thermometer immersed in the calorimeter it is with changes in its. temperature
that we have chiefly to do.

+ An error of ‘05 millim. in the setting of the bridge-wire contact-maker would correspond to a
difference of 000455" at 40°, and the radiation, &c., due to such a difference would be negligible. The
radiation, &c., coefficient of this calorimeter when full was about ‘00009 per l° per sec., or the loss in
temperature due to a difference of 1° would be about ‘324° = 100-4 thermal grams per hour (assuming
the capacity as 310), thus a difference of ‘01° throughout an experiment would have caused a loss or
gain of 1 thermal gram. Of course, the differences in temperature rarely attained to ‘01°, and again, the
differences were alternately + and —, so that the radiation, é&c., loss or gain was evidently negligible.
The radiation, &c., coefficient can be deduced from the experiments on the rate of rise made when
determining the value of Cs, (Appendix II.).

MDCCCXCV.—A. 24 1

a

290 MR. E. H. GRIFFITHS ON THE LATENT

probable error was certainly less than 2, and, I believe, less than 1). Assume the
probable error to be as great as 2, it follows that the differences of temperature
could be determined to :0004°, and I am confident that differences of :0001° could
be detected.

There can be little doubt therefore that the quantity =q¢=C,, {()— 6) + (d’—d’)}
could be determined to a far higher degree of accuracy than subsequent experience
proved to be necessary.

Norr.—December 4, 1894. At Mr. Heycocr’s suggestion, I have to-day tested
as follows the oil supplied to me by Mr. Tomas, and referred to in the preceding
section. We placed a lump of sodium in a test-tube filled with the oil, and gradually
raised the temperature to above 160°C. No action whatever was visible, and the
surface of the melted sodium remained as bright as that of pure mercury. We may
assume, therefore, that the manufacturers are justified in their statement that it
consists of hydrocarbons only, and the probability that different samples would
possess approximately the same composition is sufficient to make the determination

of its specific heat of some value.

Section VII.—TuEe Heat DUE TO THE STIRRING (Q,).

I have already pointed out the necessity for rapid stirring. Throughout these
experiments the stirrer revolved at a rate of about 310 to 320 revolutions per minute,
which is a slow rate as compared with that adopted during my enquiry into the value
of J. The conditions, however, are different. In my former work I had at times to
make observations with the calorimeter only partially filled with liquid, and I found
that unless the water was thrown over every part of the calorimeter, its capacity for
heat varied with the depth of the liquid. Throughout my present work the calori-
meter was full, the liquid almost touching the lid, and, in consequence, I considered
the slower rate sufficient to ensure an even distribution of temperature.

In my aniline experiments previously referred to, I eliminated the effect of the
stirring-heat by finding the temperature (Ax) at which the stirring supply exactly
balanced the loss by radiation, &c., and thus the rate of rise at @, enabled me to
determine the effect of the electrical supply. As throughout my observations on
latent heat I had to maintain the temperature of the calorimeter at an equality with
the surrounding walls, this mode of elimination was not applicable.

Two methods of finding the value of the mechanical supply suggested themselves.

I. That of finding the mass of water which it was necessary to evaporate per hour
in order to maintain the calorimeter at a constant temperature, when the supply of
heat was that due to the stirring only.

II. That of determining the rate of rise across the null-point (a) when the heat
supply was that due to stirring only ; (b) when the heat was due to the stirring and

a given potential difference.

HEAT OF EVAPORATION OF WATER. 291

I. I made a large number of determinations by this method, especially during the
“preliminary experiments,” of which an account is given in Section IX., where the
evaporation was promoted by passing a current of dry gas through water.

As I shall give details of the operations when describing the “ preliminary experi-
ments,” I will not enter into particulars here, but I may now mention that the results
by this method were by no means satisfactory, either as regards the determination of
the stirring heat supply (Q,) or of the values of L. The discrepancies in the value of
Q, are, however, not alone sufficient to explain the comparative failure of this method
of finding L, for when both the rate and the temperature were the same, the varia-
tions in Q, never attained to 1 in 20, and as Q, was but about one-hundredth of the
total supply, the approximation was nearly sufficient. I omit any detailed account of
these experiments, as I made no use of them in my final calculations, and it would
needlessly fill much space. I will, however, give the conclusions they led to, as they
corroborate the results obtained by the method finally adopted.

Let
m; = mass of water evaporated per 1 second by the stirring supply,

and
7 = the rate of stirring (7.e., number of revolutions per second).

When @, diminished, the value of m, increased, and this rate of increase was much
greater after the aniline was replaced by oil; the change being evidently due to the
increase of viscosity as the temperature diminished. When the stirring took place
in aniline m, varied very nearly as 7’, but when oil was the liquid m, varied nearly
as 7,

In a former paper* I have proved that when the liquid was water the stirring heat
varied almost exactly as 7?, and I gave particulars of 108 experiments bearing out
that conclusion. Again, in Paper A., I have shown that when using aniline with a
different form of stirrer Q, 0 7? approximately. Now with the same stirrer as that
used in aniline we get with oil Q,~«7*; at 50° the power of 7 should be slightly
higher, at lower temperatures rather smaller. These differences, although surprising,
are none the less real.

In the case of water the conditions were so different (e.g., 7 was about 30 instead
of about 5) that no comparisons could be drawn, but, in the case of the aniline and
the oil, the conditions were almost identical. My incredulity with respect to the
relations between Q, and 7 led to considerable delay, as I repeated these experiments
unnecessarily, and it was not until a different method of observation led to the same
conclusion that I felt any confidence in the results.

II. I now pass to the method indicated in II. (supra), in which no weighings were
involved, and where I was also able to dispense with the passage of air through the
apparatus,

* Paper J.
2P2

292 MR. E. H. GRIFFITHS ON THE LATENT

Let ¢ be the time of rising through a small range of temperature from below to
above the surrounding temperature (6).

If the heat supply is in one case due to both an electric current and the stirring,
and in another to the stirring only, we have

(d6,/dt)., — (d0,/dt), = (d0,/dt). .... - = 2 ey

where 6, is the temperature of the calorimeter, and the suffix denotes the nature of
the supply.
And (using the notation on pp. 272 and 273)

(d0,/dt), = Q./C,,, and (dé,/dt), = Q,/C,,
therefore

Qe (dO, /dt), Ey
Ce CCC Perna (TIT),

Eq. (II.) will be true on any scale, and thus it is unnecessary to convert the
bridge-wire readings into degrees C., and since

Q;=70. eo os) ee eee

if e, n, and R, be known, we can find Q,, for
QrS er Ry 2 ee. oe

Thus Q, can be found, although the capacity for heat of the calorimeter and
contents and also the scale of temperature are unknown.
If we convert the bridge-wire degrees into C. degrees (N. thermometer) then, since

(d0,/dt)., — (d0,/dt), = Q./C,,

we get

m2 Qe
Co = (ja. — (dB, ]dl), Ree oi)?

and thus C,, can be found.

In Appendix I. I give particulars of the experiments by which the values of Q, for
different values of 6, were found. I regret that the observations are so few in
number. Unfortunately I did not adopt this mode of experiment until the eleventh
hour, and as these experiments were very lengthy, I should consequently have been
unable to complete sufficient direct determinations of L to establish its value at the
two points to which want of time compelled me to limit the investigation.

On comparing the results with those obtained in oil by the previous method,
I found that the agreement was sufficiently close to warrant a postponement of further

HEAT OF EVAPORATION OF WATER. 293

investigation on this point, and I am confident that the values of Q, given in the
following table are correct to better than 1 in 50, at temperatures 30° and 40°, although
T am less certain about the values at 20° and 50° C.* The latter, however, are not
required for the purposes of this paper, except in so far as they affect the specific heats
of the oil in Table ITI.

Taste VI.—Thermal grams per sec. (Q,) at rate (7) 5°300 revolutions per sec.

| 6. Q.. e —Hies
50 ‘00235 298 x 1078
40 -00466 590 x 10-8
30 ‘00665 843 x 10-8
20 -00834 1056 x 10-8

Let Q’, be the thermal grams per second due to a rate 7.

Then
Qifrt = Qfrt = b,
therefore
Y.-—Q, =k(rt— ry,
therefore
OF SOT (Gr Sine aie te alt ek Gs)
Hence

Temperature 40°, then Q’, = ‘00466 + (7, — 789) x ‘0000059.
ee 30m as Q’, = 00665 + (ae! — 789) x 0000084.

I do not, of course, suppose that Q, = fr* is the exact relation. I have already
indicated that 7* was too small at high, and too great at low temperatures. It must
be remembered, however, that the variations in 7 were small, and thus the relation is
sufficiently close for the correction of such variations as occurred during these
experiments.

If we assume that the work done (for a given value of r) is proportional to the
viscosity, the values of Q, denote how great a change in viscosity is produced by

raising the temperature from 20° to 50°. I repeat, however, that the values at 20°
and 50° must be regarded with suspicion.

* I have no corroborative experiment (by the former method) at 20°, and only one at 50° (see
Appendix IT.).

294 MR. HE. H. GRIFFITHS ON THE LATENT

Section VIII.—MEAsuREMENT OF THE Heat DEVELOPED BY THE CURRENT (Q,). ©

A sketch of the electrical connections is given in Plate 6, fig. 3, and a full
description will be found in Paper J., pp. 382-388, therefore I will here give only a
brief description.

Measurement of E.

Leads marked 2 and 4 were connected with the storage cell circuit, leads 1 and 3
with the Clark cells. A special form of rheochord was used consisting of two long
barometer tubes (7 feet in length), which were so arranged that they could be raised
or lowered by the rotation of handles; thus the length of the vacuous space could
be altered at will. Platinum wires passed down these tubes into the mercury.
The wires were placed in parallel arc and thus one acted as a shunt to the other.
The change in resistance depended, therefore, not only on the movement but on the
ratio of the two resistances, and the instrument could be set so that a large move-
ment caused but little change, or vice versd. The contact between platinum and
mercury i vacuo was found to be very satisfactory. The resistance of the storage
circuit could thus be altered at will. The Clark cell circuit contained a high
resistance galvanometer G,, with a resistance of about 9000 ohms, and joined the
storage circuit at the roof of the calorimeter (at M and N, small sketch, Plate 6,
fig. 3). By adjusting the rheochord the ratio of the external resistance of the
storage circuit to the coil resistance could be altered at will, so that the D.P. at the
ends of the coil became equal to that of the Clark cells, and the balance was
maintained by watching the indications of G,, and, when necessary, adjusting the
rheochord. The spot of light from G, passed down a tunnel 4 feet in length on to a
sheet of ground-glass placed opposite the rheochord. In Paper J., p. 384, I have
given the experimental numbers on which the following statement was based :—

“Tt thus appears that the variations in E (the potential difference at the ends of
the coil) were certainly within yo90o00 of the mean value during the experiments,
and changes in E, consequent on changes in the coil resistance, or the E.M.F. of
the storages, could be disregarded.”

The effect of any error in determining E would be serious (the quantity EK? being
used in the reductions), and hence its accurate measurement was of great importance.
Tam satisfied, however, that (assuming the value of E for the Cavendish standard
Clark cell to have been accurately determined) no error in the measurement of Q, is
due to uncertainty as to the potential difference. The thirty-six Clark cells used
have been fully described, in Paper J., pp. 385-388, as well as in the Paper by
Messrs. GLAZEBROOK and SKINNER.* They have been compared with each other at
regular intervals up to the present time, and their relative changes are small. At
least three of these cells were always placed in parallel arc. Sometimes when

* «Phil. Trans.,’ A, 1892, pp. 622-624.

HEAT OF EVAPORATION OF WATER. 295

working with a D.P. of four cells at least sixteen were really in use. Throughout
these experiments they were maintained at a temperature close to 15° C., by a
regulator which warmed the tank when below 15° C. and turned tap-water through
the tank when above 15°C. As full particulars are given in the pages of Paper J.,
I think the above summary will be sufficient.

There is one alteration in the electrical connections to which I wish to draw
attention. In former experiments some time always elapsed, after the current was
established, before any observations were taken. It, however, appeared probable that
in this work I should occasionally have to cut off and put on the current during an
experiment. For some time after the establishing of the current, a constant
re-adjustment of the rheochord was required, as the temperature of the wires, &c.,
forming the external circuit was gradually raised, and the external resistance in
consequence increased. During this period of adjustment the balance could not be
as accurately maintained as when the temperature of the external wires had become
steady. In order to avoid this preliminary adjustment, a coil of the same wire and
resistance as that in the calorimeter was constructed and placed in a tube containing
the same oil as that in the calorimeter, and this tube was fixed in the tank at F
(Plate 6, fig. 3).

At k, a key was so arranged that one movement brought the storages into
connection with the calorimeter coil by means of leads 2 and 4, while another move-
ment caused the current to leave the calorimeter circuit and pass through F. A
second key (not shown in fig. 8) enabled the Clark cell to be also connected to F.
The current was sent through F for 10 minutes or so and the balance adjusted, before
an experiment commenced. On moving the key at ,, the current was switched on
to the calorimeter, the Clark cell circuit was then also shifted and the balance once
more made perfect. Thus the current through the externals was kept constant
whether it was passing through the calorimeter or not, and therefore the rheochord
required far less manipulation.

Again, the key k, was so arranged that whenever the current was shifted, a
connection in a chronograph circuit was established, and thus the times of “making
and breaking” the calorimetric current were automatically registered. True, the
marked time was in each case a fraction of a second before the “ make and break,” but
the actual duration of the intervals was truly recorded.

Measurement of Ry.

The holes in the paraffin blocks P, and P, (Plate 6, fig. 3) contained mercury.
Connection could be made by two cross pieces of copper rod, between either of the
slots in P, and any of the holes in P,. These copper rods, when in position, rested on
the wires which passed through the bottom of the holes. Denoting the resistance of
the coil by Ry, that of the leads from P, to the lid of the calorimeter by 7, 7, 73, 4;

296 MR. E. H. GRIFFITHS ON THE LATENT

it is evident that by a movement of the connecting rods, the following resistances
could be taken, viz. :—

Mtr, MYR +75, ro + B+, 73 +7)
If N,, N,, N3, and N, are the resulting numbers, we get
R, = {(N, + Ns) — (Ni + Ny) }/2,

and there is no necessity that 7, 7, 73, and 7, should be equal. The value of R, was
always obtained in the above manner, and then expressed in terms of the box ohm at
17°. A full account is given in Paper J., pp. 407-410, of the comparisons of the
individual coils of my resistance box with the B.A. Standards, and the values of R,
were reduced to true ohms in the manner there indicated, with the further corrections
given in a later communication.*

In Appendix III. I give an example of an observation together with the reductions.

It was next necessary to find the increase in R, (6R) due to the rise of temperature
caused by the current. This was done in substantially the same manner as that
described in Paper J., pp. 404-407 ; dR was in this case found to be very small—as
shown by the following table.

TasBLe VII.

Potential difference |
in terms of a ok.
Clark cell.

“00076
00198
00377
00630

HE 0 Doe

The resulting curve was (as in other similar cases) practically a parabola.

A further correction was necessary for the heat developed in leads 2 and 4 in the
portion that passed from the steel to the calorimeter lid. Their total resistance was
0068. We may assume that half the heat here generated passed into the calorimeter,
and therefore consider their resistance as ‘(0034 ohm = 7. Now the points kept at a
constant D.P. were between these wires and the coil, and since JH = E?/R (1+7/R) 4,
we get the effective resistance = R — 1.

The following table gives the values (after the application of all corrections) of R,
at the temperatures at which the L experiments were performed, the potential dif-
ference being denoted by the suffix.

* “Roy. Soc. Proc.,’ vol. 55, p. 25.

HEAT OF EVAPORATION OF WATER. 297

Taste VIII.
| Temp. Ro. | Rye. Ree. Ry.
|
20 103246 i 10:3266 103284 10:3309
30 10-3482 | 10-3502 10-3520 10-3545
40. 103720 | 10°3740 103758 10:3783
50 10-3966 10-3986 10-4003 10-4028

dR, per 1° C. = 0024.

This coil has shown no signs of any change throughout its history.

As Q. = (ne)?/R,J, I have now indicated how the value of Q. could be accurately
ascertained.

Had full details of the method not been given in previously published papers, it
would have been necessary for me to give further particulars as to the various
measurements.

There can, I think, be little doubt that the value of Q, could be determined with
great certainty.

I have already (see p. 272 supra) pointed out that even if my value of J (4:199 x 107)
be in error, it is the correct value to use for these experiments, and that even if e
(the D.P. of a Clark cell) and the units in which R, is measured (7.e., the value of a
“true ohm ”) are in error, the results are unaffected, provided that no changes have
taken place in my Clark cells, or the coils of the resistance box since they were used
for the determination of the value of J.

[ Note, May 4, 1895.—During the spring of this year my Clark cells were carefully
re-compared with the Cavendish standard, RI. Comparisons were made at regular
intervals, and Mr. Skinner was so kind as to take some independent observations.
The differences are expressed in hundred-thousandths of the E.M.F. of the standard.
The highest of the thirty cells exceeds R I by 40 such units. The lowest is less than
RI by 36. The mean value of the whole set is less than RI by 3 such units (7e.,
by 000004 volt). Thus, although the individual cells show larger discrepancies than
in 1892-4, the mean value is almost exactly that of the Cavendish standard. The
previous history of that standard shows that it had remained unchanged during the
interval of eight years which had elapsed between the absolute determination of its
E.M.F. by Lord RaytercH in 1883, and that by Messrs. GLAzEBROOK and SKINNER
in 1891. There is no reason to suppose that it has altered since the latter date, and
this conclusion is borne out by comparison with other standards at the Cavendish
Laboratory. I think, therefore, that I am justified in assuming that the mean E.M.F.
of my cells remains practically unaltered.

Cells 37 to 42 have been compared at Manchester by Professor ScuusTeR with his
standard. These six have the highest mean E.M.F. of any of my sets. Their mean
value exceeds RI by 22 units, and they exceed Professor ScuusTER’s standard by

MDCCCXCV.—A. 2Q

298 MR. E. H. GRIFFITHS ON THE LATENT

70 units. It would thus appear that R I exceeds Professor ScHustTER’s standard by
48 units, 7.e., by about 0°0007 volt. It must, however, be remembered that between
these comparisons the cells had been subjected to several transits by railway. |

Measurement of Time.

The chronograph was controlled by the electric clock described in Paper J. (p. 414).
The clock has remained untouched from July 16th to the present day—November 18th,
and during that time it has gained 12 minutes, z.e., a gaining rate of about 1 in 15,000.
The gain has been regular throughout the interval, the clock being singularly indifferent
to small changes of temperature. I therefore consider that the measurements of time
require no correction.

Section [X.—TuHeE ResuLtts oF EXPERIMENTS IN WHICH EVAPORATION WAS
PROMOTED BY THE PASSAGE OF A GAS.

I have hitherto referred to the experiments I describe in this section as “ pre-
liminary” for want of a better name; but I had originally hoped that the method
would have given satisfactory results. Although these experiments have had but
little influence on my conclusions, I will briefly describe them, as I am yet at a loss to
account for their comparative irregularity.

Dry air, or other gas, was forced in a continuous stream through the water 40 be
evaporated ; the cooling thus caused was balanced as before described, and the weight
of water evaporated determined by the increase in weight of drying bulbs. I wished
to adopt this method, because by adjusting the flow of air the rate of loss of heat
could be (by proper arrangements) regulated with nicety, and the thermal balance
maintained with great accuracy. When water is made to boil by diminished pres-
sure, the regulation of the cooling presents many manipulative difficulties that I was
anxious to avoid.

The experiments were conducted as follows. About 20 cub. centims. of water were
placed in the flask F (Plate 6, fig. 1),* the water force-pump set going, and the air
first passed through the H,SO, bottles and “tower” S, then through the U-tube
and drying tower P—both containing P,O;. It then passed through the 3-way
tap (T,) into the 30-feet copper coil (C,) in the tank water, thus attaining the tem-
perature 6, of the tank, and after traversing the immersed tap T;, bubbled through
the water in the silver flask. The air and vapour now rose up through the 18 feet of
silver coil (C,) within the calorimeter, passed out through the 4-way tap (T,), which
was opened in such a manner as to direct the air current into some H,SO, bulbs (not

* This figure is diagrammatic only, and conveys no idea of dimensions or actual position. For example,
the coil C, surrounded the steel vessel, and the 4-way tap T, was on the same side of the apparatus as
the tap T,. The pipes, &c., crossed and re-crossed each other in such a manner as to render any direct

representation. impossible. The drying bulbs and connections are not indicated in the figure, as they
were afterwards replaced by the condenser (B) and manometer (M,).

HEAT OF EVAPORATION OF WATER. 299

shown in figure) containing the same depth of H,SO,as the bulbs to be weighed.
Thus when T, was afterwards so turned as to change the direction of the current to
the weighing bulbs, no alteration tock place in the rate of flow, which was adjusted as
required in the following manner. A T-piece (not shown in sketch) was inserted in the
tube between the drying tower P and the tap T;. The vertical leg of the T-piece was a
wide graduated tube, open at its lower extremity, and immersed in a deep, narrow
vessel (a hydrometer jar) filled with H,SO,. If the air pressure within the pipes was
greater than that due to the column of H,SO, above the open end of this leg, the
excess of gas bubbled up through the H,SO, and escaped into the open air. Thus by
raising or lowering the vessel the pressure and quantity of air passing through the
whole apparatus could be regulated with exactness. I found it possible to so adjust

the flow that when the heat supply was Q. and Q,, the galvanometer showed no
change for nearly an hour. A further advantage of this arrangement was that I could
close any tap without increasing the pressure within the apparatus, the whole of the
gas then passing out through the regulator. The pressure of the gas near the flask
was read on the manometer M,, which had two wide bulbs near the base, the mercury
filling the lower bend and three-quarters of the bulbs. The narrow tube on the scale
side contained water resting on the mercury, and thus a very open scale was obtained.
The instrument was carefully standardised, and a movement of 7°78 centims. in the
water level corresponded to a change in the pressure of 1 centim. of mercury. The
water was completely cut off by the mercury from all] communication with the gas
tubes.

The electric connections having been made and the rheochord adjusted until the
high resistance galvanometer (G,) showed that the D.P. at the ends of the coil was
that of the Clark cells (I shall speak of this hereafter as the “ electric balance,” and
of the adjustment of the loss or gain of heat as the “thermal balance”), the gas flow
was then diminished until the platinum thermometer galvanometer showed that 0,
slightly exceeded 4, (#; = calorimeter temperature, 6, = temperature of surrounding
walls). The current was then switched on to the alternative coil F (fig. 3), 6, now
decreased and at the moment when 6, = 6, the current was switched back again,
the key itself recording the time on the chronograph tape. About the same time,
the 4-way tap T, was turned so as to cause the escaping gas to pass through the
weighing bulbs. This time had not to be recorded, nor was there any necessity that
it should be nearly or at all coincident with the time of establishing the electric
current. If, however, 6, did not exactly equal @, at the moment of turning T,, the
swing of the galvanometer was recorded and the tap only closed at the end of an
experiment when the swing was identical with the initial one.

When necessary the thermal balance was maintained for 1, 2, or, in some cases,
3 hours by adjusting the flow of gas. At the close of an experiment 0, was again
allowed to rise slightly above 6), the current: switched off (again itself recording the
time) and as @, descended the tap was turned back to its old position when 0, = 6,,

2Q 2

300 MR. E. H. GRIFFITHS ON THE LATENT

or when the swing was the same as the initial one. The taps T, and T,, were then
turned so that the dry air instead of passing through the tank, &c., went straight
through T, to the weighing bulbs, and thus any moisture left in the connecting tubes
was swept into the bulbs.

The swing of the galvanometer was rarely as much as 50 (indicating a difference of
about 0°01 between @, and @) throughout one of these experiments, and when such
oscillations occurred care was taken to alter the adjustments so that a swing to the
right was invariably followed by a similar swing to the left. The whole apparatus
could easily be managed by two observers and, on occasions, it was unnecessary to
make an alteration of any kind for half-an-hour at a time.

As before stated, the stirrer automatically recorded on the chronograph tape the
time of each 1000 revolutions.
The weighing bulbs were of peculiar construction and specially designed for this
work. The gas passed through four washings of H,SO, and then through a tube of
P,O;, on the further side of which was attached a CaCl, tube. The latter was not
included in the weighings, but only used to prevent any access of the laboratory air
to the P,O; when the gas current was not passing. The weighing bulbs were
connected with the exit tube by a mercury trap* and had simply to be lowered into
place, no. fitting of rubber tubes being necessary. To avoid condensation, the
mercury trough and also the whole of the exit tube exterior to the tank were

maintained at a temperature above 6, by means of small gas jets.

At the close of an experiment the weighing-bulbs were removed (with their precisely
similar tares) to the balance case. A careful weighing was made about an hour
after the experiment, and again next morning; an apparent increase of about °0005
gram generally presenting itself.

As (especially in the stirring experiments) small differences in weight had to be
measured, I took every precaution I could devise, and I also followed the suggestions
of friends whose experience in this matter was greater than my own. The balance
was a short-beam one by VERBECK and PEcKHOLDT, and was constructed so as to give
aswing of 2°5 divisions per 1 milligram when loaded up to 500 grams. The actual
weights to be measured were about 120 grams. I made special efforts to keep the
temperature of the balance case steady, and noted the effects of changes in tempera-
ture on the ratio of the arms, etc.

The weights used were by Messrs. OFRTLING, and re-standardised by them last year.

The increase in weight during the electrical experiments varied from ‘8 to 3°5 grams,
the increase during the stirring experiments from ‘06 to ‘08 gram.

I think it certain that the weighing error was neverso much as ‘002 gram, and it
was probably much less; thus I do not believe that any discrepancies in the values of
L greater than 1 in 1000 can be due to errors of this description.

As before described (p. 291) the mass of water evaporated by the stirrmg supply was

* Neither bulbs nor trough are shown in fig. 1, Plate 6.

HEAT OF EVAPORATION OF WATER. 301

determined in a similar manner. Thus, if m, be the mass evaporated per second by
the stirrer, we have (using the same notation as before)

ML — mt, = Qt. + %¢.*

I spent some weeks over these experiments, but the results were so uncertain, that
at last I was compelled to give up all hopes of attaining my object by this method.
I will therefore omit details and give results only.

TABLE [X.—Evaporation Caused by Passing Dry Gas.

| Date. ae - malls : Temperature. L. Remarks.
5) © 5 Bu 5
September Z : 3 cals ae \ Calorimeter filled with aniline
cistevrsleli. 1 50:01 566:6
Preriil 3 50:00 566°3 : ey eer
Ss lide 2 50°00 567°8
Mean . 49°82 566°5
August 29 . 2 39:98 5769 5]
i 29 al 39:97 572:2
el 2 39-98 5745
PEUSIONS 1 39°98 572°9 - Calorimeter filled with aniline
September 2. 1 39:99 569°8 |
= 2. 2 39°99 5729 )
A 2S 1 39°98 5699 3)
5 12 3 40:0] 5722
| = 12 2 40:00 569°4: Oil in calorimeter
+ 13 Z 39°98 - 572°7* *Nitrogen passing
Mean. 39°99 572°4
| August 19 . If 24°97 582°6 a)
a5. AG 1 24°96 580°6 |
ononeietie e'4Y 1 24-96 584-2
53 cig22 1 24°96 o81°7* *Nitrogen passing
op ee 1 24-97 580°0 >Calorimeter filled with aniline
em er. aes 1 24°97 584°7 :
ayaa. 1 24°95 5815
sy ey 1 24-95 580°3
| # 128 1 24°95 581-4 J)
‘Mean .| 24:96 | 581-9

* %q in this case = Ca, {(0', — 0) + (d' —d")} + C'o, (T’ — T") where C's, is the ‘mean mass” of
the water in the flask, and T’ and T” the initial and final temperatures of that water as indicated by the
flask thermometer G, i

302 MR. E. H. GRIFFITHS ON THE LATENT

I have included in the above table all the experiments with the exception of two,
which were performed on the same day (September 3rd), and whose extreme diver-
gence from the others led to the discovery that the insulation of one of the leads had
fallen off. In consequence, the value of R, was uncertain. Between September 3rd
and 11th the whole apparatus was taken to pieces and fitted with new leads and
insulators. From this time onwards the calorimeter was filled with oil in place
of aniline (see Paper A., p. 77).

I think it is evident that the discrepancies are greater than can be accounted for
by errors in weighing, as they sometimes amount to nearly 1 per cent.

I at first suspected that some moisture was escaping uncaught by the weighing
bulbs, or that the entering air was not dry. I believe, for two reasons, that this was not
the case. (1) The P,O; bulb, through which the gas finally passed, in no case increased
in weight by as much as 0°0040 gram, and usually only by about 0°0020 gram, which
showed how completely the moisture had been removed by the H,SO, (2) Before
entering the apparatus the gas passed also through H,SO, and P,O,, therefore any
quantity of moisture which escaped these drying agents would be likely to also escape
the similar agents at the exit-end, and thus would not affect their weight. I had
good evidence that this was the case, for I thoroughly dried the flask and tubes at a
temperature of 40°, and then passed the gas through the apparatus into the weighing
bulbs for an hour and a half; but the increase of weight in that time was not as much
as 0005 gram. Again, if the gas was more completely dried at one end than at the
other, the effect would have been to make all the values of L too low or too high. nOn
course, I was entirely in the dark at the time of these experiments as to the real
value of L, but I now find that the mean of each group gives a close approximation
to the true value, hence there was no permanent raising or lowering cause at work,

It will be noticed that the rate of flow of air was greatly changed during these
experiments ; when three cells were used the rate of evaporation had to be nine
times as great as when the D.P. was that of one cell. Inspection of the table will
show that the variations in the values of L do not appear to be functions of the rate.

For some time I fancied that “ priming” might be taking place, but, if so, the
experiments with a rapid flow would probably all have given lower values than those
with a slow flow, the carrying of particles of unevaporated water being much more
probable when the velocity of the gas current was increased nine times.

Again, it has been suggested that, as the pressure of the gas diminished during its
passage through the apparatus, some heat would in consequence disappear. I would
point out that the only constricted portions of the passage (after the air had once
entered the tank) were within the calorimeter, and, if all the work done by the gas
was performed within the calorimeter, the cooling, owing to expansion, would be just
balanced by the warming of the tubes at the constricted points. Also, a persistent
lowering of the values of L would be caused, and (as above pointed out) I now find
that such is not the case. To test this matter at the time, however, I observed the

HEAT OF EVAPORATION OF WATER. 303

rate of rise due to the “ stirring supply ’—firstly, when no air was passing ; secondly,
when the air was passing through the dry flask and tubes and I could detect no
difference.

So long as the thermal balance is maintained with the same potential difference,
the rate of evaporation must be the same, whatever method is adopted. I cannot
see that the external work to be done is likely to alter because the space above the
water is de-saturated by passing a gas instead of removing the saturated vapour by
an exhaust, and this view is borne out by the close agreement between the means of
those groups and my later experiments.

There is one curious fact which may possibly throw some light on the matter. I
performed two experiments (August 22 and September 13), passing nitrogen instead
of air. Of course I had at that time no means of judging of the comparative value of
the different experiments, and therefore was ignorant of the close approximation of
the nitrogen values and my final ones. Had I then been aware of the coincidence, I
should have continued the nitrogen experiments in order to ascertain if the agreement
was fortuitous.

The close agreement is shown in the following table :—

TABLE X.
Temperature. | Results of nitrogen experiments. | Final values.
0 |
24-96 581°68 (1 cell) | 581-73
39-98 572°72 (2 cells) | 572°69

When time allows, I propose to repeat these nitrogen experiments, in the hope
that some light may thereby be thrown on the matter; in the meantime, I am
unable to suggest any sufficient explanation of this phenomenon.

Section X.—THE MertHop FINALLY ADOPTED. “ EXHAUST” EXPERIMENTS.

A study of the results obtained from the experiments described in the last section
led me to the conclusion that it was necessary to seek some other method of
attacking the problem. I have not described many of the precautions I gradually
adopted during those experiments, but since none of them had produced any appre-
ciable improvement it was evident that the real cause of the irregularities had not
been ascertained. Even the entire change involved by the replacement of aniline by
oil, the removal and refitting of the calorimeter, &c., appeared to have had no effect
of any kind.

__ I determined, therefore, to adopt an alternative method of producing evaporation,
viz., by reducing the total pressure below the pressure of the saturated vapour. It

304 MR. E. H. GRIFFITHS ON THE LATENT

possessed the following great advantages: (1) there would be no necessity for the
passage of gas through the apparatus, (2) the weighing-bulbs, &c., for catching the
aqueous vapour could be dispensed with. I was, however, reluctant to adopt this
method, for I anticipated that several practical difficulties would present themselves ;
for example, it would be necessary to insert a known weight of water into the flask,
and continue the experiments until the whole of that water was evaporated, thus I
should not be able to finish the experiment at any time when 6, = 6), as was the case
during the “ pressure ” experiments.

It would also be more difficult to maintain the thermal balance at such perfection
as in the former experiments, for it would be less easy to control the rate of
evaporation.

Again, when air was passing through the apparatus, the water in the flask was
efficiently stirred and its temperature in consequence approximated closely to that of
the calorimeter, even when the rate of evaporation was rapid. A thermometer (G,)
was, during the preliminary experiments, placed as described in Section V., with its
bulb near the bottom of the flask, and I found that the difference in temperature
between the flask water and the calorimeter liquid did not, in the greatest case, exceed
0°15 C. If no gas was passing, the water would not be stirred, and it appeared
probable that the difference in temperature might greatly exceed this amount. In
this case not only would the observed temperature (0,) exceed the real temperature of
the water, but also the vapour when escaping through the coil would abstract heat
from the calorimeter, and thus (as pointed out by WINKELMANN in his criticisms of
REGNAULT'’S experiments) the resulting value of L would be too great.

It did not appear possible to determine the interior flask temperature accurately by
means of a mercury thermometer, whose bulb was placed in a chamber where the
pressure was reduced to something between 10 and 100 millims., and if I placed a
platinum thermometer in the flask, a third electrical circuit and galvanometer would
have had to be added with a third observer to read the indications—additions which
circumstances did not render possible.

I did not feel that it would be of any use to adopt RecNauut’s method of
determining the temperature by the vapour pressure (see Section II.), and I
endeavoured therefore to find some means of preventing the temperature of the
evaporating water from falling below that of the walls of the flask.

It was evident that the smaller the quantity of contained water, the more nearly
would its temperature approximate to that of the surface upon which it rested. If
it was possible to discharge the water drop by drop on to the silver surface, the
difference in temperature would probably be negligible, and after some trials I found
a method of effecting this. A glass tube, exactly fitting into the communicating
tube h h’ (Plate 5, fig. 1) was closed at one end, the other end being drawn out so
that it would pass through the constriction at the calorimeter lid (see p. 279), and the
narrow tube which thus projected into the flask, terminated in a very fine opening.

HEAT OF EVAPORATION OF WATER. 305

A tube of this kind (which I shall call a ‘ dropper”) is shown in place in Plate 5,
fig. 1. It was filled with water in the same manner as a “ weight thermometer.”
To ascertain its action, I placed it within a wide glass tube whose lower end was
closed. A constriction in the wide tube enabled me to stand the “dropper” within
it, so that the narrow portion projected downwards (without touching the bottom) in
the same manner as it would do when 7m situ above the flask. The upper end of the
enclosing tube was connected with the exhaust pumps, a clamp being fixed on the
connections. I found that when the pressure fell below that of the aqueous vapour,
the water in the dropper was discharged into the surrounding chamber in a succession
of small drops, but that if the communication with the exhaust was closed the
dropping ceased. If the vacuum was maintained, the drops first thrown on the walls
disappeared while a fresh supply was ejected. I concluded that when the space was
absolutely saturated there was equilibrium, and I found that the disturbance of that
equilibrium, caused by an almost imperceptible decrease in the pressure, was sufficient
to maintain the flow. The size of the orifice of the dropper did not appear to be of
any consequence, as I ascertained by experiment. Of course a certain amount of
water-vapour must have been formed to saturate the space left within the dropping
tube as the water retreated. It is evident, however, that the quantity thus evaporated
would be very small. At the highest temperature at which I have yet worked (50° C.),
the specific volume of water-vapour is somewhat below 12,000, and as the volume of
the droppers used did not exceed 4°1 cub, centims., the weight of water required to
saturate this space would be about ‘001 gram, and at lower temperatures much less.
The greater portion of the heat required for such evaporation must, however, have
been taken from the calorimeter, for the shoulder of the dropper rested on the metal
ring at the base of the tube hh’ (Plate 5, fig. 1), and this ring formed a portion of the
calorimeter. In order to make certain of this matter, I lowered the filled dropper
into place, the contained water being slightly cooler than the calorimeter temperature,
and deduced its water equivalent in the manner described in Appendix II., where I
show how the capacity for heat of the thermometer (G,) was ascertained. The weight
of water and glass in the dropper being known, its water-equivalent could also be
alternatively obtained by calculation. It was difficult to accurately ascertain the
temperature of the dropper just before lowering it into place, but the experimental
results were in practical agreement with the calculated ones, and heat which dis-
appeared within the dropper must therefore have been taken from the calorimeter.

It is thus evident that no correction is rendered necessary by this internal
evaporation.

The adoption of the exhaust method involved certain changes in the exterior
connections. The weighing bulbs and mercury trap were replaced by the bottle B
(Plate 6, fig. 1). The connecting tubes which passed into this bottle were ground to
fit and no corks were used. The calorimeter exit tube did not dip into the H,SO,
but terminated about an inch above the surface of the acid. The manometer gave

MDCCCXCV.—A. 2R

306 MR. E. H. GRIFFITHS ON THE LATENT

(after comparison with the barometer) the pressure of the vapour in the condenser.
The tube H branched into two; one was connected with a water pump, by which
the pressure could be brought down to about 20 millims., and the other with a
GEISSLER’S mercury pump.

Description of an Experiment.

The dropper was filled by alternate boiling and cooling,* and was allowed to stand
in a vessel of warm water until the temperature had fallen to about 5° above that
to which it was to be exposed during the experiment. After removal from the water
it was thoroughly dried externally and placed in a short glass tube closed at both
ends by rubber corks, a precisely similar tube closed in the same manner being used
as atare. The case and dropper when full weighed about 20 grams.

The dropper was always filled some hours before an experiment and placed in the
balance case until wanted. After the tank temperature had become steady the
dropper and its case, having been weighed, were placed within a larger tube
immersed in the tank water.

The connections of the electric circuit having been completed, the calorimeter
temperature (@,) was made coincident with the tank temperature (8), the current
being then switched on to the alternative coil, and thus (as previously explained)
the temperature of the external resistances was kept steady, even when the current
was not passing through the calorimeter. The dropper and case were then removed
from the tank, a silk thread was passed through a platinum loop, fused into the top
of the dropper, and it was lowered into its place at the bottom of the tube h
(Plate 5, fig. 1). The thread was withdrawn and an air-tight piston, consisting of a
section of a rubber cork mounted on a glass rod, was thrust down / until it arrived
at the top of the dropper. A slightly larger conical rubber cork, mounted on the
same rod, closed the top of the tube h, therefore all diffusion or evaporation up the
connecting tube was prevented, and no difficulty was experienced in closing it in
such a manner as to be absolutely air-tight.

It was necessary to delay the commencement of the experiment until the dropper
and contained water had assumed the temperature of the calorimeter (6;). This
took some time, although the temperature of the former must (owing to the previous
immersion in the tank) have been very nearly 6,. Observation of the thermometer-
galvanometer gave the extent of the cooling caused by the introduction of the
dropping tube. The current was then switched on until 0, again equalled 6), the
galvanometer was observed, and the process repeated until no further cooling effect
was visible.

It appeared possible that slight evaporation through the fine opening of the dropper
might during this interval be the cause of some cooling, and I was for a time very

* T found that it was necessary to fix a small capillary tube within the dropper, otherwise the
contained water refused to start boiling when the external pressure was removed.

HEAT OF EVAPORATION OF WATER. 307

uneasy about this point. I found, however, that if the tube, after filling and weighing,
was placed in a desiccator for 12 hours with the opening uncovered, the loss of weight
was less than 0°005 gram; it was, therefore, not probable that any appreciable
evaporation took place during the interval occupied by the temperature adjustment.
Again, the dropper, after being filled, was removed from the beaker at a higher tem-
perature than that of the tank, so that immersion in the calorimeter would not lead
to the expulsion of any water, provided that the small air-bubble formed at the.
lower end when the dropper was cooled in the balance case did not rise into the
upper part of the instrument, in which case the re-heating would possibly cause a
small expulsion, owing to the warming of the air-bubble, which was previously absent
from the tube. I think it just possible that this happened in some of the earlier
experiments (Nos. I. to V.), but, after No. V., I adopted a new form of tube, of which
the lower end was first turned up for about 1 centim., and then bent at right angles.
Thus any air-bubble formed during the cooling remained at the open end, and also the
water, when ultimately expelled, was thrown against the side of the flask (see Plate 5,
fig. 1).

The results of experiments performed after this alteration are in closer agreement
than preceding ones.

When @, was found by observation to have become quite steady, the contact-maker
of the bridge was carefully adjusted to the bridge null-point (see p. 288), and the
swing (if any) of the galvanometer was read. If 6, was found to be lower than 6), a
further adjustment was made. In cases where 6, slightly exceeded 6), no adjustment
was possible without again removing the dropper, so, unless the difference was
considerable (¢.g., a swing exceeding 50 or 60, that is, a difference of about 0°01 C.,
see Table V., supra), the experiment was proceeded with. Three observations were
taken of the swing, and the chronograph tape was marked during the second observa-
tion. This gave the commencement of the interval of time ¢,, 7.e., the time during
which the stirring supply had to be estimated.

The pressure in the condenser B had been previously brought down below that
required during the experiment, and, immediately after the observer at the gal-
vanometer had registered the swings, the tap T, was opened. The manometer M at
once showed an increase of pressure, due to the air in the flask and tubes expanding
into the condenser. The expansion of this air produced a visible cooling effect,
causing a galvanometer swing of about 90—equivalent to nearly 0°02 C. (Table V.,
supra). The manner in which this loss of heat was compensated for will be described
later.

The water pump having been cut off by the tap Ty, the mercury pump was if
necessary brought into action. ‘The moment at which the discharge from the dropper
commenced was indicated with great accuracy by the galvanometer and announced
by Observer No. II. The electric current was at once switched on to the calorimeter
circuit (the action recording itself on the chronograph tape) and the electric balance,

2R 2

308 MR. HE. H. GRIFFITHS ON THE LATENT

if not perfect, immediately adjusted by Observer No. I. Owing to the alternative-
circuit method previously described, only a very trifling adjustment was as a rule
required. Observer I. had now to direct his attention to the maintenance of the
thermal balance. This, as I have anticipated, was found at first to be matter of some
difficulty, but practice rendered the task comparatively easy.

The discrepancies observable in the earlier experiments (Table XI.) are, I expect,
in some measure due to fluctuations in the value of 6, As a general rule, the
evaporation at the start was too rapid, the pressure having been too much reduced
by the last stroke of the pump—the galvanometer swing amounting to as much as
— 500 or — 600 (nearly 0°11 C.). The tap T, was closed and (evaporation being
thus prevented) the electric current was allowed to raise 6, until the + galvanometer
swing announced by Observer I]. was about equal to the previous negative swing ;
the time occupied by these two large oscillations being only a minute or two. T,
was then partially opened until it was found that @, was slowly falling. When 6,
became equal to @) the rate of cooling was further decreased and during the remainder
of the experiment the galvanometer swing (which was called aloud by Observer II.
every 15 or 20 seconds) rarely exceeded 50 or 60 (2.e., about 0°01 C.) and in many
cases the difference between 6, and 6, did not exceed 0°:002 C. in the course of half-
an-hour.

As the whole of the aqueous vapour passing into the condenser was not at once
absorbed by the H,SO,, the pressure slowly increased, and thus gave a further power
of adjustment. The large bulb of the Geissler was kept vacuous and thus, by
opening the tap T, the pressure in the condenser could at any time be decreased.
By one rapid turn of the tap an almost imperceptible rise of the manometer M was
caused, and a very slight difference in pressure produced a considerable alteration in
the cooling rate; thus, if @, was rising, a single revolution of the tap T, would check
the rise, another revolution would probably give the cooling a slight mastery. The
operations by which the thermal balance was maintained may, as I have described
them, appear both cumbersome and difficult. I can only say that (after the first
three or four experiments) the control was nearly perfect and a single oscillation of
as much as 0°01 C. would have been considered excessive. From beginning to end
of each experiment great care was taken that each positive oscillation should be
succeeded by a corresponding negative one.

The electric balance was also maintained by Observer I.; but as the temperature
of the coil did not appreciably alter throughout, this balance required but little
attention.

The taps T,, Ty, T;, and T,,.as well as the handles of the rheochord and all the
electric keys, were so placed as to be within reach of Observer I. without change of
position. The high resistance galvanometer screen was immediately in front of him,
and also the manometer, M, whose readings were constantly observed. Near the
commencement and end of an experiment the physical strain was great, but when both

HEAT OF EVAPORATION OF WATER. 309

thermal and electrical balances had been finally adjusted there were often intervals of
more than ten minutes when no alterations had to be made.

From beginning to end, the task of Observer II. was that of announcing the
galvanometer swings—a monotonous and uninteresting operation, which, however,
required constant attention.

When the experiment was approaching its termination a close watch had to be kept,
for, unless the current was switched off the instant a sudden rise showed that all the
water had been evaporated, the lapse of a few seconds would have raised 6, consider-
ably above 6. If, on the other hand, the current was turned off too soon, it was
always possible to switch it on again and raise @, up to @. After the first
experiment it was easy to calculate (knowing the weight of the empty and the full
dropper) the approximate time of ending. As a rule I cut off the current two or three
seconds before that time, then increased the vacuum considerably to make sure
of evaporating off the last drop of water, again established the current, and brought
6, to just below 6, repeating this process as often as necessary——all the actions
recording themselves on the chronograph tape. When @, had become absolutely
steady, or only showed the slight increase due to the stirring, it was safe to assume
that all the water had been evaporated.

The tap T, was then finally closed, the tap T, slowly opened, and the air from the
drying bottles S and P allowed to pass in through the 30-feet coil, C,, in the tank. The
increase of 0, caused by the compression of this air was found, by observation, to be
the same as the depression (previously referred to) which took place during exhaustion;
and it was to allow for this rise that @, was set slightly below @)._ When the internal
_ and external pressures had become equal, T, was closed and the current again switched
on if necessary, until the swing became the same as the initial swings. If, however, 0,
exceeded @,, this was not possible, and a correction had afterwards to be made for any
difference.

After repeated observation had shown that @, was steady, Observer II. read, as
before, three galvanometer swings, pressing his chronograph key at the middle one.
This record gave the termination of the interval ¢,, the time during which the stirring
heat had to be estimated.

It will be seen from the preceding account that ¢, always considerably exceeded ¢,,
the time of electrical supply.

The plugs closing the tube h h’ (Plate 5, fig. 1) were now withdrawn, a wire ending
in a hook passed down the tube, the dropper extracted by means of its platinum loop,
and immediately returned to its case, which was at once corked and placed on the
balance, and afterwards weighed, with the various precautions previously referred to.

The only remaining operation was that of translating the chronograph tape which
gave the value to 3/5 second of ¢,, t,, and the time of each thousand revolutions of
the stirrer.

Remarks on Tables XI. to XIII.

Tables XI., XII., and XIII. give the experimental results; Table XI. those at

310 MR. HE. H. GRIFFITHS ON THE LATENT

temperatures approximating to 40°; Table XII. those at temperatures near to 30°;
and Table XIII. two experiments at 30°, where the rate of evaporation was but 3% of
the former rate. Any inaccuracy in the values of Q,, ¢,, and =q would in these last
experiments tell with double force. Also, the rate of evaporation being so greatly
diminished, it was probable that any depression of the temperature of the evaporating
water below @, would be about half of what it was when four cells were used, and
thus the magnitude of any error, caused by such depression, would be indicated.

Had time permitted, I should have repeated these experiments with a still slower
rate of evaporation. I was, however, surprised to find that it was more difficult to
maintain the thermal balance with the lower than with the higher D.P.

A large number of differently shaped and sized “ droppers” were used, hence the
difference in the values of M.

As I preferred to alter the conditions as much as possible, no effort was made to
keep the stirring rate the same for different experiments.

In most cases the droppers when removed after an experiment appeared to be
absolutely dry. In two cases, however, some signs of moisture were visible. I am
at a loss to account for this, as I feel sure that evaporation had ceased, and that
there was no water left on the surface of the silver flask. The moisture thus
remaining was, of course, included in the final weighing, and would not therefore
introduce any error provided the flusk was dry. It is noticeable, however, that the
two experiments at the end of which this moisture was visible (Nos. V. and IV.)
give, as shown by Table XI. (0), the highest values for L.*

The value of d’ — d” will be noticed as unusually high in No. I. Here we had no
idea of the time when the experiment would finish, and did not allow for the rise in
6, caused by the introduction of the dry air at the end, hence the close of the experi-
ment found 6, too high by nearly 0°°028 C. Also we could only approximate to the
value of ¢,, having in the hurry of the initial experiment forgotten to mark the time
of finish. The remembrance of a casual observation of the clock, however, enabled us
to fix it approximately. An error of 100 seconds in ¢, would in that experiment
produce an error of not quite + °25 in L, and the value assigned to ¢, is probably
within a minute of the truth.

During Experiment II. a portion of the mercury covering the core of tap T; became,
owing to careless manipulation, sucked into the apparatus, and in some unexplained
manner stopped the evaporation for nearly ten minutes, during which the electric
current had to be switched off. However, the accident had but little effect on the
resulting value of L.

No. XI. was an almost perfect experiment, the thermal balance being maintained
very closely throughout. I do not think that the variations in 6, during this experi-
ment at any time amounted to 0°-005 C., and the external temperature (@,) remained,

* Even when the same dropper was used, and the bulb was afterwards found to be dry, the values of
M were not identical. The mass of contained water depended on the temperature of the dropper when
removed from the beaker after filling, and as the beaker was only roughly brought to a temperature
somewhat above 6,, the values of M varied.

HEAT OF EVAPORATION OF WATER. 311

as shown by Col. III., absolutely unchanged. It is noticeable that its result
(Table XI. (b)) is almost exactly the mean value of Experiments VI. to XII.
I have included in these tables every experiment performed by the exhaust method

with the exception of one, during a portion of which the chronograph ceased to mark,

or rather marked continuously. Both accident and its cause were only discovered at

the end of the experiment, when it was found that a loose piece of wire had short-

circuited the chronograph circuit.

32

32>

WEEE

Notation used in Tables XI. to XIII.

Number of experiment and date.

Temperature of the experiment (4) on the nitrogen scale.

m, the initial mass of dropper and contents, m, the final mass ; hence
Mm, — Mz = mass evaporated = M.

(M is in all cases the weight corrected to vacuo.)

Time (in seconds) during which the electric current was passing through
the calorimeter = t,.

Time ¢, (in seconds) during which the stirring supply of heat was main-
tained. ¢, = duration of experiment.

Number of revolutions per second of the stirrer = 7.

Ditference (6°) — @”)) between the initial (@)) and final (6”,) temperature
of the surrounding walls. This is expressed in the nitrogen scale, the
value of each millimetre of thermometer II. having been previously
determined by the comparison referred to in Section IV.

Let 6’, (initial calorimeter temperature) exceed 0’, by d’, and let 6”, (final
calorimeter temperature) exceed 0”, by d”.

Then this column gives value of d’ — d” deduced from the galvanometer
swings by Table V., Section VI.

Gives the capacity for heat of calorimeter and contents (C,,) at the tem-
perature of the calorimeter 6, (‘Table IIL).

The temperature of the Clark cells during the experiment.

The value of R, at temperature 0, from Table VIL., Section VIII.

The average pressure (p”) in the condenser during the experiment (in
millimetres of Hg).

The approximate pressure of saturated vapour (p’) at the temperature 0,
(from ReGNAvLt’s tables).

The difference between Cols. XIII and XII. This indicates the limit of
fall of pressure from the flask to the condenser, 7.e., along about
19 feet of narrow tubing. It must be remembered that owing to the
presence of the H,SO, the pressure in the condenser fell off greatly,
and Col. XIII. is only useful as indicating a value considerably
exceeding the real difference between p’ and p’”. No use is made of
this quantity in the reduction of the observations.

LATENT

MR. E. H. GRIFFITHS ON THE

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HEAT OF EVAPORATION OF WATER.

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MDCCCKCV.—A.

314 MR. HE. H. GRIFFITHS ON THE LATENT

Reduction of the Observations given in Tables XI. (a) to XIII. (a).
(See Tables XII. (b) to XIII. (d).)

Col. XV. gives the value of Q,t. = (ek x
1x J

The correction for temperature of the cells was made by Lord RAYLEIGH’s coefficient
(00077), but, as an inspection of Col. X. (supra) will show, the correction was in
every case very small, except in XI. During the night of September 25 the Clark
cell tank regulator ceased to work, and I found the cells at a temperature of 15°°8 the
next morning. I considered it better to keep them at that temperature throughout
the day than to raise it to 15° a few hours before an experiment. The correction in
this case amounts to 1 in 1500, but is probably accurate to 1 in 5000.

In a communication to the Royal Society, on November 22, 1894, Professor ScHUSTER
pointed out an error in my determination of the value of J, viz., that I had not made
a necessary correction for the specific heat of the air displaced by the water, for the
method I adopted gave the difference in the rate of rise when a certain space was
filled first with air and then with water. This correction raises my value of J by
1 in 4000. Hence, in the following reductions I assume J=4°199 in place of 4°198.*
As I have before pointed out, if in consequence of errors in my standards, &c., my
value of J is inaccurate, it is still the right value to insert here, where I use the same
standards, for errors of the kind referred to are thus eliminated.

Co]. XVI. The value of Q, as deduced from Col. VI. by means of Table VL,

Section VII. (supra).

, XVII. The “stirring supply ” Q,t, from Cols. XVI. and V.

, XVIII. The term 2q = C,, {(4’9 — 0”,) — (d’ — d’)} from Cols. VIL, VIIL, and
IDG

XIX. Gives the sum of Cols. XV., XVII., and XVIII., that is, the total
number of thermal grams used in evaporating the mass M (Col. IIL.).

3 XX. Repeats the value of 65, in order to render the reference less trouble-
some.

s
_ XXI. The value of L, deduced from the equation L = Qetesises Greate

M

* This correction should xot be applied to the yalues of the specific heat of aniline given in Paper A.
In that case the results also depended on the observations of differences, and if the corrected value of J
was there used, a further correction for the specific heat of the air displaced by the aniline would have
to be made, the final values remainiug practically unaltered.

HEAT OF EVAPORATION OF WATER. 315
Taste XI. (b).—Reduction of the Observations in Table XI. (a). (x = 4.)
lEsperimelit XV. XVI. Saya, ill saan XIX. XX. XXII.
12 d Qute. Qs. Qsts. Sq. st Oo. L.
| I. 2164-0 00443 143 —88 2169°5 40°147 57311
Il. 2152-1 004.54. 185 +17 21723 40:146 572°31
uae 1987°3 00509 194 +0°2 2006-9 40°147 572°77
IN 1999°5 00449 16°8 +18 2018°1 407144 57261
We 2000-9 00471 16°6 +34 2020-9 40:145 5 73°80
Wale 2189-1 60486 23°8 —3°4 2209°5 40°147 57301
| Vil. 2133-4 00546 20°3 +3°3 2157-0 40°147 572°50
Vill. 2191-0 00480 19:1 —0°4 2209°7 40:14:77 573-00
IX. 2271°7 00452 20°3 —01 2291-9 40°149 57228
X. 2269°7 00517 22°7 +11 2293°5 40°157 57212
| XI. 2273°6 00468 19:3 | —0°2 2292-7 40°153 57261
Mean of all . 40:146 57274
Mean of Nos. VI. to XI. 40:147 57259
TasLe XII. (b).—Reduction of the Observations in Table XII. (a). (n = 4.)
|
: XV. XVI. XVII. SXGV ITE ee NeEXe XX. XXI.
| Experiment. Qute. O;. Qyts. Sq. Sy 0%. i.
Xi. 2288°5 00672 30-4 | —38 | 2315-1 29°987 | 57858
XUI. 2277-2 00723 316 —05 || 2308°3 29°983 | 57864
XIV. 2276°9 “00710 32-1 —13 || 2307-7 29:998 | 578°78
XY. | 2279°3 00663 30°7 +09 | 23109 29-999 57890
XVI. | 2400°1 00614 30°7 +0:2 | 2431-0 30:004 57860 |
| | |
Mean | 29-994 57870 |
Tape XIII. (b).—Reduction of the Observations in Table XIII. (a). (n = 3.)
| |
| . | AXON XVI. XVII. ete XIX. XX. XXII.
Experiment. | Qute. Qs. Qsts. E Sh >: L.
| | a if
XVI | 1750-1 00644 36-7 01 | 1786-7 29°993 | 57883
XVIII. | 17534 00696 36-7 17 1788-4 29-993 57860
Mean 29:993 578°72

316 MR. BE. H. GRIFFITHS ON THE LATENT

I have already remarked that I attach more value to Experiments VI. to XI. than
to the preceding ones, and I shall therefore assume the mean value of L at 40°15 as
572°60. |

The close agreement between the means of Nos. XII. to XVI. and Nos. XVII.
and XVIII. is very satisfactory when it is remembered that the rate of evaporation
is in the last case nearly halved.

I need searcely say that, had time permitted, I should have performed more experi-
ments, especially at 30°. I do not, however, consider that the evidence would have
been greatly strengthened.

In the whole of the series from VI. onwards (v.e., after the adoption of the bent
form of dropper) there is no experiment which gives results differing from the mean
at that temperature by more than 1 in 1430, and in the groups at 30° the greatest
divergence is 1 in 2900. The probable mean error of a small group of experimental
results of this kind is therefore less than the probable error of some of the constants
on which our conclusions are based, and a larger accumulation of such experimental
numbers would not necessarily bring us any nearer to the absolute value.

Conclusions.
Temperature. Value of L
Nitrogen thermometer. (in terms of thermal unit at 15° C.).
AOSD. sy pont A ere aa ks Mee Meta Oe OO
S000 Coo ik es oe te hk a aie aed OSLO

Section XJ.—Driscussion OF THE RESULTS.

From the conclusions arrived at in the last section we obtain (over the range
30° to 40°15 C.) dL/dé = °6010.
Suppose we assume with Reanavtt that L is a linear function of 0, it follows that

wien! O-—==10 saa) 9 Gwe
uO = 100% Wi 53663

I admit the folly of attempting to extrapolate to such an extent where we have no
evidence but that given by the experiments themselves. It is a different matter
when we can bring forward independent evidence.

In Section II. I dwelt upon the importance of the experiments of Dizrerict at low,
and of REGNAULT at high temperatures ; the agreement between the values obtained
by those observers and the ones resulting from the above extrapolation is so extra-
ordinary that I give in detail their experimental numbers.

As stated in Table I., ante, the mean value of all Diererici’s experiments was
596°8 at 0°. He, however, regards certain of the experiments (whose results are
given in his Tables II. and IV.) as of greater value than others, because the
evaporating water was included in a platinum instead of a glass tube, and thus its

HEAT OF EVAPORATION OF WATER. 317

temperature must have approximated more nearly to the external temperature. His
numbers are as follows (‘ Wied. Ann.,’ vol. 37, 1889, pp. 502-4) :—

Taste XT V.—DrerTerici’s Experiments.

(597-29
597-19
595-99

Table ot ae acs

| 95°74
| 596-51
(597-06

597-07 (with lower pressure)
TAPIEELVE 4 PMPS\ -4 eacie

Mean of all experiments 596-73
in platinum tubes . .

His own summary of these results is as follows :—
“ Die Versuche mit dem Platingefiisse ergeben
(P= Oya}
mit einem wahrscheinlichen Fehler des Mittels von + 0°13.”*

REGNAULT performed forty-four experiments at temperatures about 100°. Of
these he rejects Nos. 1 to 6, as merely preliminary ; the remainder areas follows. It
should be remembered that the numbers in this table give the values of the “ total
heat,” not those of L.

Taste XV.—ReEGNAULT’S Experiments.

Experiment. | Temperature. | “Total heat.” || Experiment.| Temperature. | ‘Total heat.”
| 7 99:49 | 6368 26 10022 6372
8 | 99-46 | 636°3 27 100-37 636-1
9 | 99°31 636-4 | 28 100-32 636°
10 9928 637-6 29 100-32 637-3
11 10019 | 636-0 30 100-31 63671
12 10019 636'8 31 7 100,22 635-6
13 100-19 638'3 32 100-22 636-9
| 14 100-19 | 637-9 | 33 100-26 635-9
15 10019 | 635°9 | 34 100:26 635°9
16 | 100-26 625°9 | 35 99-09 635°7
17 10026 | 637-9 | 36 99-09 63671
18 100-26 637-9 3 99-07 636-6
19 100-26 | 635°6 | 38 99-07 636-9
20 100-26 635'8 39 99-36 636-1
21 10026 | 636°7 | 40 99-36 636°8
22 | 10022 | 637-6 | 4] 99-33 637°3
3 100-22 638°4 | 42 99°33 636-4
24. 100-22 636°8 43 99-27 635°7
25 10022 | 636°6 44, 99-27 636°8
Mean. . 99°88 636°67

* ‘Wied. Ann.,’ vol. 37, 1889, p. 504.

318 MR. EH. H. GRIFFITHS ON THE LATENT

This value of 636°67 at 99°88 would become 636°60 at 100°. If we assume that
1 gram of water gives out 100 thermal units in cooling from 100° to 0°, we get

L = 536°60 at 100°.

VALUES of L.

On 100°.
Tee Gb op oo Goo Oo 536°60
DIETERICT .. )-) fica) Geen 596°73 a0
GRIFriTHs (extrapolated). . 596°73 536°63

I have learned to regard experimental coincidences with suspicion, they are so
often misleading, but such an unusual case as the above merits attention.

These coincidences are the more extraordinary on account of the following con-
siderations.

DIeTERICI assumed (ante, p. 265) as his thermal unit the “mean thermal unit”
from 0° to 100° C. Now according to Regnautt* the ratio of the “mean thermal
unit” to the thermal unit at 0° is as 1:005 to 1.

If we assume Rownanp’s or Barto and Straccrati’s determinations of the
changes below 15° (my own have not extended below that temperature) we should
get

“mean thermal unit” 1:005

“thermal unit at15°” ~ -994 approximately

au and thus Dirrerict’s value of L, if expressed in terms of the same thermal
unit as I have used, would be increased to 603°3.

Again, according to REGNAULT we ought to subtract 100°5 from 636°60 in order to
obtain the value of L at 100. This would give L = 536'1.

Some further considerations, however, tend to show that the agreement at both
ends of the line given by my observations is not merely fortuitous. We can deduce
the values of L resulting from my “exhaust” experiments (at any temperature 0) by
the formula,

O52a5

L= 596-73 — 60106... (G,).

Now the preliminary experiments (see Table IX., ante) although irregular, carry
some weight and the mean of each group is in fair agreement with formula (G)).

* “De la Chaleur Spécifique,”’ ‘ Mémoires de l’Académie des Sciences,’ tome 21.

HEAT OF EVAPORATION OF WATER. 319

TABLE XVI.
Lfrom “ preliminary ”
Temperature. observations L from formula Gy.
(Table IX.)
| ° f :
| 25:0 581-9 581°70
| 40-0 572°4 572°69
49°8 566°5 566°80

I have given in Section II. my reasons for rejecting ReGNAULT’s experiments at
low temperatures, where he determined the temperature in the calorimeter from the
pressure of the vapour in the condenser. The objections there brought forward,
however, lost all force as regards these experiments above 63° in which the methods
of observation and experiment were altered.

Column III. of the following table gives the results of all RecNAvLt’s experiments
above 63° and below 100°... (R.), Column IV. gives the values resulting from
ReGNAULTS own formula 606°5 + °305¢....(R), Column V. contains those given
by WINKELMANN’S formula*..(W), which includes RecGnautt’s expression for
the capacity for heat of water, and Column VI. the numbers obtained by assuming’
the validity of formula G, (supra), from which we deduce

Total Heat = 596°73 + 39900... . (Gy).
Column VII. gives the difference between (R.) and (R), in Column VIII. are given

the differences between (R,) and (W), and Column IX. shows the differences between
(R.) and (G,).

* L = 589°5 — 0:2972¢ — 000321472? + 0:00000814 70.

320

MR. E. H. GRIFFITHS ON THE LATENT

TaBLeE X VII.—Comparison between REGNAULT’s Experimental Results (R.) over the
Range 63° to 88°, with the value given by formule (R), (W), and (G,).

| ! |

ite Il. III. TV. Ve VI. | VIL. | VIII. Ix.

Experi- |

No. - | Tempera-| mental | |

of experi- | Tempere-| mental | (py | (wy | (G) |@)—@).|@)—(W(R)—G).
ment. ee |

| () | | |
1 SoM | GEER I GRRMA IN GRR || Gaile) || @ 2) | eic8
2 CYAGS} || Geer i) GaeHy 632°3 631°8 — Ol + 08 +13
| 3 a SoD Ae » G28:45 1638277 25 163127 631:0 = 418} => 83} —2°6
4, | 85:24 6286 || 632°5 | 631-5 630°7 — 39 | — 29 —2:1
5 eSo:20he) 630577 632°5 63815 630°7 — 08 | + 0:2 +1:0
6 8468 | 629:°9 || 632°3 le 631E2 630°5 — 24 | —13 | —06
7 83:08 | 628°9 631:8 | 630°7 629°9 =) | = 13 in SLO)
8 82°66 631:0 631-7 630°6 629°7 — 07 + 0-4 | +13
9 81-03 628'8 631-2 630-0 629'1 ay = 12 | —O8
10 80:60 627-7 631-1 629°9 | 6289 == 34) — 22 | —1:2

11 80°37 628°8 | 631:0 629°8 628°8 — 22 =e) 0
12 8017 | 630°2 6309 | 629°7 628°7 — 07 + 05 e115)
13 79°55 63071 6308 | 629°5 628°5 — 07 + O07 +16
14. | 78:28 627:0 | 630°3 | 629:0 |. 628:0 — 33 — 20 . —10
15 76°50 628°6 | 629° | 6283 627°2 — 12 +03 | 41-4
16 71°35 624-4 || 628-2 626'4 | 625°2 — 8Y3 — 2:0 —0°8
17 7111 622°2 628-1 6263 |) - 625-1 — 5:9 — 41 —2:9
18 | 70°49 626:9 | 628°0 62671 624-9 — 11 + 08 +2°0
19 69°70 626-4 | 62772 62537 6245 | — 1:3 | + 10:7 +19
20 | 68:01 622°5 OA || Gar 623°9) eS er tO G —1-4
21 | 66°30 624°7 626:7 | 6245 623°2 — 20 |} + 02 +1°5
22 | 64°34 6229 | 626-1 623°9 622°4 = i = Id) +0°5
23 63°02 625°5 625°7 623°2 621°9 — 02 + 23 +3°6
Sum of differences . | —49:3 —176 +52
Mean difference . — 214) — 077 +0°23
If we omit Experiment 23, we get

Sum of differences . . |) —49-1 —19°9 +16
Mean difference . | — 223) — 0°90} +0:07

The results of the above comparison show that over the range 63° to 88° the
formula (G) gives a closer approximation to REGNAULT’S experimental numbers than
either of the other formule.

The only reasonable explanation of these various coincidences which occurs to me is
that the value of the “mean thermal unit” is practically the same as the value of the
“thermal unit at 15° C.”*

* Further evidence can be adduced in support of this view. In Section II. I-pointed out that if we
express the results of the observations of Bunsen and Reenavtt, on the latent heat of fusion of

HEAT OF EVAPORATION OF WATER. 321

I see nothing impossible in this supposition. As stated in Section IT. there is
sufficient evidence that at low temperatures the capacity for heat decreases with rise
of temperature. RowLaNp found a minimum indicated near 34°. If therefore the
capacity for heat increases gradually above some such temperature, but more rapidly
near 100°, it is quite conceivable that the “‘mean thermal unit” should closely
approximate to the “thermal unit at 15°C.” Our only experimental evidence to the
contrary is that given by RecNautr in his paper, “ De la Chaleur Spécifique.” We
know that his conclusions at low temperatures are incorrect, and [ do not see that
those at higher temperatures have greater value, for his methods of observation and
experiment were, in this case, unaltered.

The matter, of course, can only be cleared up by a direct determination of the
capacity for heat of water over the range 0° to 100°.

In the meantime I contend that the evidence in favour of the formula “ total
heat = 596°73 + °39900” is stronger than that upon which either REGNAULT’s or
WINKELMANN’S formule are based.

At temperatures above 100° the values of “the total heat” deduced by formula
(G3) would be higher than REGNAULT's experimental numbers. The capacity for heat
of water at higher temperatures is so uncertain, and it has so great an influence on
the values of L at high temperatures when deduced from the “ total heat” formule,
that I do not feel that a discussion on these results would at present be of any value.

The results of the experimental work described in preceding sections, and of the
evidence brought forward in this section, may be summarised as follows :—

THE VALUES OBTAINED BY DIETERICI AT 0°, BY REGNAULT AT TEMPERATURES 63°
To 100° C., aND By GRIFFITHS AT INTERMEDIATE TEMPERATURES ARE (ASSUMING THE
APPROXIMATE EQUALITY OF THE “‘ MEAN THERMAL UNIT” AND THE THERMAL UNIT AT
15° C.) CLOSELY REPRESENTED BY THE FORMULA

L = 596'73 — 0°60100.

[Note, May 7, 1895.—The suggestion that the “mean thermal unit” does not
exceed the “thermal unit at 15° C.” has been eriticized as over bold. It is, therefore,
with peculiar pleasure that I include in this paper a communication which I have
to-day received from Dr. Joty, to whom I return my sincere thanks for his permission
to publish it.

Dr. Joty informs me that he regards his experiments as preliminary; their
importance, however, is undoubtedly great. They are (I believe) the first experi-
ments since those of RecNavutt which throw any light on the relative values of the
two units. It will be seen that (assuming Barront and Srraccratr’s conclusions as
to the changes in the capacity for heat of water from 0° to 15° C.) the results of
Dr. JoLy’s experiments indicate that the ratio
ice in terms of the same unit, by means of the ordinarily accepted comparison of the values of their
respective thermal units, their difference becomes excessive.

MDCCCXCV.— A, 2

322 MR. E. H. GRIFFITHS ON THE LATENT

Mean thermal unit 9952 __-0:9957
Thermal unit at 15° OC. 9995 = 1

: ‘011
in place of a .

It is apparent that there is sufficient evidence to justify scepticism as to the
validity of the commonly accepted ratio, and J] hope that the demonstration of this
uncertainty may quicken further investigation into the actual value of this important
constant.

Note (by Dr. J. Jory, F.R.S.) on the Ratio of the Latent Heat of Steam to the
Specific Heat of Water.

Upon receiving from Mr. GRIFFITHS a copy of the abstract of his paper on the
latent heat of steam, I determined upon making some experiments with the steam
calorimeter on the ratio of the latent heat of steam to the mean specific heat of
water over the range air temperature 12° to 100°. Pending the completion of a form
of the calorimeter which will enable me to make this comparison over suitable and
definite ranges of temperature, I gladly add, at Mr. Grirrirus’ request, the following
note on the experiments already made.

The weight of water operated upon was 12°8545 grms. This was enclosed in a
thin blown glass bulb, sealed while the water was boiling, and having an internal
volume of 15°714 cub. centims. Ten experiments were made—these were in close
agreement. The mean initial temperature was 11°89; the mean steam temperature
99°96. The first temperature was determined by 2 Kew-corrected thermometer
reading tenths on an open scale; the second temperature determined by a standard
barometer. ‘The mean weight of steam condensed was 2°32917 grms.

To correct this for the effect of the glass vessel, six experiments were made on the
latter when containing dry air only. Further corrections were made (a) for eyapo-
ration within the vessel when containing water; (b) for buoyancy or displacement
effect on the apparent weight of the vessel, the densities being not quite the same in
the experiments on the filled and empty vessel; (c) for the specific heat of the air
contained in the vessel when empty of water. A total subtractive correction of
0°2298 grm. was obtained.

If we now calculate the mean specific heat of water between 11°89 and 99°-96,
assuming the value of the latent heat of steam given by Mr. Grirritus’ formula, 2.e.,
L = 596°73 — ‘6010 6, where @ has the value 99°'96, we get

20994 x 536°66
Om bea ay
T have little doubt that this will remain —closely—the mean specific heat, 12°-100°,
according to the steam calorimeter. It will, of course, be necessary to check the

result by further experiments. It is true I formerly made experiments in the steam

HEAT OF EVAPORATION OF WATER. 325

calorimeter and obtained a higher value, but it was in an early and very defective
form of the instrument, and an error of positive sign, as I afterwards found, very
certainly obtained in those experiments.

Considering this number in the light of Mr. Grirrirus’ remarks, it certainly
supports his contention that REGNAULT made an error of excess in his value of the
mean calorie—0° to 100°. The above number is however, even less than the value
supposed by Mr. GrirrirHs to be the true number. For, as I understand,
Mr. Grirrirus’ L is calculated on the calorie at 15° C. as unity. If this is also
—as Mr. GRIFFITHS suggests as probable—in close agreement with the mean calorie,
0° to 100°, then the mean specific heat from 12 to 100 should come out only a very
little less than unity. In fact, by plotting Barroxt and Srracctatt’s observations
below 15°, we can estimate what the mean specific heat from 12° to 100° ought to be
if the mean from 0 to 100 is the same as the specific heat at 15° and both equal
unity. A rough estimate gives this to be 0°9995.

My value is therefore too low to be in harmony with the supposition that the mean
calorie and the 15° unit are zdentical. The value of the latent heat of steam is, of
course, involved, for the steam calorimeter can only give a ratio, and, if the number
now obtained is correct, it follows that either the latent heat assumed is too low, or
the specific heat of water is even lower than it is supposed to be, or possibly both are

somewhat incorrect.
J. JOLY.

Physical Laboratory,
Trinity College, Dublin. |

Section XII.—Tue Density anp Sesciric VotumME ofr SATURATED WATER-
VAPOUR DEDUCED BY MEANS OF THE THERMODYNAMIC EQUATION FROM
THE VALUES oF L GivEN By ForMmULA (G)).

WINKELMANN (as previously stated) assigns to what he terms the “theoretical
density ” of water-vapour the value 0°6225 (air = 1). He gives, however, no informa-
tion regarding the data for this statement.

The most recent investigation of the comparative volumes in which oxygen and
hydrogen combine is that by Scorr, whose conclusions are as follows :* “That
100,000 volumes of oxygen unite with 200,245 ‘volumes of hydrogen to form water.
Applying this to the density of oxygen found by Lord Rayueien to be 15°882, we
get for the atomic weight of oxygen 15°862.”

In close agreement with this conclusion we have—-

Ditmar . . Pa ee PL SECGG
Cooke and Ries A) ici bales rabe ig Sacha al pyre A)

* Phil. Trans.,’ A, 1893, p. 567. Also ‘ Science Progress,’ August, 1894.
ZT?

324 MR. E. H. GRIFFITHS ON THE LATENT
Assuming Scorr and RAYLEIGH’s values we get—

Molecular weight of water-vapour = 17°862.

Lord RAYLEIGH in 1888-9* pointed out that Reanavut’s conclusions as to the
weights of unit volumes of hydrogen and air required correction, as REGNAULT had
not allowed for the change in volume of the bulb consequent on changes in pressure.
Crartst has applied this correction, and finds the resulting comparative densities of
air and hydrogen to be as follows :— .

| REGNAULT’S value. | Corrected value.

Dre Oe bh | 1 1
Hydrogen. . | (06927 06949 (p. 1664, ibid.)

OstWALp} deduces from these numbers the weights of 1 litre at 0° and 76
centims., as
Air, 1°29349 grams. Hydrogen, ‘08988 gram.
Hence we get

“Theoretical Density ” of water-vapour = ‘6206 (air = 1).

I will now proceed to deduce the density at various temperatures by means of the
thermodynamic equation
dp

T Qe =
te Ac — 8) op?

and I assume the values of the various quantities to be as follows :—

J = 4199 X 107. (My value after ScHusTER’s correction for the specific heat
of the displaced air, see p. 314, swp7a).

L = 596°73 — 60100. . . formula G, (supra).

T= 2730:

The values of dp/dT are taken from Brocu’s reduction of ReGNAULT’s experimental
results,§ and are as follows :—

* €Proc. Roy. Soc.,’ vols. 43 and 45.

+ ‘Comptes Rendus,’ vol. 106, pp. 1662-4, 1888.

tf 2nd ed., vol. 1, p. 181.

§ ‘Trav. et Mém. du Bur. Intern. des Poids et Mes.,’ 1, A, 1881.

HEAT OF EVAPORATION OF WATER.

Taste XVIII.

I. Il. iil. II
(millim. of Hg). ee (dynespersq.centim.).) p (millim. of Hg).
| \¢
|
° | |
0 330 | 44.0 1-1 4-569
20 1073 | 14308 17-363
40 2:936 | 39150 54°865
66 6:922 | 92301 148-89
80 14°388 191850 30487
100 26981 | 359800 760°

325

The numbers in Column III. are obtained by assuming g = 980°94 and density of
mercury = 13°596.

The resulting values of s’ (specific volume) and d (density, air = 1) are given in the
following table :—

TABLE XIX.
| 1. II. | Te IV.
Temperature. 8. | Specific volume of air. d.
|
° |
0 207970 | 128600 6184
20 58430 36318 6215
40 19581 12278 “6270
60 7644 4814 6298
80 3395°6 2141 6305
100 16769 1056°2 6299
The specific volume of air was calculated by the formula
1 (273:0 + 0) _ 760 a, FBO O
0012935 273-0 Nine fio

The value of dp/dT at low temperatures is not known with sufficient precision to
enable us to attach any weight to the resulting values of d. For example, if we take
dp/dT = 331 millim. at 0° instead of °330 millim., we get d = ‘6204 in place of
6184. At temperatures above 20° or 30°, not only is the value of dp/dT known with
greater certainty, but the effect of any small error is diminished.

A comparison of the ‘“‘ Theoretical Density ” (-6206) with the numbers in Column IV.
of the last table, indicates that aqueous vapour at low pressures approximates in
density to that of a perfect gas, but that, at higher pressures, its density exceeds that
of a perfect gas.

Above a pressure of about 140 millims., it appears to attain a practically constant
density about 1015 times that of the “ theoretical ” one.

326 MR. H. H. GRIFFITHS ON THE LATENT

I have previously pointed out that the values of L given by my experiments are
independent of errors in the electrical standards used during my determination of J.
This, however, is not the case when the density is obtained from the thermo-dynamic
equation, as the results then depend upon the absolute value assigned to the
mechanical equivalent. Now my corrected value of J exceeds Professor SCHUSTER
and Mr. Gannon’s by about 1 in 1000, hence the values of d in Col. IV., Table XIX.,
would, according to ScuusTER, have to be increased by ‘0006, whereas if we use
RowLaAnv’s value (4190) the increase would be about °0012.

I have given the above determination of the relative densities of water-vapour and
air, because it was the method of calculation adopted by WINKELMANN, and therefore
enables a comparison to be made between his conclusions and those arrived at by the
use of formula G, (supra). It appears to me to be an unsatisfactory method, as it
involves unnecessary data regarding air. A more direct way of obtaining some
information concerning the density of water-vapour, is that of finding PV, z.e., the
“volume energy.” Now PV= RIT, and the value of R for a true gas is 0°0815,*
when P is pressure in atmospheres, and V the volume in litres occupied by the
molecular weight in grams, Assuming as before the molecular weight of water to be
17°862, and obtaining the values of V and P from Col. II., Table XIX., and Col. IV.,
Table XVIII, we get :—

Temperature. = = R.

| 0 | 0827
9 “NR95

5 ee as compared with

60 | 0813, ‘0826 in the case

| OS of hydrogen.

80 | O811
100 0812

and here again we find that at temperatures near 0° water-vapour resembles a
true gas.

* This value of R depends on the assumptions that 1 litre of hydrogen at 0° and 76 centims. weighs
008988 gram. (supra), and that the coefficient of expansion of hydrogen = -0036613 (the value
obtained by CaLLENDAR and myself in 1893). Dr. Suietps, however, assigns to R the value 0:0819
(see ‘Science Progress,’ December, 1894).

HEAT OF EVAPORATION OF WATER. zi

Appendix I.—Deratis or Stirring EXPERIMENTS WHEN THE CALORIMETER
WAS FILLED WITH OIL.

The tank temperature having become steady (at 6)), the calorimeter was raised to
a temperature 6, slightly below 6. In order that the conditions should become
steady, the stirring was allowed to proveed for half-an-hour to one hour, before
observations were commenced. The battery key (f;, Plate 6, fig. 2) was kept
continually oscillating and, as the temperature rose, the swings of the galvanometer
diminished, until no motion was observed on reversing the battery circuit. The
observer then pressed a key communicating with the chronograph, and thus the time
was recorded. As before stated, the stirrer automatically registered its own revo-
lutions. At the same moment that the observer at the galvanometer pressed his
recording key,* a second observer took the readings on the mercury thermometer,
which gave the temperature of the steel walls.

As any change in the mercury thermometer was of great importance, this observa-
tion was made with the micrometer eye-piece before referred to.

Groups of five observations were taken about certain previously fixed bridge-wire
readings, and each group of five was meaned to find the time of passing the given
points.

The following Table gives full particulars of a stirring experiment. It is by no
means a good one, but I give it simply because it is the first one done aiter the
introduction of the oil. The exterior temperature was unusually unsteady.

* In the slower experiments, however, instead of using the chronograph, I called the transit, and my
assistant recorded the time, as alsc the time of the revolutions, the stirrer ringing a bell at each 1000.

328 MR. EH. H. GRIFFITHS ON THE LATENT

TaBLe XX.—Stirring experiment No. I., September 17. Temperature of
bridge-wire = 64°'2 F.

8 2 g : . Reading No. of Time of
Bridge-wire reading. | ‘Time of transit. thermometer If. revolutions. revolutions.
P.M. millims. ;
589°8 9 45 16 882°40 0 9 47 36
590°2 9 48 48 882:40
590°6 9 52 58 882°42
591:0 9 56 58 882°42
591°4 9 59 49 882°40 4000 10 O 12
| :
| Means . 590°6 9 52 46 882°41
Se |
594-2 10 20 11 882°41 9000 | 10 15 55
594-6 10 24 39 882-40
5950 10 28 34 88241
595-4 10 32 20 882°48 14000 10 31 39
595°8 10 36 36 882°45
Means . 595:0 10 28 40 $82°43,
| 598:7 | ILL. 83 XO) 882:46
599'1 | 11 6 58 882°42 |
599°5 Hal dal @ 882 40 27000 11 12 30
599°9 | 1114 4 882°40
6003 | 111830 | 982-40 |
| Weems . 953 | mioe | eave
602°9 11 48 28 882°38 39000 11 50 15
603°3 LT 51 52 882°38
603°7 11 56 54 882°38
604-1 12 1 44 882°39 42000 1L 59 42
604°5 12 6 12 882°40 45000 12, 9-9
| [seca
4 : | iy Mean time per 1000 = 188°73
Means 5 603 7 11 57 2 882 39 Hence, rate per 1 sec. = 5-299

882:41, No. II., = 40°143 C., and 1 millim. of No. II. at 882 = :0501° C.
1 millim. of bridge-wire (temperature 15°) at 40°1 = -009101° C., therefore,
millim. of No. Il. = 5°51 millims, of bridge-wire.

ar

The times of transit may appear, and no doubt are, very irregular. It must be
remembered, however, that the rise in temperature between the individual observa-
tions in each group was not so much as 0°:004C. As this rise took about four
minutes, it is evident that the time of transit of so slow a movement cannot be accu-

HEAT OF EVAPORATION OF WATER. 329

rately determined, but observational errors of this kind are precisely those where a
close approximation is secured by taking the mean of a group. If the middle observa-
tion of each group is compared with the mean, it is evident that an individual
observation might be in error by as much as 20 seconds (the greatest difference in the
above table is 12 seconds), but it is improbable that the mean is in error by more than
5 seconds. The example given is the one which had the slowest rate of rise, and hence
the discrepancies are more marked than would otherwise be the case. As the total
time of the experiment was about 2 hours 20 minutes, an error of even 10 seconds in
the mean of each group would affect the result by but 1 in 800, and as an error of
1 in 50 in the value of Q, would only affect my final values of L by 1 in 5000, the
above order of accuracy was more than sufficient.
I will now give the reduction of the observation in the above table.

REpvctIon of Stirring Experiment No. I.

: dl a brs Correction
Bridgeawire |e Time jleneo =| Heeuleine)| ge, |\Coumection 00) tor eo
yaoi Ue meter II.| inrange.|| @% bridge-wire. temperature || orrected.
‘S) 2 bridge-wire.
590°6-595'0 | 2154 +-02 Stole 002094. --0°4 +1°7 002090 A
595°0-599'5 | 2528 — 014 — 07 001753 —12 +15 001753 || B
999°5-603°7 | 2772 —-030 — 17 | 001454 +43 +12 001460 || C

Since A, B, and C should, if the exterior temperature (No. II.) had not changed,
fall on a straight line, the most probable path is obtained by taking $ (2A + B) and
3(B + 2C) as the rate of rise at the corresponding bridge-wire readings, hence
we get

Bridge-wire. d0, dt.
59428 001978
600°15 001558

Now the bridge-wire null-point = 598°35 + ‘036, (see p. 288).
point at 40° = 599°55.
We get ‘001600.

Hence

Therefore null-
We can now deduce the value of d0,/dé at this null-point.

(d0,/dt), = 001600,
when 7, = 5°299 and @, is measured in millims. of the bridge-wire scale.

I think that there is no necessity to give details of the remaining experiments ;
MDCCCXCV.— A. 2U

330 MR. HE. H, GRIFFITHS ON THE LATENT

the following table shows the results of all those experiments at different rates
where 0) = 40°'1 approximately.

TaBLe XXI.
|| Let t = time of rising 1 millim. of bridge-wire, then
Experiment. Date. (4) | F f 1
Fe ep Pe rm) Ae all aed rom formula
a -2 =2 8 .
| x 107. | x 10-. | x 1077.) x 167%. Gi.

If Sept. 17 001600 5299 || 331 176 930 492 ‘001606
IX. Oct. 27 001626 =| 5310 | 327 173 921 489 ‘001619
VI. Peed | = SOOM Ss alieoa sonny urs Os 166 906 494. 001805

IT. Sept. 23 002152 5670 || 263 149 847 480 002104:
III. » 24 008152 EY) I > OF 76 605 478 007930
| |

Experiments II. and III. were only performed with the object of ascertaining the
effect of changes of rate. Although the differences between tr* may appear consider-
able, it must be remembered that this constant was only required in order to reduce
experiments at different rates to some standard rate; in reality, when we consider
that we are dealing with the fourth power of rv the uniformity is remarkable.

If we plot the values of (d6,/dt), obtained from the formula

dé, ir
Go) =a ROR eh (1,

the results are in close agreement with the experimental ones, especially when the rate is
between 5:2 and 5:5 (the extreme limits of rate during the Latent Heat experiments,
the usual value being about 5°3). True, if we assume (d6,/dt), = 7°/92000 our results
would be nearly as close over the above limited range, but Experiments II. and III.
indicate that the true relation is more nearly given by the previous expression. In
any case, the difference between the experiments and the results as deduced from
(A) do not differ by 1 in 100 over the above range of rate, and a difference of 1 in
100 in Q, would only cause a difference of about 1 in 10,000 in L.

Taste XXII.—The experiments at 30° give the following results.

| 1 | From formula
Experiment. | Date. (=) vr. | 8x10". | tx 1078. B
| at }s- | (infra).
| |
TV. Sept. 29 ‘002330 | 5-280 629 333 002314
VIII. Oct 2 002380 | 5320 632 337 | 002383
VII. | ” 7 002568 | 5416 619 335 002560
Wo | 7 005973 | 6°750 515 348 | 006178

HEAT OF EVAPORATION OF WATER. 331

If we assume
tr* = 336000,

we get

dé, 7
C= aa: a Cea tnem alee adc 310/753)

And here again the differences between the experiments and the results from (B)
are much below 1 per cent. at rates between 5:2 and 5°5, and again the experiment
at higher speeds (Expt. V.) indicates that tr* is more constant than ¢7%,

Applying formule. (A) and (B), we can deduce the rise for a rate of 5°300.

Values of (d@,/dt), at rate 5°300 :—

| Temperature. | (d6, /dt),.
| 40°1 001608
| 002348

Now (see Appendix I., Experiment IV.) it was found that when a similar experiment
was performed at 40°°1, where the heat supply was that due to a potential difference
of three Clark cells at 15° together with a stirring supply (at rate 5277), then

(d@,/dt).,; = °14853 (mean bridge-wire millim.).
Now (from A) we get

(d0,/dt), = °00158 at rate 5°277, therefore (d6,/dt),, = °14695,
therefore

(d6,/di), ==

= 016335
hence
(d0,/dt), 161
(d0,/dt). 1633

at rate 5°300 (supra) = ‘0986.

Now the corrected resistance at this temperature (Table VIII.) was 10°376 ohms
where the D.P. was that of one Clark cell, and since

e 143422 ,
yy UE See, We have 10376 x 4198 — 04728 thermal gram,

therefore
Q, (rate 5300) = 04723 X °0986 = 004659 thermal gram.

2 wi 2

332 MR. E. H. GRIFFITHS ON THE LATENT

In the same manner (Appendix II., Experiments V. and VI.) it was found that
at temperature 30°

(d0,/dt)s. = 15035, and (d6,/dt), = ‘002348 (formula B, supra),

hence

(dO,/dt), 2848

GUD, = ial
and at 30°

R, = 10°348,
therefore
1:4342?
H= 10348 x 4198 — 04735 thermal gram per sec.

therefore

Q, (rate 5°300) = 04735 x 1405 = 006654 thermal gram.

Now assuming (A) and (B), it follows that 7*/Q, is constant, and we can deduce
that if 7, be any rate and 5°300 the standard rate

At temp. 40°°1, Q, = -004659'-- (7,4 — 789) <x "0000059" 2) 2 3 a(@):
At temp. 30°-0, Q, = -006654 + (rt — 789) x 0000084. . . . (D).

I performed one stirring experiment at 50° and two at 20° and I give the results
only, as the values of Q, at these temperatures are not required for the reduction of
the L experiments described in this paper. I was unable (for want of time) to prove
how nearly the effect of changes of rate could be expressed in the same manner as at
30° and 40°, but as the rate was nearly 5:3, the corrections introduced by the reduction
to rate 5°3 were very small. The results were of use, as on plotting the curve for
the values of Q, at the four different temperatures it showed no signs of irregularity,
and thus gave additional strength to the determinations at 30° and 40°. The values
are as follows :—

At temp. 50°, Q, = -00235 + (rf — 789) x 0000030 . . . . (E).

At temp. 20°, Q, = 00768 + (m4 — 789) x 0000098 . . . . (F).

The values of Q, at 30° and 40° receive a certain amount of support from the
preliminary experiments referred to in Section VII. Although my results by that
method varied considerably amongst themselves, the mean of five experiments at 40°
gave ‘00000802 gram of water evaporated per 1 sec. by the stirring after reduction
to rate 5°38, and the mean of four experiments at 30° gave ‘00001137 gram of H,O
evaporated per sec. at the same rate.

HEAT OF EVAPORATION OF WATER. 333

Now, if we assume L at 40° = 573 and L at 30° = 579, we can deduce the values
of Q,, which are as follows :—
At 40°, Q, = 00460
» 30°, Q, = -00658.

These results differ from those obtained without any weighing or passing of air
(equations Cand D supra) by 1 in 77 and 1 in 94 respectively. As an order of
accuracy of 1 in 50 was sufficient for my purpose, I considered this independent
evidence valuable, although I believe the former method to be by far the most exact.

T also performed a determination of Q, at 50° by an evaporating experiment. This
gave ‘00000521 gram per sec, Assuming L = 567, this would give Q, = ‘00295,
far too high a value as compared with that given by equation (EZ). This evaporation
experiment was a very unsatisfactory one, however, and I attach but little importance
to it—in any case, the doubt would not affect the values of L.

To conclude this portion of the subject, I admit that it would have been advisable
to perform more of these stirring experiments at 30° and 40°, but at the same time,
I think the evidence is sufficient to warrant the assumption that the values of Q,
cannot be in error by as much as 1 in 50 and are probably correct to better than
1 in 100.

Appendix IJ.—Deraits oF THE EXPERIMENTS BY WHICH THE CAPACITY FOR
HEAT OF THE CALORIMETER AND CONTENTS WAS ASCERTAINED.

The temperature of the calorimeter was adjusted in the same manner as that
described in Appendix I.

The time of transit across five bridge-wire divisions about the readings 50, 60, and
70 centims. was taken, and the times at 50, 60, and 70 deduced. I give particulars
of Experiment IV.,as that was the one quoted in Appendix I., from which the
value of Q, at 40°1 was deduced.

334 _ MR. E. H. GRIFFITHS ON THE LATENT

TABLE XXIII.—Experiment No. IV., September 17.

Number of Clark cells 3 (each consisting of 4 in 11!). Temperature cells, 15°14 C. ;
temperature bridge-wire, 63°°5 Fahr.

Reva na ana Time | Revolutions Ti External temperature
riage-wire reading. (chronograph). | a 000’s). ime. by thermometer TI.
|
49 81:7 882-35
49°5 WBS | 0 100-1
50 1446 | | \
50° VD | |
51 207°5 | 882°39
144-9 | 882°37
59 730°5) | 3 6690 882-40
59-5 | gen |
60 | S|
60°5 | 831-4
61 865°6 4 858-5 €82:40
yo | | 882-40
|
69 14210 | | 88240
69°5 14566 =| 7 | 1426°6
70 1493-3 | |
70°5 1529-0 | |
71 1565°7 882-40
| 1493:1 | Time per 1000 18950 | 88240
| | om = 5277
| | |

The operations necessary for the reduction of Experiment IV.* are as follows :—
Data required.

Mean value of 1 centim. of range in terms of mean bridge-wire centim. (given by
calibration of bridge-wire; see p. 285)—

DOO 6 5 6 6 oF oo LOOHOBL
GOSGOUTO Ae shia lca poe Whe) SIL

Correction for temperature bridge-wire to 15° C. = range {1 + °00016 (F.° — 59)?

* Fuller particulars concerning this method of reduction will be found in Paper A.

HEAT OF EVAPORATION OF WATER. 339

1 millim. of No. Il. = 5°51 millims. of bridge-wire, and 882°40 millims. = 40°:142.
Bridge-wire null-point = 599°55 millims.

| Change Correction to| Co™rection for |
Time A oe Al Resulting temperature | Corrected |
Range. over | omPerature change d@,/dt x 104. eet C. cells and de,/dé |
on therm. | bridge-wire. . : Li
| range. Ir | range. 104. bridge-wire X10 s|
| ; x 104 |
centims. |
| 30 to 60 | 652-9 +°03 +16 | =1533°9 +13 +'4, +11 1536°7
| 60 to 70 | 695°3 0 0 1438°1 —6-4 +°3, +10 1433-0

Hence we get ‘15367 and ‘14330 as the values of (d60,/dt)., at 55 and 65 centims.
respectively. We can thus deduce the value at the null-point (599°55). We get
"14853.

Now (Appendix I.) the value of (d6,/dt), for rate 5°277 = °00158, therefore
(d0,/dt),, = 14695.

16, \ OF 6 ‘ hs : 2 :
Now a) « a a gives the rise per second in degrees C. with unit resistance
/ 3e née )~

and unit potential difference, where R, is the resistance in true ohms of the coil at
temperature 6,, n the number of Clark cells of P.D. e volts, and C; the value of the
mean bridge-wire millim. at 15° C. when 0, = 40°11, expressed in terms of the N
thermometer (see p. 289). Hence if T is the time of rising 1° C., we get

a (ne)?

7 GOildi), x RYXiC;
and

R;, = 10°377 (see Table VIII.), (ne)? = 18°513, and C, = 009100,
therefore
i — wo 4ale
and
= ; (where C,, is capacity for heat at 0,), and J = 4199,

therefore

C,, = 317'82 thermal grams.

The following table gives the results of all the experiments made with the object of
obtaining the values of C,.

ON THE LATENT

MR. E. H. GRIFFITHS

336

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HEAT OF EVAPORATION OF WATER. 337

In Paper A. I have given a full account of the determination of the ‘ water
equivalent ” (W,) of this calorimeter, and I have every confidence in the values there
given.

From Table VI. of that Paper I extract the following :—

6, W).
20 80°11
30 80°90
40 82°19
50 83°39

During these experiments, the silver flask contained a mercury thermometer (G,)
which was used, during my earlier L experiments, to indicate the internal temperature
of the flask. As described (ante), a metal conical tube had been cast on to the stem
of this thermometer by means of the alloy, and the tube carefully ground into the
neck of the flask to prevent any diffusion of vapour up the glass tube, down which
the thermometer passed. After I adopted the “ exhaust” method of performing the
L experiments, this thermometer was removed from the apparatus; this occurred
between Experiments II]. and IV., Table XXIV. I had forgotten the circumstance, and
when I reduced the results, I was much troubled as to the different values of C,, given
by Experiments II. and IV., which were at about the same temperature. It was some
time before the cause of the discrepancy suggested itself to me. I then obtained an
approximation to the capacity for heat of thermometer G, and tube, as follows: The
temperature of both calorimeter and tank being steady, the bridge was adjusted until
the galvanometer ceased to swing. Thermometer G, was then suspended above the
tube communicating with the flask, and its temperature read by the reading micro-
scope. It was then rapidly lowered into its place, and observed until its temperature
became steady (this took place in about 4 to 5 minutes). The tank being at 40° and
the external temperature about 20°, the thermometer rise was about 20°, and a small
error in reading was of little consequence. The bridge contact-maker was then
re-adjusted, and the change in temperature of the calorimeter deduced trom the
difference in the readings. Hence the capacity for heat of G, could be found. Four
experiments were performed with the following results :—

(al) aise
(2) 1°65
(3) 1:62
(4) 1°58
Means 92. 159

MDCCCXCV,—A. xs

338 MR. E. H. GRIFFITHS ON THE LATENT

If we assume the capacity as 1°6, we cannot be greatly in error, and this quantity
must be subtracted from the values of W, (supra) for all experiments after No. 3.
Now the values of C,, from Experiments II. and IV. differ by 1:89. This apparent
difference of ‘3 in the results has, however, to be further diminished. On September 14,
I found it necessary to withdraw thermometer AB from the calorimeter. Before
doing so, I weighed a “ weighing bottle” containing a roll of blotting-paper, and on
removing the thermometer, I wiped its stem and bulb with this paper in order to find
the weight of oil withdrawn, which proved to be -104 gram. Hence the differences
in Column VI. of the next Table.

TaBLE XX V.—-Specific Heat of Oil.

|
II. III. VI.

I, 5 | IV. V. 6 VIL.
Experiment. eee 3 oe | W, (supra). || Cap. of oil. laee Zl Sy.
IIt. 50°024. 324-74 83°39 241-35 474-12 5090
II. 40°122 319-74 82:20 23754 47412 5008
VEC 40°142 31788 | 80:60* 237-28 474-024 5005
ile 31-996 31487 81-14 233°73 474-12 “4930
Vv. 29-979 312-41 79°30* 23311 474:02+ 4917
VI. 29:998 | 312:35 79°30* 233°05 474:02+ ‘4916
VII. 20:031 | 307°50 78:51* 228:99 474-02+ “4830

Appendix IIJ.—Derains oF DETERMINATION oF R,.

In Paper J., p. 409, is given a table showing the errors of all the individual coils in
my dial resistance box. These errors were, by kind permission of Mr. GLAZEBROOK,
ascertained by direct comparison with the B.A. standards.

T extract the following from the remarks on that table (p. 410, cbzd.) :

‘A table was constructed giving the total difference between the reading and the
real value (in terms of ‘‘ legal ohms”) for every position of the plugs in each dial.
This difference we termed the “plug correction.”{ Having made this correction, we
had then to correct for any maccuracy in the ratio arms of the bridge, and as all
determinations of the calorimeter coil resistance were made with 1000 (right) and
10 (left) as the arms, it is only necessary to here give the correction for those coils.

“ Now
10L/1000R = 9:9977/1000-30 = 0:0099947.§

* After removal of thermometer Go.

+ After remoyal of ‘10 gram oil.

+ The correction for the temperature of the coils was made before applying the “ plug correction.”

§ There is here a mistake in Paper J. This was corrected in a subsequent communication, ‘ Proc,

Roy. Soc.,’ vol. 55, p. 25.

HEAT OF EVAPORATION OF WATER. 339

“ This we termed the “ bridge correction.”

“ The resulting values are expressed in legal ohms, and true ohms = reading in legal
ohms (1 — °0024275).”

The above extract is sufficient to explain the operations. I now give a complete
example of a determination of R, and the subsequent calculations.

The value of @, we obtained by direct observation of thermometer I]., and d’ by
observation of the bridge reading. Then 0, = @+d’.

TABLE XX VI.—Determination of Coil Resistance. October 11.

| Correction ||
| 4 Galvanometer | Observed | Tempera- us for tem- || Plug R+7r
cor ENE. swings.* : ture coils. aE perature correction. (box ohms).
| coils.
|. 331 170
N, 191 341 58140 aio 58°450 +:002 +007 08459
1460 171
417 296
N, 222 350 1095225 | 17°08 1095°783 +:033 +°777 1096°583
(art OSmemo4:
407 281
N, 201 322 1095228 Se 1095°834: +:033 +:777 1096°634
| 206 41
| 282 128
N, | 173 329 58108 ie 58°352 +002 +007 58361
109° 201 | |

As previously remarked, the difference in the resistance of the leads accounts for

the difference between N, and N,, and N, and N,.
We thus get

RR, +7r= {(N,+ N,) —(N, + N,)}/2 = 1038199 box ohms.
10°37648 “ legal” ohms.

10°35128 true ohms.

I

Reading of thermometer No. Il. = 684°77 millims. = 29°:997 C.
3 bridge-wire == 590°1, and null-point = 599'25 (see p. 288).

Therefore
d= — 0842 ¢

* Resistance in battery circuit (2 Leclanchés) = 700 ohms when observing N, and Ny, and 2900 chms
wheu observing N, and N,.

Dy Ok Ws

340 MR. E. H. GRIFFITHS ON THE LATENT

Hence 6, = 29°°913 and R, + 7 = 10°3513 true ohms.
therefore, when 6, = 80°:000 Ips oP SLO BHI 5, % op

The values of R vr at about 30° were also ascertained on other dates and were
1 ’
as follows :-—

Date. | - Temperature. Ry + 7. R, + 7 at 30°.
ea ne
September]5 . .. . | 30°003 10°3516 10°3516
October 5. er ae 30:245 10°3522 10:3516
5 0s | 30-044 10-3518 10-3517
elite | 29-913 10:3513 10°3515

I think it unnecessary to multiply examples at cther temperatures, the above will
show the order of accuracy.

From the above values, the value of 7 (= ‘0034, see p. 296) must be subtracted in
each case to get the value R,, given in Table VIII., p. 297.

DeEscRIPTION OF PuaAtes 4, 5, and 6.

PLATE 4.

The lower figure is a vertical section of the steel chamber and tank. The spaces
filled with mercury are printed in black. The tube at D communicated
with the regulating apparatus.

The upper figure is a plan of the lid.

PLATE 5.

Fig. 1 is a vertical section of the calorimeter. When gas was driven through the
apparatus it entered at f, passed into the bottom of the silver flask F at G
and left it near the roof at d. It descended to the bottom of the 18 ft.
silver coil (sections of which are shown by the small circles at C,), then
ascended a gentle slope and finally left the calorimeter by the tube e.
Although in different planes from the section, the position of the platinum
thermometer is indicated as well as S, the bottom of the stirrer. A “dropper”
is shown in position in the tube h.

Fig. 2 is a horizontal section across the calorimeter at AB in fig. 1.

Fig. 3 is a plan of the lid.

The stirring shaft passed through $8, the platinum thermometer down T,
and ‘the tube h’ established communication with the flask F (fig. 1). The

ends of the silver spiral are shown at c and /-

HEAT OF EVAPORATION OF WATER. 341

Fig. 4 shows the method of insulating the leads where they passed through the lid of
the calorimeter at / and /’ (fig. 3), and also the insulation of the four leads
where they passed through the steel lid (see small sketch, Plate 6, fig. 3).

PLATE 6.

Fig. 1 is diagrammatic only, for the various tubes, &c., repeatedly crossed each other.
The gas on entering passed through H,SO, at 8, then through P,O; at P,
afterwards through the 30 ft. coil indicated at C, and thus attained to the
temperature of the tank water. M, is an open scale manometer to show
the pressure of the gas when entering the flask F. Leaving this flask near
the top, the vapour traversed the coil C, and thus attained the temperature
of the calorimeter; it then passed through the four-way tap T,, and on
emerging from the tank passed over a row of small gas jets, shown at G.
The tubes between T, and B could be swept by dry air, by use of the taps
T, and T,. All the apparatus within the dotted lines was immersed in the
tank water.

Fig. 2 shows the arrangements of the differential thermometers and the bridge.
The coil of AB is in series with the compensators of CD and vice versd.

Fig. 3 shows the electrical connections with the calorimeter coil.

A coil in the tank at F was of the same resistance and wire as the
calorimeter coil. By means of the key K, the current could be switched on
to either coil. K, was also connected with the chronograph in such a
manner that all its movements were recorded.

By means of the Rheochord the external resistance of the storage circuit
(leads 2 and 4) could be so adjusted that the D.P. at the points M and
N was always that of the Clark cells. Wires numbered 1 and 3 are in the
Clark cell circuit.

Phil. Trans. 1895 A. Plate 4.

Griffiths.

WITTE
ZZ yy,

GALA

YG
Y

Gy fifi Vif SPSS, ff, Vf, VILE f, fy Ct,
GY Mi ji Mitt llh Li pp)

L.s1ze.

/

Fra

Phil. Trans. 1895 A. Plate 5.

Grifiiths.

Calorimeter.

Yanat size.

Section.

SSG
MGS

Sas NGG) |

SSYS59
v

Lid.

\ S
IPOOOQKOHHHHOHHOO |
<=

|

Fig.J

Se ee

‘eC BLY
p1oyo oayy
$//92 YAMID
yaa ebn10)g =
_ Gon
4osDOIpUy
'y

Phil. Trans. 1895 A. Plate 6.

x0Qg a9U20)SIS AY

‘1 Bly “YINasIQ. seH JO Mal, o/,eWWeIFeIG

A SE OSD BO OSS BB OO SSS SOO OOOO S SOAR Oa
adel aia et te ee ay

dung bye

dung az1ey ‘L
CTE V7)

Grifiths.

dung
12)

[ors4s sy

X. Contributions to the Mathematical Theory of Evolution.—Il. Skew Variation in
Homogeneous Material.

By Kart Pearson, University College, London.
Communicated by Professor HENRICI, ERS.

Received December 19, 1894,—Read January 24, 1895.

Puates 7-16.

CONTENTS.

Part I.—THEORETICAL.

Page.

Section 1.—Classification of asymmetrical frequency curves in general. -Types actually
occurring . . > 9 Be BlnG see Oi 344
Sections 2-5 —Fitting of point Ginomuale be methods of quadvatio nad eats cae vee le wo ee 345
Section 6.—TI]lustrations in cases of barometric heights and crab measurements . . . . 351

Section 7.—Fundamental geometrical relation between symmetrical binomial and normal
frequency curve. . . 6 . 6 : By a coke et ae 855

Section 8.—Extension of this Heaisa to the deatenon of a Eee eqnenoy curve from
the asymmetrical binomial. . . . : ket cbs el liGuG 356

Sections 9-10.—General remarks on the defects of the ‘seal fy equency curve as applied to

actual statistics. Skewness and limited range. The five types of theoretical curves . . 357
Section 11—The hypergeometrical series as replacing the point-binomial. Curves related to

the hypergeometrical series in the same manner as the normal curve to the ae ae

point-binomial . . . 360
Sections. 12-13.—Equations i the paasible feoueney curves deaiteoa sot ine yer

geometrical series . . cA OR aaeaes tegen 4 ee tcuct its Sp eB) | Bynes hic 362
Section 14.—Curve of Type L Fics eric with range limited in both dizeations Criterion

for the existence of this type and method of fitting . ......4.4.2.422.4. +, 367
Section) 15:—special case of range being/piven 2. a OO
Section 16.—Special case of one end of range being given. . . : ee 371

Section 17.—Curve of Type II. Symmetrical with range limited! in ibottl directions! This
curve better than the normal curve, if observations vary on the side of a point-binomial

from normality... . EEE TO OS Oho Ban Db \ a. ew OS ome one OMS 372
Section 18-18 bis.—Curve of Troe. UT. ane and range limited in one direction only.

Criterion and method of fitting . . 373
Sections 19-20.—Curve of Type IV. Ranes anlinntedle in hoth disedtions, eit siudwtibas!

Criterion and method of fitting. Discussion of the G-integral . . . . ... .- 374

16.7.95,

344 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Part II.—PRractican.

Statistical Examples.

Page.
Section 21.—The range of the barometer. . . ay iag Sst al SS) “US ee ye De 381
Section 22.—Crab-measurements (Weldon No. 4), an OEE te Lcd Vee AN A W'S” A 384
Sechions23:—Viariationyineherghbotmcecruits yee ca nineteen enn rnin n-ne ne nO 385
Section 24.—Variation in height of school-girls aged 8. . . E. 4a(h Sey Some aE ane 386
Section 25.—Variation in length-breadth index of 900 Bavarian Aieills fl a ee ee 388
Section 26.—Frequency of enteric fever with age. . . .....2.2.+.+:5. +... 390
Section 27.—Distribution of guesses at mid-tints . . ...... +... .2. =~. . 392
Section 28.—Distinction between “skewness” and ‘“‘compoundness” in case of crabs’
SUTOrcheadsiacp yes nes Kieec ars mrieh he Re rma ey ee MN eee Nera Cin ak GN sal ech" 6. + 394
Section 29. Civequency of divorce with aaeation OMENGEEY 955g Noho 1g 0 DO 395
Section 30.—Frequency of houses with given valuations . . . . ........ +5 396
Section 31.—Variation in number of petals of butterceups. . . . 2. 1. - 1 ee ee 399
Section 32.—Variation in number of projecting blossoms in clover. . . . ..... .- 402
Section 33.—Variation in number of dorsal teeth on rostrum of prawn . ...... . 403
Section 34.—Variation in pauper-percentages in England and Wales. . . . .... . 404
Section 35.—Resolution of mortality curve for English males into components. . . .. . 406
Section 36.—Concluding remarks on skewness, variation, and correlation (correlation ovals
forswhist) eee ene ee re ARR rE Meet m saul! GS Pano. 6 410
Note on THIELE’s treatment of Meare praqtenes See Oe eee Pee en? calla Mra. ™c 412

‘Part 1.—THEORETICAL.
Asymmetrical Frequency Curves.

(1.) AN asymmetrical frequency curve may arise from two quite distinct classes of
causes. In the first place the material measured may be heterogeneous and may
consist of a mixture of two ar more homogeneous materials. Such frequency curves,
for example, arise when we have a mixed population of two different races, a homo-
geneous population with a sprinkling of diseased or deformed members, a curve for
the frequency of matrimony covering more than one class of the population, or in
economics a frequency of interest curve for securities of different types of stability—
railways and government stocks mixed with mining and financial companies. The
treatment of this class of frequency curves requires us to break up the origina! curve
into component parts, or simple frequency curves. This branch of the subject (for
the special case of the compound being the sum of two normal curves) has been
treated in a paper presented to the Royal Society by the author, on October 18, 1893.

The second class of frequency curves arises in the case of homogeneous material
when the tendency to deviation on one side of the mean is unequal to the tendency
to deviation on the other side. Such curves arise in many physical, economic and
biological investigations, for example, in frequency curves for the height of the
barometer, in those for prices and for rates of interest of securities of the same
class, in mortality curves, especially the percentage of deaths to cases in all kinds of

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 345

fevers, in income tax and house duty returns, and in various types of anthropological
measurements. It is this class of curves, which are dealt with in the present paper.
The general type of this class of frequency curve will be found to vary (see Plate 7,
fig. 1) through all phases from the form close to the negative exponential curve :

— Ce-??,
to a form close to the normal frequency curve

— (Cenez
where C and p are constants.

Hence any theory which is to cover the whole series of these curves must give a
curve capable of varying from one to another of these types, @.e., from a type in
which the maximum* practically coincides with the extreme ordinate, to a type in
which it coincides with the central ordinate as in the normal frequency curve.

It is well known that the points given by the point-binomial (4 + 4)” coincide very
closely with the contour of a normal frequency curve when 7 is only moderately
large. For example, the 21 points of (5 + $)” lie most closely on a normal frequency
curve, and the author has devised a probability machine, which by continually bisecting
streams of sand or rape seed for 20 successive falls gives a good normal frequency
curve by the heights of the resulting 21 columns. Set to any other ratio p:q of
division other than bisection, the machine gives the binomial (p + q)”, or indeed any
less power and thus a wide range of asymmetrical point-binomials. Plate 7, fig. 2,
represents, diagramatically, a 14-power binomial machine.

Just as the normal frequency curve may be obtained by running a continuous
curve through the point-binomial ( + 4)” when vn is fairly large, so a more general
form of the probability curve may be obtained by running a continuous curve through
the general binomial (p + q)”. As the great and only true test of the normal curve
is: Does it really fit observations and measurements of a symmetrical kind ? so the
best argument for the generalised probability curve deduced in this paper is that it
does fit, and fit surprisingly accurately observations of an asymmetrical character.
Indeed, there are very few results which have been represented by the normal curve
which do not better fit the generalised probability curve,—a slight degree of
asymmetry being probably characteristic of nearly all groups of measurements.
Before deducing the generalised probability curve, it may be well to show how any
asymmetrical curve may be fitted with its closest point-binomial. This will be the
topic of the following five articles.

(2.) Consider a series of rectangles on equal base c and whose heights are respec-
tively the successive terms of the binomial (p+ q)" X a/c, where p+q=1. Here «is
clearly the area of the entire system. Choose as origin a point O distant $c from the

* J have found it convenient to use the term mode for the abscissa corresponding to the ordinate of
maximum frequency. Thus the “mean,” the ‘‘ mode,” and the “median ” have all distinct characters
important to the statistician.

MDCCCXCV.—A. 2

346 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

boundary of the first rectangle, on the line of common bases, and let y, be the height
of the 7™ rectangle, or

T= eos GSP aE) ey
Yr = ie a ) p r+1 q ui

c
while |
yy, = ap"/c.

<C x C3 CH CS CH CC® CC® CP
N

Let us find the values of

where s is any integer, for values of s from 0 to 4.
It is easy to see that
E l @\ if @
Set 10\st — # = (g 5- — / nu
SAS UA) |) Eee = (7 -) ---9(p +49)",

where the operation d/dq is repeated s times.
The operations indicated can easily be performed by putting g = e” when

du

Sy nrr\S 2 auc? d a 2 u\n
Sine x (rey} =“ (4) fer(p + e9"},

and the successive values can be found by Lerenirz’s theorem. After differentiation
we may putp+gqorp+e"=1. There results:

YrC) ae
> (KO x TON | ms xg: al SEN ops
J) = ac + 8ng + n(n — 1) 3
= (yc X (re)?) = ae {1 + 7ng + 6n (nv — 1) + n(n — 1) (n — 2) 3
c)*) = act {1 + long + 25n (n — 1) @ + 102 (n — 1) (n — 2)
+ n(n — 1) (mn — 2) (m — 8) g.
Let NG be the vertical through the centroid of the system of rectangles, then

clearly
ON = = (y,¢ X re)/a =c {1 + ngt.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. . 347

We shall now proceed to find the first four moments of the system of rectangles
round GN. Jf the inertia of each rectangle might be considered as concentrated along
its mid vertical, we should have for the s™ moment round NG, writing d= c(1-+ gq),

ap, = S{y,c X (re — d)°}.

The resulting values are

Hy = npge
Hs = mpg (p — 9g)
Hy = npg {1 + 3 (7m — 2) pq} ct,
whence, remembering that p + ¢ = 1, we find that p and q are roots of

(Bpg" = Hy) Me + Ms”

9
home ag - = 0
2 4 (Bply” — ply) Ma + Bg” ‘

Wes 2 p98 2 iS VS 12 (Bp? = by) Ma + 8ps"}
(Bug — Ha) Ba + Ms? P2

Thus, when pz, pz, and p, have been calculated for the frequency curve, the
elements of the point-binomial are known. ‘These results were given by me in a
letter to ‘ Nature, October 26, 1893.

They give quite a fair solution so long as n is large and ¢ small, 2.e., so long as the
asymmetry and the “excess” (‘ Phil. Trans.,’ vol. 185, A, p. 93), measured respec-
tively by ps; and py — 3p.” (which vanish for the normal curve) are not considerable.*
In many cases, however, they are considerable, and the following solution is perfectly
general.

* If y, denote the largest term in (p+ q)" and y, the ‘th term beyond it, then an application of
Srieiine’s theorem—if n be large—shows that

EE Nt= f t \-—t-—qn—-k
vin =(1— =) (+2) :

‘ | qu
Take
t X
log wu = (tf — pn — 3) tog (1 Fp)
t
log ¢ = (—t— qn = }) og (1 + ra

and expand the right hand side in powers of #, we find

1 Za il me if 1 es 3
ee ‘(1 ug om) ~ Qn { IL zs} 6p?n? (1 me =) ~ 12p8n3 (1 = al Ue:

Hence, remembering that p + ¢g = 1, we have

AUD Oy ( cs he200) reid) ae =)
2pqn 2npq 2upq ) 29?

log w = —

te 3 (1 = 4pq + 2p*q")
= 12piqin’ (1 — 3pq — Qnpq + ete.
Now, making use of the values given in § 2 for jy, wz, and m,, and writing t X c= a, and y;= y,
we find

4 XB

348 - MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

(3.) To find the nth moment of a trapezium ABCD about a line parallel to its
parallel sides, y, and y, being the lengths of the parallel sides, «,, x, their distances
from the moment-axis, and x, — #, = ¢.

A

Y)

WN
VRNALAAAYAV AL

iN

AN

a
As

A

ANAAAARRAAYER

PAA

Sy
8

OF SS) f
‘ 2, 1

Let M, be the mth moment. Then

M, = | ya" de

Yo — I xint? —7 n+2 ai Ifa — YoLy poittl —7. a+1
fy — 2, n+2 Ly — 2; n+1
[29/26 Di ees DQ p26 9 OG) (@=2) 5 an
Sy ee EL
WE |e [4 [5 /
Bie nN Pp ie Dee INCOR) is \
= Se Ob i a XL, ; PM ee
ule type + ee ee

(4.) Now consider a curve of observations made up of a series of trapezia on equal
bases, as in the accompanying figure :

2

(1—B,-3(8—:)) Mate Hs" (1—§ B\—3 (3—Bo)
aaa IPr“BB-BM) x 0 FE x 0 Gags IE A—3 BAe)

ane MX O— Toa GPIB B-P)-38- Ba —9 BP 2-8) BD) ye ote,
where By = ptz?/uo° and Bg = py! p19”.

This appears to be the more general form of a result given by Professor Epcrworra, ‘Roy. Soc.
Proc.,’ vol. 56, p. 271.

For the normal curve “3; = 0, “4, = 3,7; hence, if p does not differ much from q, A, and B, — 3 will
be small, and we may neglect their products with x//n. Thus approximately

2? 5 ne
Y = YoC” my, By, ( ina)
This agrees with Professor Epcrworvn’s special case if we expand the second exponential. His

“negative frequency ’’ is accounted for by the fact that he has only taken the first terms of a long

series, 7.e.,

¥ —22/2n5 J Bay #3
PSOne ll = 25” (2 os 3) ;

I have not considered this form of the skew-curve at length, because it is only a first approximation to
the more general forms considered in this paper, and further, because it is only applicable in practice

within extremely narrow limits.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 349

XL, - >

Here 4, yg, Us, +--+ y, are the frequencies of deviations falling within the ranges

a +4c, x, +4¢, x, +4c...2%,+4¢..., and the tops of the ordinates are joined
to form a frequency-curve in the usual manner.
Let M’, be the nth moment of the system of trapezia about the Jine Oy, then

M., — S 2y; ( a

Vie

n we 1) 2," — 203 + uv (a ae 1) “ 2) (a el 3) GUST G2 + eee )t.

+

ww)

In particular, if we take Oy in the position O'y’ at distance ¢ from y,, we have
x, = re, and accordingly,
n(n — 1) (m7 — 2) (wv — 3)

uv (n—1) _, “
12 Noo t 360 Ni

n(n —1)(n — 2) (n — 3) (1 — 4) (1 — 5) LL,
1 20160 N

Miee—t62 (W’, ar

n—6 ar ete.) 2
where N’, = S (y,7°).

In particular,
, y

/ as p) y

7 CONIC.

M
M
M, = (N, + ¢N),
M
M

I

sO: (N’, ote aN);
4=e (N’, + Nj T5N%),
M’, = o® (N’, + EN’, + 4N)).

When we put M’,/M’, = p’,, and N’,/N’, = v’,, these reduce to

by aa cv,

jig =O (vg + GM0)s

Bh, = (v's + 3r);

Big = CF (4 +g + T5Y0)s
Bs =e (V's + 3y'5 + 3r))- |

Now let pw, be the value of the mth moment of the trapezia system about the
vertical through its centroid divided by its area.

390 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

We have:

D(@=N) 45 7 m (m — 1) (m = 2) j

[hp = [in = TOD i [Bien ie ae it Poe 1.23 1? baa + ete.

Thus we find:

by = 0,

Py = (vg — vy + i65),

Hts = CO ('5 — By, v'y + 2n'),

Py = Cy (v'g — Avy v's + 6 Pv'g — Bv44 + {rn — v'? + H5}),

Bs = 8 (v’, — Sy’) vy + 10? v's — 10n'? vg + 40’? + f3 0’, — dv, v’, + HP 7).

Comparing these results with those given in the ‘ Phil. Trans., vol. 185, p. 79,
Eq. (4), we see that treating the curve as built-up of trapezia instead of loaded
ordinates introduces the parts into the values of the p’s enclosed in curled brackets.
These additions are small, but in many cases quite sensible. Since the series of
trapezia gives in general a closer approach than the series of loaded ordinates to the
frequency curve, and, further, since the calculation of these additional terms is not
very laborious, it will be better for the future to calculate the moments of any
frequency curve from the above modified formule.

(5.) Returning now to the point-binomial, we have :

Yale eG ;
vg = 1+ 8ng + n(n — 1) @?,
v's = 1+ 7ng + 6n (n — 1) + n(n — 1) (a — 2),
v= 1+ ling + 25n (n — 1) q? + 10n (mn — 1) (n — 2) 4°
+ n(n — 1} (n — 2) (n — 8) q¢.
Thus :
Hy = & (npg + ¥),
— npg (¢— P),
by = C8 (q's + npg (2 + 3 (n — 2) pq)).

=
oo
I

If, instead of taking trapezia, we had taken a series of rectangles, but not, as in § 2,

concentrated their areas along their axes, we should have found the following -

system :
Ho = © (npy + 1),
Hs = — npg (q — P)s
Hy = (so + npg (3 + 3 (1 — 2) pg).

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 351

Hence if we write :

o* (npg + «),*

Hs = — pq (g — Pp);

py = ct (G + npg (e+ 8 (n — 2) p9)),

=
w
I

we have:

For trapezia : — Lo

|
pac

fay)

g

I

{
5S
|
l—
21
&
|
—
ol

For rectangles : G25 3
For loaded ordinates: . =0, «|=0, 6

I

and the above general system may be applied to all cases.
Writing

9

ae mets
210. B= :

we have by elimination the cubic for z:

2° (6 + 38, — 28.) + 2 (2e3 — 3 + 9Bie, — 48 €))
+ 2 (Ze, + 9B Ee” — 2B,€,") + 38,6? = 0

The remaining constants of the binomial are :

ops a5 = (el sae GIP)

= a/-#+
ete

(6.) Let us illustrate these results by a numerical example. Plate 8 gives
Dr. VENn’s curve for 4857 barometric heights. Along the horizontal, 1 cm. equals *1”
of height of barometer, and the scale of frequency is 1 sq. em. = 28°304 observations.
The centroid vertical and the second, third, and fourth moments about it were found
for me{ by the graphical process described, ‘ Phil. Trans.,’ vol. 185, p. 79. We have
the following results :—

and

fey
|

# This result seems of considerable importance, and I do uot believe it has yet been noticed. It gives
the mean square error for any binomial distribution, and we see that for most practical purposes it is
identical with the value “pq, hitherto deduced as an approximate result, by assuming the binomial to
be approximately a normal curve.

+ If we take z+ «4 =x the fundamental cubic reduces to

(6 + 36; — 262) x3 — 2-3) x? + ox — as = 0;
a form in which the coefficients are easily calculated and the nature of the roots discriminated.
t By Mr. G. U. Youre, who has given me very great assistance in the laborious calculations required
in the reduction of frequency curves. We have used, with much economy of time, the “ Brunsviga”
calculator. é

352 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

a = 171°6, fig = 10°14,
fy = 15°95, ju, = 826°34,
all in centimetre units.
These give
B, = °24401, By = 3°1739.
Hence for trapezia,
*38422° — °7499172? + 0180082 + 003389 = 0,

and for rectangles,
*384223 — °874962* — -003832z + 000424 = 0.

These give the following solutions :—

Trapezia. Rectangles. Lines.

Z 192516 2°28034 2°6028
a 19°379 23-983 28°5293
p 8881 "8936 89985
q “1LLO 1064 ‘10015

C 2°2017 20712 1974
a/c 77:94 82°85 86:93

d 6:976 | 7:3562 7614

Here d = c(1 + nq) gives the distance of the start of the point-binomial from the
centroid vertical. The three point-binomials are therefore

77°94 (8881 + -1119)9%%,

82°85 (8936 + °1064)"°*,

86°93 (89985 + °10015)"°™,
respectively.

These three point-binomials are represented in Plate 8, fig. 3. It will be noticed
that they all lie very close to the barometric curve; they would be still closer if that
curve were a real curve and not a polygonal line. The total areas between bimomial-
polygons and observation curves, treating all parts as positive, are for the three cases,
10°3, 10°5, 11°0 sq. centims. respectively, or taking the base range to be 23 centims., we
have mean deviations from the observation curve of ‘448, ‘457, 478 in the three cages
respectively. Thus the method of trapezia gives slightly the best result ; the method
of concentrating along ordinates the worst result. The total area of the curve being
171°6, we have from another standpoint, mean percentage errors* in the ordinates
of about 6°03, 6:06, and 6:3, respectively. The generalised probability curve, if fitted
to the same observations, gives an areal deviation of 7 sq. centims., or a percentage
error of about 4. Thus it is very nearly one-third as close again as the point-binomials.

* The “ percentage error” in ordinate is, of course, only a rough test of the goodness of fit, but I have
used it in default of a better.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION, 353

As typical samples of mean percentage errors considered by various statisticians to
give good results, I may note the following, the frequency being about 1,000 or
upwards :—A1ry, 9 ; MEeRRIMAN, 13°5 ; Gatton (Anthropometric), 7 to 15 ; WELDON
(Crabs), 6°7, (Shrimps), 8°8; StrepA (Skulls), 7°6; Porrer (School Girls), 7°7; PERozzo
(Recruits), 6°8 ; BRADLEY’s observations, 5°85 ; PEARSON (Lottery), 6°7, (Tossing), 6°6.

It is therefore clear that our point-binomials and generalized curve may be con-
sidered to give good results.* It will be noticed, however, that a little difference in
the method of calculating the point-binomials leads, without much alteration of the
percentage error, to a considerable change in their centroid-positions and the magnitude
of their constants.t Generally speaking we may conclude that in round numbers the
barometric frequency corresponds to the binomial (‘9 + *1)”, or to the distribution of
zeros when 20 ten-sided teetotums, marked 0, 1...9, are spun together. There is
an apparent upper limit to the height of the barometer, and its deviation below the
mean can be much greater than its deviation above. At the same time within the
narrower range round the mean, the frequency of a high barometer is greater than
the frequency of a low barometer; the odds against a “ contributory cause” tending
to a low barometer being about 9 to 1. I propose to investigate a wider series of
barometric observations, in order to test how far the conclusions which may be drawn
from Dr. VENN’s statistics are general.{

A rather interesting point may be considered at this stage. Is it always possible
to fit a point-binomial to a series of observations with a chance frequency ? Can we
better the normal curve by a point-binomial ? The answer is Yes, if the fundamental
cubic in y (second footnote, p. 351), has a real positive root. Now for the normal curve
2 (8p? — by) Ha + 3pyy°, or 6 + 38, — 26, is zero. For the loaded ordinates ¢ will
only be real if this expression be positive. It may, however, take small negative
values for the trapezia, in which case y itself will be small and only within narrow
limits give suitable values for n.

Hence, for real values of n, p and q, it is impossible to fit a point-binomial to a
series of observations for which 6 4- 38, — 28, has a large negative value. The normal
curve, for which p, = 3p”, is nearer to any such observations than a point-binomial.

For example, by aid of the modified expressions given in this paper, p. 350, we have

* As another manner of testing, compare the ten-points of the point-binomial for lines with obser-
vations :—

WMineomy Eo eG GRO BRS) pale). IS) TL), GP eee 8 0S)
Observation . .. 57 158 221 188 12 58 23 11 -2 -00

+ A curve drawn through the 30 points of the three point-binomials would be very close to the obser-
vations. As a matter of fact, the skew probability curve passes very near to all 30 points.

+ [Miss A. Lee has since calculated the constants of three years of Hastbourne barometric observations
for me. While x and c differ widely from the Cambridge values, she finds p = ‘89375, q = (10625, a
striking and suggestive agreement. |

MDCCCXCY.—A. 22

dé

354 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

for the data given for Professor WELpDon’s Crab Measurements, No. 4, ‘ Phil. Trans.,’
A, vol. 185, p. 96. :
up = 76759, pig = 3°4751, pr, = 184°3039.
Hence,

By = p3"/by? = 0267022,

8, =" fal po — ol 2807.

Thus 6 + 38, — 28, is positive, and accordingly no rational point-binomial is likely
to fit as well as the normal curve. Asa matter of fact the fundamental cubic is now

176032? + 1:0453272? + 0337732 — 0003709 = 0.

The two negative roots of this equation give imaginary value for p and g. The
small positive root gives p greater than unity and q uegative, n is also negative.
Although I can give no interpretation to these results, it seemed well to complete in
the latter case the solution and test how near the resulting point-binomial fitted the
curves. I found

2— (00866, p= 119268) .¢,=— 19268)
n= — ‘087685, c= 661662, d= 6'6645.

These give for the binomial
150°0983 (1°19268 _— PIS ARiS))

151°89.(1 — *161552)— 087685,
or,
151-89 + °92532 + ‘07756 + &c.

Thus the sensible part of the binomial to the scale of our figure is a triangle. I
have drawn this binomial, see Plate 8, fig. 4. The reader will mark a fit very close
on the whole to the observations. We have the following percentage mean errors of
the ordinates :—

INormalvcurve™. =o ee Sue enone
Skew probability curve. . . . . 4°4,
Bimomnvayl 2%) 1 ae ae hee ete rer aseenl toe

We may conclude, therefore, that even if our binomial constants-have unintelligible
values, yet our method will give, in many cases, a closely-fitting polygonal figure.
This remark should be read in connection with Professor EpGEWoRTH’s somewhat
divergent views* on fitting chance distributions with curves other than the normal
error curve. It is possible in almost every case to find simple combinations of lines,

* See ‘ Phil. Mag.,’ vol. 334, p. 24, et seq., 1887.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 38095

circles, or parabolas of various degrees which give results extremely close to any given
set of observations.

For example, taking the range of frequency to be sensibly 7 times the standard
deviation, we have the following close expression for the error function by harmonic
analysis

z 2a 3
y = Y {899 + “482 cos + 109 cos + “009 cos Ff

Here y, is the maximum ordinate, x any deviation, and o the standard deviation.
A couple of wave curves* will thus very frequently give us a close approximation to
a set of statistical measurements, quite as close as statistical practice shows the error
curve to be.

The above expression further allows the normal curve to be constructed by aid of
scale and compasses—geonietrically, or its ordinates calculated from a table of cosines.

Another example of the fitting of a point-binomial will be found in Part 2, § 34,
Pauper Percentages.

(7.) Consider the point-bimomial e xX ($+ 4)", where e is any constant, and
suppose a polygon formed by plotting up the terms of the binomial at distance ¢
from each other.

Then, corresponding to x, = rc, we have

DO. WG Ac os (Ge ae) pany
Yo = € [p—1 (3)”
and
Yror a Yr ee Ae (1 ate 2) ian (a + @r 41) Ure (wy We, wy 4)
£ (Yrs, + Yn) Xe sate I AGED Se

if w’, = a, — 4c(n + 2).
Now (y,+, — y;)/e is the slope of the polygon corresponding to the mean ordinate
4(Y,2,+ ¥,), or, writingt P® =} x t(n4+ 1)2e,

slope of polygon 2 x mean abscissa

mean ordinate 20°

* Jt is often sufficient to take

ae 2x
y= (8 + 7 COS ~~ + 7 Cos ar
+ The divergence of this value of o? from the ordinary value 4 x 4 x nis to be noted. The two agree
sensibly if n be great. [Drawing on a large scale, however, the point-binomial ($ + 4)!° and the two
normal curves with standard deviations of 1°5811 and 1°6533, I find that the latter has a mean percentage
error of only 1°76 as compared with 5:1 of the former. Thus it would appear that the normal curve
corresponding to V(n + 1) pq fits the point-binomial closer than one with the standard deviation Vv apq
usually adopted. |
22

bo

356 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Now compare this property of the polygon with that of the curve:

y = OOS
We have by differentiation :
slope of curve __ 2 abscissa
ordinate ~ 2c

Hence: this binomial polygon and the normal curve of frequency have a very close
relation to each other, of a geometrical nature, which is quite independent of the
magnitude of n. In short their slopes are given by an identical relation. By a
proper choice of o and y, we can get the normal curve to fit closely the point-
binomial, owing to this slope property, without any assumption as to the indefinitely
great value of n. It is this geometrical property which is largely the justification for
the manner in which statisticians apply, and apply with success, the normal curve to
cases in which 7 is undoubtedly small. No stress seems hitherto to have been laid
upon the fact that the normal curve of errors besides being the limit of a symmetrical
point-binomial has also this intimate geometrical relationship with it.*

(8.) Now let us deal with the skew point-binomial in precisely the same manner as
we have dealt with the symmetrical binomial. Taking its form to be e(p + q)", we
have, if x,= 7 X cand \ = q/p:

VERS Oh 2G eae Nie OG ae Dy es ae)
Yap tye ¢(m—r+)aAfr+17 cAam+1)+7r0—A))

Let us write Ay = 4, — Yn Av =e.
Ya = z (Yr aa oF Y,), Nee ee 45 (2, ap il aF Dyn
Then X,..,/e=7-+ 3, and:

* The following table shows the closeness of frequency within a given range as determined by the

binomials :-—
= See = Le aa
Frequency per cent.
Range oF Normal curve.
deviation.
| el =p 110. | qd ae 15) 20
aa a Ee
| 3 | 24 23 24
5 | 37 3 38
7 50 52 52
11 | 71 73 73
V5 | 87 87 87
21 96 96 96
33 100 100 100

Here the distribution of 100 groups each of 100 events is seen to be practically the same whether we
take n = 10 orn=om.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 357

n(n + 1)— (+a) (A — 3)

c

NO ae

> aay, [X; :
Bex tes ae 4 =a) (A 4)

or, if X42, = X%.,-—e(4+¢(n4+ ))),
— ean XG

Tay - Oss
paint e+ (p— OX ra

feu | ne y Xia
—— eae
at Xp,

angi eee
(p—e D4
The curve which has the same law of slope as this skew binomial is :

ify=

I= YO (1 + x/aye7%,

(9.) This curve accordingly stands in the same relationship to the skew binomial
as the normal curve to the symmetrical binomial.* There are several points, however,
to be considered with regard to it. In the first place it is usually assumed that n is
indefinitely great and c indefinitely small, and then it is supposed that we may
neglect (p — q) cX’..; as compared with pg (n + 1)c*, and so we deduce the normal
error curve whether p be equal to q or not. But I contend that this is unjustifiable
except for very small values of X’.,:, When the deviation X’ is considerable and
¢ vanishingly small, X’ will be an indefinitely great multiple of ¢; c must be in fact
the unit in which X’ is measured and unless p = q, the ordinary normal curve is only
an approximation, even if 7 be large, near the maximum frequency. In the next
place, when we speak of 7 being large, are we quite clear as to what we mean in the case
of physical or biological frequency curves? We speak of a multiplicity of small
“causes” determining the actual dimensions of an organ, or the size of a physical
error, or the height of the barometer. But it is less clear why this multiplicity
should be identified with the infinite greatness of n. If we take Dr. VENN’s
frequency curve for barometric height, we see that the closest point-binomial is by no
means consistent with either p= q, or with n being indefinitely great, Further,
many statistical results in games of chance are given with great exactness by the
normal curve, although we are then able to show that n is quite moderate.

Now, it is true that the biological and physical statistics to which we are referring,
give essentially continuous curves, but it does not seem to follow of necessity that 7
must be infinite ; while their frequent skewness sufficiently indicates that the neglect

* Note again the deviation of the constant pq (n + 1) c? from its usually adopted value pgnc?.

358 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

of X’.,, as compared with @ is unjustifiable. Thus, the maximum of a fever
mortality curve cannot be an infinite distance from birth, which limits the curve in
one direction, nor an age-at-marriage curve have a maximum frequency infinitely
distant from the age of puberty, nor a frequency of interest curve separate its
maximum, between 3 or 4 per cent., by an infinite distance from 0 per cent. It is
clear, therefore, that if such frequency curves as those referred to are to be treated
as chance distributions at all, it would be idle to compare them to the limit of a
symmetrical binomial. We are really quite ignorant as to the nature of the contri-
butory ‘‘ causes” in biological, physical, or economic frequency curves. The continuity
of such frequency curves may depend upon other features than the magnitude of n.
If I toss twenty coins, a discrete series of 0, 1, 2, 3,... 20, heads is the only possible
‘contributory cause’

¢ ?

range of results. Each individual coin, here representing a
can only give head or tail, and so many whole coins must give head, so many tail.
If I want to make any ratio of head to tail, I have to take an indefinitely great
number of coins, for each ‘ contributory cause” must give a unit to the total. But
it may possibly be that continuity in biological or physical frequency curves may
arise from a limited number of “contributory causes” with a power of fractionizing
the result. We cannot conceive on the tossing of 20 coins that 13°5 will give heads
and 6°5 will give tails, we are obliged to deal with 200 coins, 135 giving heads and
65 tails. Yet the two things are not identical. The former corresponds to a value
intermediate between two ordinates of (4 + 4)*°, and the latter to a definite ordinate
of (+4). So long as we remain in ignorance of the nature and number of
‘contributory causes” in physics and biology, so long as we do find markedly skew
distributions, it seems to me that we must seek more general results than flow
from the assumption that p = g and i = «. The form of curve given in § 8 above is
suggested as a possible form for skew frequency curves. Its justification lies
essentially, like that of the normal curve, in its capacity to express statistical
observations. :

(10.) But it must be noted that the generalised probability curve in § 8, although
it contains the normal curve as a special case, is not sufficiently general. It is
limited in one direction, indefinitely extended in the other. This limitation at one
end only, corresponds theoretically to many cases in economics, physics, and biology.
But there are a great variety of cases in which there is theoretical limitation at both

Cc

D

ends ; that is to say, there is a limited range of possible deviations. For example,
let a trapezium, ABCD, of white paper be pasted on a cylinder of black surface with

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 359

ef, the axis of symmetry parallel to the axis of the cylinder. Then, if the cylinder
be rotated, we shall have a series of grey tints from a darkish e to a lighter f.
Now, if we ask several hundred persons to select a tint which would result from
mixing the tints at e and f, we shall obtain a continuous frequency curve, falling,
however, entirely within the range e to fi Or, again suppose a frequency curve
obtained by plotting up the frequency of a given ratio of leg-length to total body-
length, or of carapace to body-length. Here the range must lie between 0 and 1.
It is not that other values are excessively improbable, they are by the conditions
of the problem absolutely impossible. Hence, it is clear that the curves obtained
by Professor WreLpon and Mr. H. Tompson in the case of shrimps, crabs, and
prawns, can only be approximately normal curves, even if it were possible for the
ratios to run from 0 to 1. But as a matter of fact, the possible range is very
much smaller. We may not be able to assert, @ priori, what it is, but for an
adult prawn to have a carapace 3 or yolgo Of its body-length, or a man a leg
3 or zo of his body-leneth, may be regarded as impossibilities ; they are abnor-
malities, which could hardly survive to the adult condition. Precisely the same
remarks apply to skull indices, and probably to the relative size of all sorts of
organs in the adult condition. We may not know the range, @ priori, but we are
quite certain that one exists, and it is a quantity to be determined—just as the mean or
the standard deviation—from our measurements themselves. We may take it that in
most biological measurements of adults there is a range of stability, so to speak,
organs not falling within this range are inconsistent with the continued existence of
the individual, with the assumption that he has lived to be an adult.* Nor is this
question of range confined to biological statistics. A barometric frequency curve
must show the same peculiarity ; there are excessively low and excessively high
barometric heights which would be not only inconsistent with the survival of any
meteorological observer, but also with the existing features of physical nature on
this earth. In vital statistics we find precisely the same thing, a curve of percent-
ages of mothers of different ages for the children born during any year in a country
would be definitely limited by the ages of puberty and the climacteric, which cannot
be pushed indefinitely towards childhood and senility respectively. Again in disease
and mortality curves, while the lower limit of life is clear, it is highly probable that
an upper limit exists, if we can only fix it by investigation of our statistics them-
selves. A man of the present day, as now organised, may be able to live 120 years,
perhaps, but we have exceeded his vital possibilities if we take, say, 200 years.

Thus the problem of range seems a very important one, it theoretically excludes the
use of the normal curve in many classes of statistics; it is quite true that, for
many practical purposes, frequency curves of limited range may be sensibly identical
either with unlimited curves, or even with normal curves, but, in other cases, this

* Absolute malformations, congenital, or due to post-natai accident are excluded. Abortions or
amputations would be naturally excluded from our measurements,

360 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

is not so, and under any circumstances the limited curve may actually give information
as to the possible range—the “ limits of stability ”—which is itself of great value.

We have, then, reached this point: that to deal effectively with statistics we
require generalised probability curves which include the factors of skewness and range.
The generalised curve we have already reached, possesses skewness, but its range
is limited in one direction only.

Accordingly, we require the following types of frequency curves :—

Type I.—ULimited range in both directions, and skewness.

Type II.—Limited range and symmetry.

Type ITI.—Limited range in one direction only and skewness.

Type IV.—Unlimited range in both directions and skewness.

Type V.—Unlimited range in both directions and symmetry.

Type V. is the normal curve; Type IV., with slight skewness, has been dealt
with by Porsson in the form of an approximative series.* Type III. has been given
above, it was first published by me without discussion in ‘ Roy. Soc. Proe.,’ vol, 54,
p. 331.

We can now turn to the general problem.

(11.) A very simple example will illustrate how a frequency curve, with limited
range and skewness, may be considered to arise. ‘Take n balls in a bag, of
which pn are black, and qv are white, and let 7 balls be drawn and the number
of black be recorded. Ifr>pn, the range of black balls will lie between o and pn;
the resulting frequency polygon will be skew and limited in range. This polygon,
which is given by a hypergeometrical series, leads us to generalised probability
curves, in the same manner as the symmetrical and skew binomials lead us
to special cases of such curves. If we consider our balls to become fine shot, or
ultimately sand, and suppose each individual grain to have an equal chance of being
drawn, we obtain a continuous curve.t It is not, however, impossible that, could we
measure with sufficient accuracy, many physical as well as biological statistics might
be found to proceed by units, much as in certain types of economic statistics we are
not troubled with fractions of a penny. For this reason we shall keep our results
in the most general form, and obtain a curve approximating to the hypergeo-
metrical series referred to without any assumptions as to the relative magnitude of
the quantities involved.

We easily obtain for the series giving the chances of r, 7 — 1,7 —2... 0, black
balls being drawn out of a bag containing pn, black, and qn, white, the expression

* “Sur la Probabilité des Jugements,” chapter 3.

+p pints of red sand and gq pints of white sand are put into a vessel, and 7 pints are withdrawn. We
have if 7 >, a perfectly continuous frequency curve for red sand withdrawn ranging between o and p
pints. We are here supposing no “ perfect mixture” of the two kinds of sand, but theoretical equality
of chances for each grain,

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 361

pn (pn — 1) (pn — 2)... (pn —7 + 1)
n(n — 1) (n— 2)...(n—7 + 1)
é qu r(r — 1) gn (qu — 1)
eet 1.2 (pn—r +1) (pn—r + 2)
7 (7 — 1) (7 — 2) gn (qn — 1) (qn — 2) ):
u 1A) (pu — 7 + 1) (pr —7 + 2) (Gaapeay Te

If y, be the s ordinate of this polygon, and we suppose these ordinates plotted up

at distances ¢ apart, we have

pen C= 8 ap EG 8 sp i

Fan aie es
LSC. Cera stew li) ces
Xu, 0 (s+ 4).
Thus
Ys+1 — Ys 2 (y +1) (1 + qn) — 8 (n + 2)

E Wert yy xe 6 (+1) +n) —s{20¢ 41) +2(q—p)} + 28

7+1)a+q)—- (A — t) (n + 2)

\ Q
“@ +d tom — (M93) BO 41 + m(g— pr 2( = §)
\ ¢ G é

Write
E (+10 + a)
Xiey = Key 0 (9+ n+ 2 }

and we find with our previous notation

Ay 1 aa Xi s43 ( )
= = =a ay eatclste om Lata oceaeeesceeeeine 1 ((E)))
Av Ys43 By + BiX’s4y + BsXs45

where
a 2 (7 +1) (w~@—7r4+1) (1 + qn) (1 + pn)
Ua (n + 2)3 ‘

__ on (n — 2r) (p—4@) ee ELS
= gaan |. * Pa ae

Now, if we attempt to find the curve which has the same geometrical relation for
the slope as the above hypergeometrical polygon, we see that it will change its type
according to the sign of 8,” — 48,63.

After some reductions we have

Vesa ieee eee og Lat
pe Ver ee a tegae V et seta)

MDCCCXCV.—A. ; 3A

362 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Hence ,/{8,” — 48,83} will be real or imaginary, according as 7/7 lies outside or

between the limits
1 1)
tt J [eta )at a}

If +/n lies outside these limits, then the integral of the right-hand side of
equation (e) is purely logarithmic; if it lies between these limits, the integral is in
part trigonometrical.

Since r must be less than n, it follows that the integral must be trigonometrical if
these limits are respectively = <0 and = >1, «.<., if

(p + 1/n) (q + Un) = or > F,

; 1
or p must lie between } + A) (1 ote = :

For example, if 1 = 100, then, if p lies between °6005 and °3995, the integral must
be trigonometrical. If p lies outside these limits, say = ‘7 for example, then the
integral will be logarithmic if 7/n does not lie between ‘04 and ‘96, z.e., if we draw
a small or large proportion of the total contents.

Let us treat the trigonometrical and logarithmic cases separately.

(12) ‘Case I 8,7 < 487 8:.

The curve having the same geometrical slope relation is

log y = constant — aif log (B, + B,« + Bx”)

ee By 2 tan 72 283% + Bs
2B; »/ {48:83 — 82°} V/ {4B Bs — Bo}

Write « for « + B,/28,, changing the origin ; further put a for ,/ {48,8, — 8,°}/(2Bs),

f for (283), and v for oe.
integration,

then we have, y, being a constant of

Yo ~y tan —) (v/a)

Uae (1 + a?/a?)

This frequency curve is asymmetrical and has an unlimited range on either side of
the origin. It corresponds accordingly to the curve required as Type IV.
Here
a = te,/{4(1 + pn) (1 + qn) — (n — 27°},
eh n(n — 27)(p— q)
ia V/{4(1 + pn) (p + gn) — (n — 27)?}
m=4(n-+ 2).

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 363

Special cases. (i.) Suppose r/n = x, and v very large, then

9
m/a? = = = — = a), Say,
DCSE aay)
Lo Gi
Sip Se ee

¢ (pa — (4 -x)”)
Thus we have
y —_ Yoe = a,x? — oar

which reduces to the normal type by a change of origin. It is important to notice,
however, that the standard deviation of this normal type

= /(1/2m)) = e/ {nr (pa — (4 — x)’)};

and is very different from the value ¢,/{(r + 1) pq} = 4ce,/ (npq X 4x), nearly, which
is the usual form. Only when we put p = q = 3 and make y small do they agree.
We thus conclude: That the normal form may fit a chance distribution, but it does
not follow that the standard deviation is of the binomial type generally assumed.

(i.) Suppose y = 3, corresponding to the withdrawal of one-half of the contents of

a vessel, then
Y = Yo (1 + 2*/ay")~,

ly = 3C/{(1 + pn) (1 + gn)}.

This is an unlimited and symmetrical frequency curve approaching more and more

where

nearly to the normal form as we increase 7. It has, however, a standard deviation
= 4¢,/(npq), while the normal curve would give 3c,/(npq X 2).
(iil.) Suppose p = q = 3, we again reach the form

y=y (1+ e/a"),

eA sal)

Make vn infinite and we have again the normal type, but a standard deviation of
the form $¢,/ {nx (1 — x)}, only approaching the usual value when y is small.

We postpone until we have discussed the remaining types the problem of fitting a
curve of Type IV. to a series of observations.

(132), Case Ll 8.7 > 46) By,

Let a and a, be the roots of B, + B,« + B,x?= 0. Then the curve having the
same geometrical relation for its slope is

where

d (log Yy) ab L
dg ~~ B,(«% —a,) (%@ — a)
= lead

ae Bs (4 — 4) dix

{a log (w — a) — a, log (w — ay)$,
3A 2

364 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

or, if
1/v = Bs (a — 2),

y= yo(e# —m)-™" (x — 4,)"
= Yo (1 — a/a,)- (1 — w/a)

by changing constants.
Assuming that yo, v, a, and a, can take any sign whatever, we see that there are

three fundamental subtypes of this’ frequency curve,

(.) y= yo (1 + w/o) (1 — e/a).

— a 0 a

This is an asymmetrical curve with limited range and maximum towards mediocrity.
Asa rule va, and va are fractional and the curve becomes imaginary beyond the

limits v= — a, and «= a,.

(i1.) Y= Yo (2/a,— De (1 as 2/9)".

<—a,—
= aes LSS —

Here the ordinate between 2 =a, and « = a, varies from infinity to zero, and
resembles the frequency curves given by “ wealth” distribution or infant mortality.

(ils) yy = yy (1 — e/a.) (1 + w/a.)

<——_ a4, —>0<——_ a z

This is an asymmetrical curve with limited range, mediocrity being in a minimum.
The disappearance of mediocrity is not a very uncommon feature of statistics ; the

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 365

“prevalence of extremes” may appear not only in meteorological phenomena but in
competitive examinations, where the mediocre have occasionally sufficient wisdom to
refrain from entering. The typeis that of Mr. F. Gatron’s curve of “consumptivity.””*
The curve contains an interesting number of less fundamental subtypes.
(iv.) Make a, = o in (i.),
y= Y)(1 + w/a) e~™.
wh

=e >0 oo =

This is the limit to the asymmetrical binomial, which has been already referred to
in § 8.
(v.) Make a, = ay,
y = Yo (1 — */a*)™.

<—4a4 0 2 x

This is the symmetrical frequency curve of limited range.
(vi.) Make v negative in (v.),
Pata Yo i
I= a= # ay"

y

———_ 7, ————> 0<-——- ———> xz
This is a symmetrical frequency curve, with limited range, and minimum of
mediocrity.
(vii.) Put v = pa, in (v.) and make a, = o,
y=yer.
This is the normal curve.
* ‘Natural Inheritance,’ 1889, p. 174,

366 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.
(viii) Put a, = © in (ii.),

y = yp (w/a, — 1)-™ e™.
y

O--a@> zr

<———_ 60

This is an asymmetrical frequency curve, with an ordinate varying from @, to «
along an infinite range.

All eight of the above types are included in the single form

Y = Yo (1 + %/a,)™ (1 — 2/ay)’,
or
y= yx (1 — 2/c),

if we give positive, negative, or limiting values to the constants. But to do this we
require to give values to 7 and 7 in the expressions for 8,, 8,, and 3, which are not
easily intelligible, if we rigidly adhere to our example of drawing a definite quantity
of sand from a limited mixture of two kinds of sand. The last type of curve given
is, however, the frequency curve for @ priori probabilities,* and readily admits of a
direct interpretation of the following kind.

Given a line of length /, and suppose 7 + 1 points placed on it at random; what is
the frequency with which the point pr from one end and qi from the other of the

series of 7 + 1 points falls on the element Sz of the line?
The answer is clearly
rela Oa
pr |qr\ 1 l U

or, we have a frequency curve of the type

y = ye?" (1 — al)”.
We may express the problem a little differently. Take 7 + 1 cards and slip them

at random between the pages of a book, the frequency of the page succeeding the

pr + 1™ card is given by the above curve.t

* See Crorron, ‘“ Probability,” § 17, ‘ Encycl. Brit.’
+ The important point to be noticed here is that we are dealing with a distribution in which
contributory causes are inter-dependent,

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 367

Until we know very much more definitely than we do at present, how the size of
an organ in any individual, say, depends on the sizes of the same organ in its
ancestors, or what are the nature of the causes which lead to the determination of
prices, or of income, or of mortality at a given age, I do not see that we have any
right to select as our sole frequency curve the normal type

Y= hor

in preference to the far more general
y= yo (1 + win) (= aly

which not only includes the former, but supplies the element of skewness which is
undoubtedly present in many statistical frequency distributions. As we may look
upon the former as a limit to a coin-tossing series, so the latter represents a limit to
teetotum-spinning and card-drawing experiments. It is not easy to realise why
nature or economics should, from the standpoint of chance, be more akin to tossing
than to teetotum-spinning or card-dealing. At any rate, from purely utilitarian and
prudent motives, we are justified so long as the analysis is manageable, in using the
more general form. It will always give us a measure of the divergence of particular
statistics from the normal type, and in many cases of skew frequency, it can be used
when it would be the height of absurdity to apply the normal curve at all.
Since Types I., II., III., and V. are all represented by the curve

y=y (1 + v/a) (1 — w/a,)"*

and Type IV. by the curve
— Ta See —vtan-la/a
Yaa Yo (1 a eel lae FP ’
we have only to deal with these two cases in general. We shall refer, in the
course of our work, to special simplifications arising in particular sub-cases. After a
description of the manner in which these generalised probability curves may be fitted
to statistics, we shall indicate, by examples, their practical applications.

(14.) On the Generalised Probability Curve. Type I.

Y = Yo (1 + w/a) (1 — w/a).
Let the range a +a,=b; let m=va,, m= vo, z= (a, + x)/(a, + a),
whence x= —a,, 2=0 and z=a, 2=1.,
Further let
1 = Yo (% + ay) ™*™/ay"049",
= Yq (m+ My)™*"/m" My”,

thus y = ne (1 poe 2);

368 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Let « be the area of the curve between # = — a and =a», ap’, its n™ moment
round a parallel to the axis of y through « = — a, and ap, its 1" moment round the

centroid vertical.
Then we have
b
Opn — | yx" da,
0

1
-— be + ‘” ( gia +2 (1 — z)"? dz,
“0

= b"*'y B(m, +n+1, m+ 1),

— pet} T(m +” +1) U(m + 1)
rie T (m, + my +2 + 2)

Thus, by the fundamental property of the I function, we have

a = bn V(m, + 1) (mz + 1)/T(m, + my + 2),

Gena) iam b(m, + 2)(m+1)
WALT, My, + My + 2’ 2 = (m, + amy + 8) (my + m4 + 2)?

diy b3 (m, + 3) (m, + 2) (m, + 1)
PO (am, + my + 4) (m, + airy + 3) (My + my + 2)’

a, b* (m, + 4) (m, + 3) (m, + 2) (m, + 1)
ees (m, + ig + 5) (at + Mg + 4) (a + Mg + 3) (M, + My + 2)

From these we easily deduce by the formule connecting p and p’, if we write for
brevity, m, +l=m), m+1=m’, andm,+m,=r:

__ 3b* m', m’, (m', m’'s (7 — 6) + 27°)
Ba a8 (y +1) (7 + 2) (7 + 8)

Bm’; i's 203m’, m’, (m', — m'))

Mee tl) MS Br +1) @ +2)

Now, @, 49, #3, and p, are to be found by the methods indicated in Art. 4 from the
polygon of observations, and may be supposed known quantities, when we are dealing
with the fitting of frequency-curve to observations.

Then, if By = py/po", and B, = ps/pm.*, € = m’',m’',, we have:

_3@ +1) (27? + € (7 —- 6))

_ 4 (2 — 4e) (r +1) 8

N= e(7 + 2) 4 alae e(7 + 2) (+ 3)
Thus :
B, (7 + 2) at ” eats B3 (st 2) (v7 + 3) Me 2 Bt,
4(7 +4 1) € 3 (7 + 1) €
whence, eliminating 7*/e, we find :
een se Ls

7
3B, — 2B; + 6

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 369

This gives 7, then :

Ted

52 — Hs (Gar) 7 eni@ae AE ae GG EP ab)
— = ea) ?
€ 4
or
i= Va {Bi (7 + 2)? + 16 (r +1} |
Since
r=, +>, €=M 1M,

m’', and m’, are roots of
m? —rm +e=0.

Thus m, = m’, — 1 and m, = m’, — 1 are determined.
Further, a, + a, = b, a/dg = m,/m,, and v = m,/a, are all determined.
Lastly :
Yo = NM." M.”/(m, + My)™*™,
and
a = bn T(m, +1) 0 (m, + 1)/P (m, + m, + 2),

give:
eee My" Mg"? T (am, + my + 2)
Y= F (m, + m,)m*™ T (m, + 1) (m, +1)’

which completes the solution,* if a Table of I functions is to hand.

Remarks.—It is clear that the solution is wnzque.

It is necessary in order that the solution may be real, that m’, and m’, should be
real or 7?>4e. Hence, if « be negative, there is certainly a solution, because 1 is
always real. The solution forms, however, one of the sub-types referred to in our
Art. 13, (ii) and (iii).

If « be positive, we must have 7*/e — 4 positive, or

Bi (3 + By?
(+ 38; — 28,) 48, — 38)

Now it is easy to prove that for any curve 48, — 38, or 44. — 3p;° is positive,
for py is always greater than p,°.
Thus, we must have
6 + 3B, ri 2B, > 0,

or
2 pea (Bprg” — py) + 3pyg° > 0.

* Very often with sufficient accuracy we may take:
io & (mt ttg +1) A (0m + 19) 5 Gant ~ mm ~ md
aan / (2m my Mg)

MDCCCXCV.—A. a) 1B

370 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Now it is theoretically impossible to fit a normal curve (uw, = 34”) to a frequency
distribution for which py > 3p”. It is, however, possible to fit this generalised curve
of Type L, although p* be >3y,”, provided there is sufficient skewness to render

Sig” > 2p (fy — Bpy’).

Hence the first stage in determining the type of curve suitable for a given set of
observations is to ascertain the value of

2p (Bptg” — py) + 3y45°.

If this expression be positive, we see that a limited range of variation is a possibility.
Passing from range to skewness we remark that the distance d between the centroid
vertical and the maximum ordinate

= 4, — p= a, — bm’, /(m’', +m’),
__ Gm’, — am’,
m, + m’,
b (m, — mg)
(a, + Mz) (mM, + Mz + 2) :

Now it might seem that d/b would form a good measure of skewness, and it would
be so if all curves had a limited range. But, as they have not, it seems to me
better to take as the measure of skewness the ratio of the distance between the
maximum ordinate and the centroid to the length of the swing radius of the curve
about the centroid vertical, z.e., the quantity d/,/py.

In our case we have accordingly,

Mh — Mg a/ (mm +m +3 *
skewness = ———— 2 1
My + Mg a + 1)(m, + 1),

~ r+2
=tVB, 9

{PZ

in our previous notation.*

Thus range and skewness are determined in Type I.

(15.) A very considerable simplification of the above analysis arises when the range
is given by the conditions of the problem itself, ¢.g., guessing between two given tints.
In this we only require the moments p’, and p’, about one end of the range, and the
solution becomes as easy as in the case of fitting a normal curve.

Since b, pw’, and p’, are known, let

Y= H3/b and yo = p'p/(w4).

* The points of inflexion of the curve are at distances + Va a,/(m, + mz — 1) on either side of the
maximum ordinate.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 371

Then
, , , a eS
Ti = Mara yet Mal. ty Vee pr eal, £1

and we have at once

eo, onG— » _ (2-1) ad-—m)
i, 2S, Nig se mg
DAL = 0% Tat VA)

Then a,/a, = (m’, — 1)/(m’, — 1), and a, + a@ = b give a, and a, Finally yp is
given as before by

a my Me" T'(m, + mg + 2)
b (my + mgmt T(m, + 1) Mm, + 1)

Yo =

(16.) A perhaps still more interesting and usual case arises when one end of the
range is given, 7.e., when p’,, but not b, is known. For example, a curve of distri-
bution of disease with age, the liability to the disease starting with birth. Here we
require to calculate from the observations a, py, @’, and p's The solution is as
follows :

Let

H's/h a? = Xoy H's) (fe of) = Xs 3
then
2 Gear) (m’, + m’) eae
Xe = omy (mi, +m’, i071) TF iate

_— (m+ 2) m+ m,) _ 1 + 20
a m’, (mM, + m',+ 2) ~ 1+ 2u

2

if vy = 1/m', and uv = 1/(m’, + m’,).

Solving *
1 + x3 — 2x2 2N3 — Xo — XoXs
= ae v= :
2 (X2 — Xs) 2 (%_ — Xs)
Thus, : opie
2 (yy — 2 (x2 — x3) (X%s — 1) 1 = x0
m ae (X2 — Xs) nil. = (Xo — x3) (x3 )¢ No)

2N3— X2— XN? (1 + x3 — 2X2) (23 — X2 — KoXs)
b= pw) (m+ m,)/m’, = p) v/u
= rie 2x3 Sam X OEE XCOXS ;
; 2 (x2 — Xs)

determines the range.
Hence, since
m,—1

Ce ARG Os) ING) CxO, = —
os WM by

we have, with the aid of the previous expression for yg, the complete solution of the
problem,

a) 15) WY

372 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.
(17.) Generalised probability curve of Type II. Limited Range and Symmetry.
Y = Yo (1 — x*/a*)™.

The solution in this case follows very easily from (14) by putting 8, = 0, we have at

once
6 (8, — 1)
Bie Bas aay
or
5B,—9 — Sp, — 9p" ;
oe OG) = FERS)
Since p, = ar , and clearly e = 7°/4,
we have b= 24 = 2/ {py (7 + 1)},
or
Gp V/ (248) eae J/2 Hops) ;
J/(3 = By) J (Bp9" — fy)
Finally

ea me T'(2m + 2)
Jo= b (2m) {TP (m + DP’

— & /(3 — B.) T(2m + 2)
2 VS (2pyBo) 2 {T (am + 1)?’

os nN) oe =H TQm+2)
me 2 popes Dems (m + 1)}?

Quo, VW 7l' (m+ 1)

For the normal frequency curve p, = 3p,”, for a symmetrical point-polygon 341.?> py.
Hence, whenever a symmetrical frequency curve differs from the normal curve on the
side of the point-binomial, we can better the normal solution by taking a symmetrical

frequency curve of limited range.

y=yo(1 _ ae ",

a

Since

and
m d8,-9 1

e 4 pty, ply

if B, = 3, we easily trace the transition from the limited symmetrical curve to the
normal curve with infinite range.

Quite apart from the extremely interesting problem of finding the range, it is clear
that better fits will be obtained for symmetrical distributions by the aid of this limited
range curve for all cases in which 3p” > py

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 373

(18.) Generalised Probability Curve of the Type III. Range limited in one
direction only.
y= (1 + a/ayre

In this case we have no need to determine the value of ,, and the analysis is much
simplified by the replacement of the B function by a single I function.
Take z = y(a-+ x) and write ya = p, we have

SE per
ae
Further, « = —a,z=0,x=0.z=0. Thus we find
= ip n pean Ye? [- +n p—2
Opts — [y (x + a)” da = eee geese dz.
Hence
_ youe? p ANG ae ae 1)
aaa I(GD sb Oy chip A=)
whence
en Distal 7 (sea ae 2)
A= via (hy = ahaa ey sey

pu (Pick Diet 2) (pin) ,__ (p+ 1)(p + 2) (p+ 3) (p + 4)
Bs = x? ? hy = yy! ;

Or, transposing to the centroid-vertical, we have

Dee 2(p +1)
Sent ee = ee wee

es (etn) (ak 3).
yf ; y'

The first two results give us at once
Y = 2p/b3, P= 4py?/ps” —- 1,

whence
“a po

eels eG soe poe eee
Yo pg) 2p? and: oar a, a0 (Oe Ds

This completes the solution of the problem, which is seen to require only the
determination of p, and ps,

Remarks.—The distance d of the centroid-vertical from the axis of y or maximum
ordinate d, is given by

Thus
skewness = d/./ pz = $p3/Po"”.

374 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

If we transfer the origin to the centroid-vertical we have

2B 3 28/43? — 1

2 fg" | fs /

e —2pot/Kg

Yi (1 ae
where

fOr (p+ Dyer" (p + UP
NS Oa) Tp +1)

It is interesting to note how this skew curve passes into the normal curve when
pz is made vanishingly small, or p= o.
By WALLIs’s theorem the limit to y, = #/4/27p3.

It remains to find the limit of

N\A Bo 1 xg \P Vp le/" as
al: + e “Pat/Ks —— e
\

2 p9?| pes au VJ (p+ 1) VA (He)
= [ia + u) aril

Now the limit of {(1 + u)e~"}" for u = 0 is easily found to be e ~?, hence

y = a= *P/ (Om)
the normal form.

Returning to the value we have found for p, and eliminating p and y between yy,
Ps, and pw, we find

2 pho (Spa? — py) + Bp" = 0.

This is the expression (see p. 8398) which must be positive in the case of limited
range. It is zero also for the normal curve, because both 3u,” — pw, and ps vanish.
Hence the more nearly the quantity 2u, (32° — 4) + 8p,” approaches to zero, the
more nearly are we able to fit our statistics with a skew frequency-curve having
a range limited in one direction only.

(18 bis).—The skew frequency-curve of Type III. deserves especial notice. It is
intermediate between those of Type I. and Type IV., and they differ very little from
it in appearance. Hence, if the reader has once studied the various forms which
Type III. can take as we alter its constants, he will grasp at once the forms taken by
Types I. and IV., by simply considering the range doubly limited or doubly unlimited.
To assist the process of realising Type III., Plate 9, fig. 5, has been constructed ; it
contains seven sub-types of this species, varying from fig. 1., in which the curve is
asymptotic to the maximum frequency-ordinate to fig. vil, which is practically
identical with the normal curve. Taking y= y (1 + «/a)’e~’** for the equation
to the curve, we have the following values for the constants p, and y’ :—

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 375

I ps — 16% va 3

II = 001 OY = 2505
ela p= ‘265 Y = 363
IV p= 1021 a ‘7676

vi D= 1 oh = 6)
VI = 6°5625 Oe 4°3125
VII p = 1890 y’ == 1700

In the diagrams vertical and horizontal scales (y) and a) have been chosen so as
to illustrate best the changes of shape in the curve. The general correspondence of
this series with actual types of frequency curve, as indicated in Plate 7, fig. 1, will at
once strike the reader.

The mean, the median, and the mode or maximum-ordinate are marked by bd, cc, and
ac, respectively, and as soon as the curves were drawn, a remarkable relation manifested
itself between the position of these three quantities : the median, so long as p was
positive, was seen to be about one-third from the mean towards the maximum.
For p negative and between 0 and — 1, this relation was not true. The distance
between the maximum-ordinate and the mean is, if the equation to the curve be

y=yure™,

equal to 1/y. Now the maximum cannot be accurately determined from observation,
but a fair approximation can be made to the median. Hence the constant y could, if
the above graphical relation were shown to be always true, be determined approxi-
mately as the inverse of thrice the distance between median and mean.

Now distance of mean from origin = (p + 1)/y,
and is maximum eee—1 cys

Hence, supposing distance of median =(p-+c)/y, we should expect to find
¢ = 2/3 about.
Equating the integral which gives the area up to the median to half the total
area, we have
Yo fie ere dx = ty | DL eCm dot,
Ean 0
y

ao

or, e

oOo ie)
| Came 4] ZiCmaOes
pte 0

This is the equation for c. Unable to solve it generally I gave p a series of integer
values and found in all cases ¢ nearly ‘67. Its value, however, decreased as p

376 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

increased. I, therefore, assumed c to be really of the form ¢ = c, 4 c,/p, and deter-
mining ¢, and ¢, by the method of least squares, found

c = 6691 + -0094/p.

Probably this is only the beginning of a rapidly converging series in inverse powers
of p, but it would appear to suffice for most practical purposes. It is only true for
p > 1 and does not explain why, when p is positive and fractional, c is still apparently
near 3; thus its value for p = 0 has only risen to ‘6931. We have then the following
fairly simple means of determining roughly the constants of a skew curve of this type:

(1.) Find the mean and the median ; these gives y, approximately.

(2.) Find p, for the mean; this gives p, since py, = (p + 1)/y’*.

(3.) Knowing p, correct the value of y by using the above value for ¢, and so obtain
a corrected p.

(4.) Determine y, from the area.

This method is not very laborious and may be of service in some cases.* It will,
of course, fail for any curves in which p is negative, and must only be applied when
the curve is known to be of Type III. If the beginning of the range is definitely
known, we may save stage (2) above and find p from the distance of the mean from
the start of the range.

(19.) Generalised Probability Curve of Type IV. Range unlimited, but form skew.

7] — Yo 4» —v tan—! (w/a)

1 > = Gia

Put « = a tan 0, hence
NS Oyj Gos *0a

ace 71/2
op, = | yar" dx = Yo qeth | cose?” 24 sin”@ e7”? dé :
a —n/2

7/2

= Oyen | cos’~"@ sin” 0 e~” dO, if r = 2m — 2,

—n/?
Ye" apa (e
Se yh (Il
Sen ee

n/e

1/2

cos’ "*?@ sin™-"6e-" d@ — v| cos’~**!@ sin” '8e—” dé I

—7/2

a

— poe {( sone 1) Op n—2 me rp aaa be, s
provided 7 > n — 1.

* The points of inflexion may also occasionally be found from the observations; they are at distances

+E /»/- on either side of the maximum ordinate.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 377
Thus, if we know @ and p14, we can find the successive p”s. Now

ar /2
cos’6 e~ 8 dé,
2

— 7/2

C= yor |
1 a .
= yen | sin’6 e*" dé,
0

and depends on the integral [sind e* "a6, which I propose to write G (7, v). The
: “0

us
result above for »’, shows us that the more general integral f cos?6 sin’@ e*” d# can
0

always be expressed in terms of G-functions. Further:

77/2
CL yo | _ cos’ ‘Osin de" dé,
— 7/2
yoaey (7 i av
=| cos’6 e~° dd = — —a.
eee 2

Thus we find by the formula of reduction above :

ees Ste eae A 2 lsat nae RORY wis Bryn dG 5)
Roma eraay + vr’), h3= Caney 2 -+ v°),

, at

aa EER CEI ES a a

Referring to centroid vertical, we have :

[Ly 7° (7 — 1) (7 SP v’), (pb) — rr — 1) (7 — 2)?
_ 3a! (+) {7 + 6) (2 +) — 879}
ba = yt (r bss 1) (7 ne 2) (r a 3)

These may be rewritten, if z= r? 4+ v’,
PS Cae ad 4032 .4/(% — 7”)
bee ei(pae ES ee 7 (r — 1) (r — 2)

_ _dsate{(r + 6) 2 — 87°}
Pa = 14 (p — 1) (7 — 2) (7 — 8)

As before, putting B; = p,7/p.? and By = py/po”, we have

(r= 2)? _

22 G2 Gee
ne) = eae te ae
Gee aE pe Me ome oe

MDCCCXCV.— A. a

378 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.
Adding and dividing out by 7 — 2, we have

yen 6 (By = Bi ae)
28, — 3B, — 6’
hence
m=4(r + 2)
is known. Further
ye

a
“~— 5

qa A (r — 2)

16 r—1

is known, whence

p= /(z—7")

Ponte a/ e v= 5)

act

is given.* Finally

and

4) See one
a| sin’ 6 ce” dé
0

completely determine the problem.
Remarks. The solution is clearly unique.
(i.) To determine the skewness we must find the position of the ordinate for which

dy/dx = 0; this is y= va/(2m) —— va/(r+2).
But
AS gyi DE, MMe Nee L OM
d=—p,+u= pr oP +2. r(r+2)

Hence
skewness = d/,/ py

2p y—1- r—2 Bn &
= an, G J: +H = 4,/ By Panes (cf. Pp: 370).

Hence, since 48, is always > 3, (see p. 369), it follows, since > 1, that we must
have
or
2p» (Bya” — py) + 3pg” < 0.

* Whether we give v the — or + sign will depend upon the sign of u, in the actual statistics.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 379

Thus this expression is again critical for the class of curve with which we are
dealing. We may say that a skew frequency curve will have limited range, range
limited in one direction only, or unlimited range according as

Zp (Bg? — py) $F 3prs”

is greater than, equal to or less than zero. Thus the calculation of this expression is
the first step towards the classification of a frequency curve given by observation.

(i1.) It is noteworthy that the values we have obtained for 7, z,a,v and y, will be
real and possible if 7 > 1. On the other hand we have required in our work that r
should be > 3. I propose now to return to this point. So long as 7 > 1 the values
of both pw’, and py will be finite, but the values of p’; and py’, and consequently of ps
and p, will be infinite if r be < 3. That is to say, the third and fourth moments
of the curve about the centroid vertical become infinite. This is quite conceivable
from the geometrical standpoint, and various interesting questions, of purely
theoretical value however, arise according as 7 > 1 and < 2, 2.¢., 4, and ps are both
infinite, or 7 > 2 and < 3, 2.e., w, alone is infinite. The solution we have given fails
in these cases. We should obtain, however, finite relations between the four constants
of the equation to the curve by taking the first and second moments am”, and ap’,
round the axis of x; we find in this case

pe = ty

Ly “costr29 o-2 6,

—7/2

Op» = AY 0° ee cos*"t#9 e—8 8,

—1r/2
or,

1 = dye *" G (2r + 2, 2v)/G(r, v),
p'n = dye G (Br -b 4, 37)/G (x, »).
These results together with

are theoretically sufficient to determine the four constants 7, v, yy and a. Practically
they would hardly be of service without very elaborate tables of the G functions.

As a matter of fact, we are very unlikely in dealing with actual statistics to meet
with cases in which pz and p, become infinite, because neither the range of observa-
tions, nor the size of the groups observed at great distances from the origin can be
infinite. With finite values of pz and py, it is, however, easy to see that we always
obtain from our solution on page 377 a value of 7>8, so that the solution is self-
consistent.

3 Cc 2

380 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

(iv.) It remains to say a few words about the integral
G(r, ») = | sin’ e* a0.
0
Provided r > 1, we find a formula of reduction

G(r, vy) = od G(r — 2, r).

Thus the value of the integral from 7 = 0 to * = 2 only will be required for diverse
values of v. The integral does not yet appear to have been studied at length or
tabulated. Dr. A. R. Forsyra* has kindly answered my inquiry for a fairly easy
method of reducing G (7, v) for purposes of calculation, by sending me the formula

2-7 ei II (7)
Cy) a Garda ea):

where II is Gauss’s function such that
Il (xn) =T (nm + 1).
Taking as definition of II that

Uo a)a nt
(2+1)(@+2)...@+2)

II (z) = limit of

when 1 is infinite, we can reduce the above expression to the form

2-v gel T(r +1)

n= yp ria
Product ed (1 + ie)

Here, since 7 can always be supposed to lie between 0 and 2, when »v is small a few
terms of the product will generally suffice for the calculation of G(r, v) to the degree
of accuracy required in statistical practice.

On the other hand when 7 is large, 7.e., generally in cases of slight skewness, I find
if tan ¢ = v/r

(Br

CG 2)

ue © 20 = gr tan gd

ee ON
cos 2 cos :

vol
|
bole
ys
a
q
—
wie
>
a
bole
S
>.
—
I

very nearly.
Hence

cos? & 1
as — — —¢r tan¢d-
127 or $

1 = aa t per eR ETT EET
Yo a Qa (cos @)’*1

very nearly.

* “Ryaluation of two Definite Integrals,” ‘Quarterly Journal of Mathematics,’ January, 1895.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 381

(20.) We have now considered methods for fully investigating whether a given
system of measurements has a limited range, and for ascertaining the degree of
skewness of the system.

Analytically, our work may be expressed as follows :—

The slope of the normal curve is given by a relation of the form

The slope of the curve correlated to the skew binomial as the normal curve to the
symmetrical binomial is given by a relation of the form

LO SG
y daz ~ ¢ + eg

Finally, the slope of the curve correlated to the hypergeometrical series (which
expresses a probability distribution in which the “contributory causes” are not
independent, and not equally likely to give equal deviations in excess and defect) as
the above curves to their respective binomials is given by a relation of the form

1 dy _ — 2

Co Ae 4b Gb OG

This latter curve comprises the other two as special cases, and so far as my
investigations have yet gone practically covers all homogeneous statistics that I have
had to deal with. Something still more general may be conceivable, but I have
hitherto found no necessity for it.

To demonstrate its fitness and the importance of these generalised frequency
distributions for various problems in physics, economics, and biology, I have devoted
the remainder of this paper to the consideration of special cases of actual statistics.

Part I[].—SraristicAL EXAMPLES.

(21.) QuETELET, who often foreshadowed statistical advances without perceiving
the method by which they might be scientifically dealt with, has treated of the subject
of limits in Lettre XXII of his “ Lettres sur la Théorie des Probabilités” (1846). He
seems to have been conscious that certain variations in excess or defect might
biologically or physically be impossible, and he accordingly introduces the terms Limites
extraordinaires en plus et en moms to mark the range of possible variation. He
makes no attempt to show how this range may be found from a given set of statistics.

“ Lorsqu’on suppose le nombre des observations infini, ou peut porter les écarts 4 des

382 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

distances également infinies de la moyenne, et trouver toujours des probabilités qui y
correspondent. Cette conception mathématique ne peut évidemment s’accorder avec
ce qui est dans la nature. . . . Les limites extraordinaires au deli desquelles se
trouvent les monstruosités, me semblent plus difficiles 4 fixer.”

Indeed QUETELET’s attempt to fix these limits in the case of the height of human
beings at 2°801 and -433 metres is purely empirical, and scientifically worthless.

I prepose in this the first section of the practical part of this paper to consider how
far the theory we have developed in the first part, enables us to find the range in
various groups of physical and biological phenomena.

Example I. The Range of the Barometer.—The following results for the curve of
barometric heights are given on p. 352.

Cn ale /aliso Pg = 1014
fi SS GOS Py = 826°34.

We have accordingly :
py (Bog? — py) + 3p? = 400°581,

that is, this expression is positive, and we have a limited range,
We have further: 8, = °24401, 8, = 3°17391.
Hence, determining the constants in the manner described in $14, we have:

r = 30'13882 e = 150°7954
b = 43°61016,
M, = 95°3302 a, = 8°2688
Ms = 22°8030 Oy = 35°3414.

Next to find d, giving the distances of the centroid from the origin, or the distance
on barometer between mean and maximum, we have by p. 370

d = — ‘8983.
Thus
Range of barometer above mean = 9°1671
x . below ,, = 84'4481.

Now, in the scale upon which our curve is drawn in Plate 10, fig. 6, each centimetre
equals =45 inch, and the mean barometer in Dr. VENN’s results equals about 297-931.
Thus the maximum possible = 30/85 and the minimum possible = 26':49 ; the range
of the barometer being about 4°36. Now, the highest barometer in Dr. VENn’s record
= 30'°7, and the lowest 28”°7; it is clear, therefore, that we reach much nearer in

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 383

practice to the upper than to the lower limit of the barometric range.* The result
here obtained for the barometric range is of course only tentative and approximate.
Far larger statistics must be dealt with, and for a greater variety of places, we shall
then be better able to judge how far the range, as ascertained from Dr. VENN’s
statistics, is local, or if general, what modification or correction may be required.
Calculating the value of y, we find for the curve of barometric heights :

y = 21-642 (1 + x/8-2688)°™ (1 — «/35°3414)?™,

This curve is traced on Plate 10, fig. 6. It will be seen to be extremely close to the
observations.

Although the expression 2, (3u." — m,) + 33° is not zero, it is interesting to see
with what closeness the skew curve which is the limit to a point binomial can be
fitted to the barometric observations. This is the curve of Type HI. Calculating
its constants by aid of § 18, we find

y — 92 (1 + LA LOG3) Gach etter

while d, the distance between the maximum ordinate and the centroid-vertical,
= ‘7864. This gives a maximum possible height of the barometer of 31”:22 instead
of 307°85, there being of course no lower limit. The curve is shown in Plate 10,
fic. 6, and will be seen to give a very close correspondence with the observations.
The “skewness” of barometric results as given by the curve with limited range
= °8983/3°184 = °2821, and as given by the curve of Type III. = ‘7864/3184
= ‘2470,—no very great difference.

The areal deviations of the two curves are almost exactly the same, being about
7"1 sq. centims. or percentage error of 4:1. The normal curve is also drawn on
the same plate. It diverges widely from the observations, the areal deviation
= 26 sq. centims. or the percentage error 15°1,—about 3°7 times as great as in the
case of either skew probability curve.

Till a wider range of barometric observations have been analysed, it may be wiser
not to draw too definite conclusions from the above results, contenting ourselves with
the remark that the new skew curve gives far better results than the old normal
curve of errors.

* J am unaware if Dr. Venn’s results are reduced to sea-Jevel. The lowest recorded barometric
height for the British Isles reduced to sea-level is 27'333 (at Ochertyre, Perthshire, January 26, 1884)
and the highest (at Roche’s Point, Cork, February 20, 1882) is 3093. A statement that the barometer
stood at 31''046 at Gordon Castle, in January, 1820, has hardly sufficient evidence. Supposing Dr. VeNn’s
statistics to be unreduced Cambridge statistics, the expression theoretically found for the barometric
range seems to be on the whole satisfactory. I have at present in hand other series of barometric
heights.

384 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Example II. Professor Wripon’s Crab Measurements No. 4. The details of
these are given in ‘ Phil. Trans.,’ vol. 185, p. 96.

We have
Cr—29 995 fini /aONOOs pg = 3°4751,

jy = 1843039, B, = 0267022, B, = 312807.
In this case
2 pla (Bog? — fy) + Bpg” = po? (6 + 38, — 2B,) = — py® X “1760334,

and is accordingly negative. In Example J. of the barometric heights we had
2 pty (Bptg” — My) + Byes” = fy’ X 98421.

Since, in the latter case, this value was sufficiently small to give a good curve of
Type III., we may expect the like result in this case. There is, indeed, a slight but
sensible skewness even in this the most symmetrical of all Professor Wrxpon’s crab
measurements, and the skew curve of Type III. is really a better fit than the
normal curve. But clearly since the critical function is negative, we are dealing
properly with a case of a curve of Type IV. The ratio of the organs dealt with in
No. 4 series of measurements does not give a “limited range” of variation. Pro-
ceeding by the method indicated in § 19, we find for the constants

Tile Zas Tis Ono p= 25°7616,
=) 212909, Hi =— 7°8802,
G—- 321407; Skewness = 077267, Yo — aioe

Thus the equation to the curve is :
en 25°7616 tan-! (a/21°909)

[1 + 2?/(21-909)?}36-812

y = 1°75509

To trace the curve, take :
x = 21°909 tan 8,
y — il "75509 cog!?64 6 @7 2°76160

If we take a skew curve of Type III., we find for its equation :
y = 14422 (1 + 2/33°683) "8 eH,
where, for the centroid

d = °226364,

and the skewness
= °081704.

For the normal curve we have:

y = 148°85 e~ Ae TOs,

* y. was calculated by aid of the approximate formula on p. 380.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION 385

All three curves are drawn in fig. 4 of Plate 8. It will be seen that they are all
very close to the observations. So far as skewness is concerned, curves of Types III. and
IV. give practically the same result (°082 and ‘077) ; in both cases the skewness is
small, The areal deviations are in the three cases respectively : 4°4 sq. centims.,
59 sq. centims., and 6°7 sq. centims., or we have mean percentage errors in frequency
of 4-4, 59, and 6°7 nearly ; the percentage error for the closest point binomial is 10°5.
We thus conclude that even in a case which has been selected as the most typically
symmetrical series of measurements out of a very considerable set of careful statistics,
the generalised probability curve is one-third as good again as the normal curve,
while the special case of that generalised probability curve—which is not the most
appropriate to our observations—is itself distinctly better than the normal curve.
This result has been confirmed by a considerable application of these generalised
curves; in good cases of normal curve fitting, the generalised curves are always
sensibly better ; in cases where the normal curve is almost useless, as in the case of
barometric observations, the new curve, 2f of the appropriate type, will represent with
a 4 to 5 per cent. mean accuracy many observations not yet reduced to statistical
theory. It is, perhaps, unnecessary to repeat that this mean percentage is much less
than the average of what has been allowed to pass muster hitherto in both physical
and biological measurements. Professor EDGEWORTH’S view* thus seems untenable ; a
curve with a comparatively easy theory of its constants has been found which excels
the accuracy of the hitherto adopted normal curve. And this for the simple reason
that it would pass into the normal curve, if that curve were itself the best fit.

23. Example I[J.—The following statistics of height for 25,878 recruits in the
United States Army, are given by J. H. Baxter, ‘ Medical Statistics of the
Provost-Marshal-General’s Bureau,’ vol. 1, Plate 80, 1875.

78-77 2 64-63 1947
77-76 6 63-62 1237
76-75 9 62-61 526
75-74 A2 61-60 50
74-73 118 60-59 15
73-72 343 59-58 10
72-71 680 58-57 6
71-70 1485 57-56 d
70-69 2075 56-55 3
69-68 3133 55-54 1
68-67 3631 54-53 2
67-66 4054 53-52 1
66-65 3475 52-51 1

65-64 3019

* «Phil. Mag.,’ vol. 24, p. 334, 1887.
MDCCCXCV.—A. 3D

386 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION

I find:
Mean height = 67°2989.

Standard deviation = 2’°5848.
Maximum ordinate, 3994:04.

This gives a very close-fitting normal curve.
The data for a generalised curve are

po = 6°68122 B, = 005769

Po — 1368 B, = 3°024801.
By = 1385°023824

Thus,
2B, — 3B, — 6 = 032295,

and being positive, we see the curve belongs to Type IV. There is, thus, exactly as in
the previous examples of crab measurements, no range of a limited character for these
statistics of height.* For a true normal curve, 6,, 8, ought to be 0 and 8 respec-
tively ; we have therefore a still closer approach (3°025) than in the case of the crabs
(8°128) to normality. In this case 7 is about 400, and on any reasonable scale, there
is no sensible difference between the normal and the generalised curves. The skew-
ness is very slight, = ‘038 about, or about half its value in the case of the crabs.

24. Example I1V.—Height of 2192 St. Louis School Girls, aged 8.—The following
statistics are given by W. T. Porter, “The Growth of St. Louis Children,” ‘ Trans.
of Acad. of Sci. of St. Louis,’ vol. 6, p. 279, 1894.

| |
| Heichts at intervals of | @ i Heights at intervals of |
| . 2 centims. Number. 8 2 centims. Number. |
| |
centims. | centims. |
| 141 and 142 | 1 119 and 120 342
| 139 ,, 140 0 4) UWS 321
| sy? s Je%s} 1 | Ws. HIS 297
| 135% e136 5 | aL Seen lela | 222
Some eelod 10 | Wo, le 137
NS, “Sy 21 109 Re lO 84
WP) NBO) 28 | 1072 S108 | 42,
Wey US) 79 | 105. 5, 106 27
125 126 138 | 103 ,, 104 8 |
NERS oo pA 183 | OTe 102 2
Weil 5 ale 248 i 995 100 1

The following are the calculated values of the constantst :—

* Tf, notwithstanding, we take a curve of Type III., we find the range limited on the ‘dwarf’ side
at about °7645".

+The unit of all these constants = 2 centims., except in the case of the mean height. The
standard deviation = 5°55244 centims., which gives a probable deviation of 3°745 centims. The mean

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 387

—— 7°70739, Mean height = 118°271 centims.,
Ps = — 2°38064, Standard deviation = 2°77622,
Pe OZR FAO! Yo for normal curve = 314:99,
B= -0123784, By = 3°235045.

Thus 28, — 38, — 6 is positive, and the curve is again of Type LV.

We have
= 35606; Skewness = ‘04885,
r = 30:8023, m = 16°4011,
v= 4°56967, a = 14:9917,

Yo = 235°323,
or, for the equation to the curve :—

x = 14'9917 tan 6,

yh 235'°323 Co0g22'80234 (Satis

the axis of x being positive towards dwarfs and the origin 2:2241 on the positive side
of the centroid-vertical.

The maximum ordinate = 324°18 and occurs at « = — 20884.

The curve of Type 1V., together with the normal curve, is drawn (Plate 10, fig. 7).

If we attempt to fit a curve of Type III., we find p about 322°14, and the range
limited on the dwarf side at about 99°812 centims. from the mean, or at a height of
about 18°5 centims. The largeness of p causes this curve to coincide with the normal
curve to the scale of our diagram. The areal deviations are for the curve of Type IV.
and for the normal curve 6°1 and 8°3 centims., giving percentage mean errors of 5°56
and 7°66 in the ordinates respectively. The advantage is again on the side of the
generalised curve. It will be seen at once that the normal curve by no means well
represents the number of girls of giant height. The theoretical probability that
these giants should occur is small, and their actual redundancy over the numbers
indicated by the normal curve suggests some peculiarity in this direction ; it is fully
met by the curve of Type 1V. The asymmetry of the curves given by anthropo-
metrical measurements on children has been noted both by Bowprrcu* and PorTER,*t
but in their published papers, to which I have had access, they do not give their
raw material, only the ogive curve arising from Gatrton’s method of percentiles.
Unfortunately, theoretical evaluation of the skewness of anthropometric statistics
can only be applied or verified when we have raw material, and not integral frequency

height and probable deviation, as given by Mr. Porrer, are 118°36 and 3:698. The latter is obtained
from the mean deviation, but I do not know how the former is to be accounted for.

* ‘Growth of Children, studied by Gauron’s Method of Percentiles.’ Boston, 1891, p. 496.

+ ‘Growth of St. Louis Children.’ St. Louis, 1894, p. 299.

33 apy 2

388 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

curves, the integral of the frequency in all suggested forms of the frequency curve
being not expressible in terms of undetermined constants. Valuable as is the
method of percentiles for representing popularly the numerical facts of anthro-
pometry, it is to be regretted that percentile statistics are replacing the raw material
in so many publications. The raw material of Professor WELDOoN’s crab-measure-
ments and BowpircH and PortsEr’s child-measurements ought to be preserved and
circulated in print, as a means of developing and testing statistical theory.

(25.) Example V. Length-Breadth Index of 900 Bavarian Skulls.—The following
statistics are taken from Tables .—-VI., VIII.-X., inclusive, of J. Ranke’s ‘ Beitriige
zur physischen Anthropologie der Baiern, Miinchen, 1883.’ They include all the
material, which may be treated as typically ‘‘ Alt-Baierisch,” both male and female
skulls.

|
Index. Frequency. Index. | Frequency. | Index. Frequency.

70 1 80 71:5 | 90 10
71 1 81 82 91 8
72 0 82 116 92 3
73 2°5* 83 98 | 93 15
74 15 84. | 107 94 2
79 3°) 85 82 95 15
76 125 86 74 | 96 0
77 17 87 58 | 97 0
78 37 88 345 I 98 1
79 55 89 | 19 | 99 0

} I

We find, as before,
Position of centroid-vertical, 83°07111,

a=, 3°468, Yo = 103°532 (for normal curve),
Wy = 12°027166, B,= ‘0078995,

us, = 3°707179, Bo = 3°649553,

ju, = 527°91696, r= 1242734,

Ob "111388, Skewness = 0321186,

m = 7'213867, vy = 853,771, a = 11°69583, Yo = 107°4706.

Thus we see that the curve is again of Type lV. This result seems of considerable
significance, but it requires, of course, wider examination of cases than I have yet
been able to make. But, so far as I have gone, in both anthropometric and
biological statistics, whether relative or absolute measurements of organs, the
frequency curves all deviate from the normal curve—however slight the deviation—
in the direction of Type IV. hat is to say, the distribution of chances upon which
the frequency of variation of an organ depends, appears to resemble the drawing of a

* Indices such as 73°5 have been divided between 73 and 74 groups.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 389

limited amount from a limited mixture. So far as this goes, it is evidence against
the usual hypothesis that in biological matters the chances of deviations on either
side of the mean are equal, and the ‘‘contributory causes” independent and
indefinitely great in number. Thus we appear in biological statistics to be dealing
with a chance system corresponding, not to a binomial, but to a hypergeometrical
series, such as that discussed in § 11.

If it be remarked that Type IV. dismisses at once the problem of range from
biological investigations, we must notice that, while this is theoretically correct so
long as we are dealing with the continuous curve by which we replace the hyper-
geometrical series, it is not true the moment we fall back from the curve on the point
series (see p. 361). Ifthe 7 of that page (or the gn) be an integer, the series is limited
in range. It seems very possible that discreteness, rather than continuity, is charac-
teristic of the ultimate elements of variation ; in other words, if we replaced the curve
by a discrete series of points, we should find a limited range. It is the analytical
transition from this series to a closely fitting curve which replaces the limited by an
unlimited range. Exactly the same transition occurs when we pass from the sym-
metrical point binomial to the normal curve. Thus, while Type I. marks an absolutely
limited range, the occurrence of Type IV. does not necessarily mean that the range
is actually unlimited.*

For the equation to the curve we have

x= 11°69583 tan 0,

y= 107°4706 cos 14427349 Cmecnies

the origin being at a distance *803515 on the positive side of the centroid vertical.
The normal curve as well as the curve of Type IV. are shown (Plate 11, fig. 8). The
result in both cases is quite good for this type of statistics—z.e., the skulls came from
eight different districts and include 100 female skulls. With the planimeter the areal
deviation in both cases = 6°8 square centims., giving in either case an average per-
centage error of 7:56. That the generalised curve does not in this case give a
decidedly better result than the normal curve I attribute to the heterogeneity of the
material. It clearly accounts better for the extreme dolichocephalic and brachy-
cephalic skulls than the normal curve. The same 900 skulls have been fitted with a
normal curve by Strepa,t but neither the constants of his normal distribution nor

* I reserve for the present the fitting of hypergeometrical point series to statistical results. The
discussion is related to curves of Type IV., as the fitting of point binomials to curves of Type HI. It
will, I think, throw considerable light on the nature of chance in the field of biological variation,
especially with regard to limitation of the material to be drawn upon, to which I referred above, and
which, I believe, finds confirmation in skull statistics.

+ “Ueber die Anwendung der Wahrscheinlichkeitsrechnung in der anthropologischen Statistik,”
‘ Archiv fiir Anthropologie,’ Bd. 14. Braunschweig, 1882.

390 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

his plotting of RANKr’s observations agree with mine. He has added together under
83, for example, all indices from 83 to 83°9. Thus, for the indices 81, 82, 83, 84 he
gives the frequencies 106, 92, 111, 99, while I find 82, 116, 98, 107, a very sensible
difference.* Stiepa’s method can introduce very sensible errors. In this particular
case it transfers the maximum frequency of observation from 82 to 84.

The last four examples have dealt with cases where the statistician has hitherto
been content to assume symmetry. They have been given to indicate (i.) an
apparently uniform trend in biological statistics of variation, and (ii.) the improved
fitting of theory to practice which arises from using the generalised curve. I now
pass to cases of obvious skewness, where the statistician has hitherto had no satis-
factory theory.

(26.) Example VI. Distribution of 8689 Cases of Enteric Fever Received into the
Metropolitan Asylums Board Fever Hospitals, 1871-93.

Age. Number of cases. Age. Number of cases.
Under 5 266 35-40 299
5-10 | 1143 40-45 163
10-15 | 2019 45-50 98
15-20 | 1955 50-55 40
20-25 1319 55-60 14
25-30 857 Above 60 13
30-35 503

I considered that the 13 cases “ above 60”
8; 65-70, 4; 70-75, 1.
Taking five years as the unit I found

might be distributed as follows: 60-65,

fy = 4070554, ag = 77598196, — pr, = 69°379605.

The centroid-vertical is at 18°9691 years, z.e., 29382 unit from 15-20.

Thus 25 (8.” — py) + 3p;”= 18°05102, or the curve is of Type I. Since, however,
38, — 2B, + 6 = 1935 is small, a curve of Type III. will also be a good fit.

We have for the other constants

yr = 72:28642, d= | °98643,
Con OF 7 Bole: Skewness = °488922,
DS KPBS,
my = 2° 79291, My = 67°49351,
ar — 307801, dy = 7420511,
Yo = 1890°83.

* T class as 83 all from 82°6 to 83:4, dividing 82°5 between 82 and 83 evenly, and 83'5 between 83
and 84 evenly. Thus in the Table above certain frequencies will be found with such values as 12°5 or
71°5 skulls.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 391

Thus we have for the curve of Type I.

zg \2'79291 i fi aes
y = 1890°83 (1 a srs0) (\— Fo)

where the centroid is ‘98643 unit from axis of y.
The curve of Type III. is

e -LOT1M5 32,

a 3°673042
y = 1894°57 (1 + )

3428094

The centroid is in this case 933313 unit on the positive side of the origin and the
skewness = °462594.

It will be noticed that the curve of Type I. extends 2706 unit or 1°353 years,
and the curve of Type III. °5676 unit or 2°838 years before birth. In both cases
the chances of an “antenatal” death from enteric fever are very, very small. Curve
of Type I. is in this respect better than the curve of Type III. The latter curve
gives no maximum limit, the former a limit of about 77 units or 385 years. In both
cases, however, the chances of a case of enteric fever with the subject over 100 years
are vanishingly small. These statistics of enteric fever thus set a maximum limit to
the duration of life, but it is a limit so high as to have little suggestiveness.

In order to see what is the nature of the difference made, when we suppose the
lability to enteric fever to commence with birth, I will treat these statistics as a
case falling under § 16.

If then p’), p’2, and p’, be the first three moments about the vertical through
0 years we have

Pi = 379382, yw'n = 1846362,
y's = 108°53175,

Xo = 1282813, x3 17549399,
u = 030435, v= 321856,
m,= 214296, My = 28°71414,
b = 401206, Yo = 1878°39,

@, = 2°78629, @y = $7°33481.

whence we have for the curve

Xv a

y 2714206 28°71414
ITY (1 us Tae) (1 = =

Here the duration of life is 200 years about, and the maximum incidence of the
disease is at 13°93 years.

Lastly for the normal curve, we have the constants « = 2:01756 units = 10°0878
years and y, = 1718°12.

All the above four curves are drawn, Plate 12, fig. 9.

392 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

We see at once that the normal curve is perfectly incapable of expressing statistical
results like these. It gives an average error in the ordinate of 25:8 per cent. and no
less than 260 antenatal deaths !

For the remaining three curves we have the following results :—

Percentage error

g Antenatal cases.
in ordinate. enatal case

Curve of Type I. (closest fit) . . . 5°75 3
S 3 (starting at birth) . 73 0
Curve of Type III. . of irate ih 5:98 g)

The percentage errors here are well within those usually passed by statisticians.
If they are slightly larger than what we have found in previous cases the source of
the error is not far to seek. We have combined both male and female cases, but the
distributions of enteric fever for both sexes are not the same. ‘The fever curves for
either sex differ in some cases markedly, although less for enteric fever than for
diphtheria, for example. We have thus, in reality, a compound curve. I have found
for about 700 male cases only a percentage error of about 5.*

Another point needing notice is the question of antenatal cases, which may at first
strike the reader as absurd. The closest fitting curve of Type I. runs, as we have seen,
1°35 years about before birth, and gives three antenatal cases. Three antenatal cases
(or, indeed, 9 in the case of the curve of Type III.) is a very small percentage of
8689 cases, and not of importance from the statistician’s standpoint. But the fact
that a curve starting before birth gives a better fit than one starting at birth, is
significant, and there is every probability that a curve starting from about — ‘75 year
would give a still less percentage error than one from 1°35 year or from birth.t

In dealing with mortality curves for infancy I have found it impossible to get good
fitting theoretical curves, without carrying these curves backward to a limit of
something less than a year. The “ theoretical” statistics thus obtained of antenatal
deaths seem to be fairly well in accordance with the actual statistics of maternity
charities. In vital statistics therefore we must be prepared in most diseases for small
percentages of antenatal cases and antenatal deaths, and it is just possible that theory
in this matter will be able to indicate lines of profitable inquiry to the medical
statistician.

(27.) Example VII—As an example of the method of Section 15, I take the
following statistics of guessing a tint. Nine mixtures of black and white were taken,

* T prepose on another occasion to deal with the age distribution of fever cases. My object at present
is only to give typical illustrations of the method of calculating skew curves.

+ In fact the case of a pregnant woman with enteric fever is to be considered as a case also of
antenatal enteric fever.

MR. K. PEARSON ON- THE MATHEMATICAL THEORY OF EVOLUTION. 393

so as to get a series of tints in arithmetical progression 1, 2, 38, 4, 5, 6, 7, 8, and 9.
These tints were then placed in non-consecutive order, and 231 persons asked to guess
a tint by affixed letters lying between 1 and 9. The results were as follows :—

| Tint. | Frequency of Tint. Frequency of
| | guess. guess.
d 0 | 6 54
es 8 | 7 94.
2 7 | 8 40
5 22 | |
! |

Now, obviously, the number of tints and the number of persons guessing were far
too limited to draw any definite conclusions as to the distribution of tint guesses.*
I propose here merely to use these statistics to illustrate the calculation of a skew
frequency curve with a given limited range. I do not wish to propound any theory
of tint guessing, nor to assert that these guesses actually distribute themselves
according to the curves dealt with in this paper.

Calculating the moments about the centroid in the usual manner, we have

ie Py ie 3 7 |
ttg= — 3°70067 Centroid lies at a distance of 5°376624 units
is a 19°6255 from the tint 1.

4 “a

We easily find 2p (39? — wy) + 3p,” = 15°96335, or the observations fall into a
curve of Type L, that is to say, have a limited range.

We obtain
[si == UBIOEMOT, B, = 427862,
(AOE oA ie e= 6°443186.
hence the range
(DD == WB Ee,

Further

m, = 4°858705, My O99KGD,

a, = 11°08997, d= ‘22769,

dono: Skewness = 1:06666.

Thus the range of the theoretical curve runs from a point 4°15233 units before
tint 1, and concludes at a point ‘734674 unit before tint 9. The curve is, however,

* I hope later to deal with the subject of tint guesses falling within a limited range, as my material
increases in bulk. I would only note here, that the geometrical mean frequency curve does not seem to
give results according well with experiment.

MDCCCXCV.—A. 3 E

394 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

practically insensible before tint 1. Considering the roughness of the experimental
method, the obtaining an actual range of about 11 instead of 8, and its covering very
nearly the range of 8 must be held to be fairly encouraging for the method. I shall
accordingly calculate the constants of the curve on the assumption that the range lies
between Tints i and 9, using the method of § 15.

We find
u, = 2623376, po’, = 9°023803,
y, = 327922, y= 429971.
Whence
Ty = PRP i BIL,
Uy = 6144435, a, = 1°855565,
and

Yy = 59°5996.

Thus we may take for the curve

275412 Pe 83172
PSC 2 acrg a (1 = aes)

The curve is figured, Plate 11, fig. 10, with the first “smooth” of the observations.
It will be seen to give the general character of the distribution, but much more elaborate
experiments would be required before any statement could be made as to whether
frequency of tint guesses really does follow a curve with limited range of Type I.
On the same plate the frequency of 128 guesses distributed over 18 tints is given,
the approximation to a curve of Type I. is fairly close considering the paucity of
guesses.

(28.) Example VIII.—The question may be raised, how are we to discriminate be-
tween a true curve of skew type and a compound curve, supposing we have no reason
to suspect our statistics d priori of mixture. I have at present been unable to find any
general condition among the moments, which would be impossible for a skew curve
and possible for a compound, and so indicate compoundedness. I do not, however,
despair of one being found, It is a fact, possibly of some significance, that the best
fitting skew curve to several compound curves that I have tested is a curve of
Type L, and not that of Type IV. which appears to be the more usual type in
biological statistics. Taking, as an example, the statistics for the “foreheads” of Naples
crabs due to Professor WELDON, and resolved into their components in my memoir,
‘Phil. Trans.’ A, vol. 185, p. 85, et seg., I find for the best fitting skew curve the
equation

5m (a a2 \1s77264 ‘ a \+0469
ioe 2320 aE ( Se

where the origin is at 1°4274 horizontal units from the centroid-vertical in the

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 395

positive sense of the horizontal scale. If, now, we place this skew curve and the
compound curve of Plate 1, ‘ Phil. Trans.,’ vol. 185, on top of the observations (see
Plate 13, fig. 11), we see at once how much better is the fit of the compound curve.
The skew curve gives a mean percentage error in the ordinates of 10°4, the compound
curve of only 7°4. The determination of the best skew curve, when the compound
curve is known, is easy, for all its details are already practically calculated.

A criterion of whether a compound or skew curve is to be sought for ab iitio,
would be, however, of great value.

(29.) Example [X.—A more markedly skew curve than any we have yet dealt
with is that giving the frequency of divorce with duration of marriage. I take my
statistics from a paper by Dr. W. F. Wittcox, entitled “The Divorce Problem,
a Study in Statistics” (‘Studies in History, Economics, and Public Law,’ Columbia
College, vol. 1, p. 25). They are as follows :—

| Duration of marriage | Divorces (1882-6). _| Duration of marriage | Divorces (1882-6).

in years. | in years. |

i 5314. 12 | 4089

| 2 7483 13 | 3563

| 3 9426 14 | 3144,

a | 9671 15 2931

5 | 9014 16 2721

6 | 8274 | 17 2217

7 7021 18 1877

§ 6093 | ©) 1577

9 5305 | 20 1459

10 | 5002 | 21 and over 9401
11 | 4384, |

Total number of divorces granted, 109,966.

Now these statistics suffer from a defect common to many of the class—the want
of careful enumeration of the frequencies near the beginning and end of the series.
It cannot be too often insisted upon that careful details of the frequencies in the
start and finish of the distribution are requisite if we are to fit skew distributions
with their appropriate skew curves. How, in this case for example, are we to
distribute the 9401 divorces which occur after 21 years of married life? How, on
the other hand, does the curve start? It is impossible to place 5314 divorces at the
mean—6 months—of the one year duration. It is obvious that the applications for
divorce will be far more numerous in the last half-year than the first half-year of
matrimony. The very time required to institute legal proceedings and get a divorce
granted must ensure this if nothing else did. Yet these two tails of 5314 and 9401,
of which the accurate distributions are not given, are between + and § of the total
number of divorces, and until we know how they are exactly distributed, we cannot
hope for the very exact fitting of a theoretical curve.

3 E 2

396 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Tn order to make the best of the “ tails” under the circumstances, their moments
were calculated on two hypotheses, (i.) that they were triangles, (ii.) that they were
logarithmic curves, and the mean of these extreme results taken.

t found

[tg = 60°7376, Ps = 809°15,
qe IOLA == Boe sIbe

Distance of centroid from start of curve = 9'1183,
¥ maximum af es NDB.

Yo = Maximum frequency = 8882'45.

Here the curve is assumed, owing to the obviously long tail to the right and the
abrupt start to the left, to be of Type ILI. Its equation is accordingly

ie) VEE ‘
e~ 150127 5 Skewness = °8547.

y == 8882-45 (2 + ae,

The curve is figured, Plate 11, fig. 12, and will be seen to rise abruptly at about °47
of a year’s duration. It may be doubted whether legal proceedings even in America
are so rapid that a divorce suit can be complete within six months of marriage. The
curve gives fairly well the general form of the frequency statistics. Could the
moments have been determined with greater accuracy, most probably a better fit
would have resulted. As it is the mean percentage error is above 6.

(30.) Hxample X.—A still more extreme case may be selected from the field of
economics. I take the following numbers from the 1887 Presidential Address of
Mr. GoscHen to the Royal Statistical Society (‘Journal,’ vol. 50, Appendix IL.
pp. 610-2). I have grouped together both houses and shops, because the details of
the two are not in Mr, GoscHEN’s returns separated for values under £20.

VALUATION of House Property, England and Wales, years 1885 to 1886.

Number of houses. || Number of houses.

| |
Under £10 3,174,806 | £80 to £100 47,326
£10 to £20 | 1,450,781 LOOM te 50een| 58,871
20 ,, 30 | 441,595 | 150 ,, 300 37,988
30,, 40 259,756 3004 75000 | 8,781
40 ,, 50 150,968 500 ,, 1,000 3,002
50 ,, 60 90,432 1,000 ,, 1,500 1,036

60 ,, 80 | 104,128 |

]

Here clearly the curve starts with the maximum frequency, and further to any

MR. K. PEARSON ON THE MATHEMATICAL TH'ORY OF EVOLUTION. 397

scale to which the curve can be drawn, it tails away indefinitely to the right. This
justifies us in the assumption that the curve will be fairly approximated to by a form

of type

U Vie: OE

where p would turn out to be a negative quantity lying between 0 and 1. But the
details given us of the start and finish of the curve are far too scanty to allow us to
proceed by moments. Jn the first place, to measure an element of area of the
frequency curve by an element of value into its mid-ordinate is perfectly legitimate

at such a point as B; it fails entirely, however, at such a point as A, which includes
the part of the curve which is asymptotic to the ordinate of maximum frequency.
The area at such a point is much greater than the element into the mid-ordinate,
and the calculation of moments on the assumption that 3,174,806 houses may be
concentrated at £5, is purely idle. The ordinate obtained from the area in this
manner may often differ 30 per cent. from the true ordinate, and yet about three-
fifths of the total number of houses fall into this first group.

Further treating the area as ordinate into element of vaiue is also true only if the
element of value be small. For “elements” such as £150, £200, or even £500, which
are all that are given in the tail of these statistics, it is perfectly idle to concentrate
the area at the mid-ordinate. The centroid of a piece of tail such as the accompanying
figure suggests lies far to the left of the mid-ordinate In other words, to attack the

problem by the method of moments, we require to have the “tail” as carefully
recorded as the body of statistics. Unfortunately the practical collectors of statistics
often neglect this first need of theoretical investigation, and proceed by a method of
“lumping together ” at the extremes of their statistical series.

Still three further points in regard to the present series of statistics. First, they are

398 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

very unlikely to be homogeneous. Houses with an annual valuation of over £300
hardly fall under the same series of causes as the bulk of houses in the kingdom
which fall under £100. Secondly, when we are told that 3,174,806 houses are valued
under £10, it can hardly mean that any houses are valued at 0, certainly not the
maximum number. Hence our frequency curve in theory must not be expected to
rise from zero, but from some point between 0 and £10, which corresponds to the
customary minimum at which a cottage can be rented.

Lastly, there is one special cause at work tending to upset, about the value of £20,
the general distribution due to a great variety of small causes. This is the value at
which taxation commences, and we should expect a larger proportion of houses to be
built just under the taxable value than is given by a chance distribution.

Notwithstanding the many disadvantages of these results, I determined to obtain
if possible a skew curve approximating to the main portion of the distribution. I took
£10 as my unit of value and 1000 houses as my unit of frequency. I started with
the ordinary method of moments, concentrating each area at its centroid as given by
the total valuation of the group, also recorded by Mr. GoscHeEn, and found a curve of
the type

Yy = you? e-™,
with
p= — 65448, y= 2008.

This was so far satisfactory that it showed even by this rough method that p was
negative, and between 0 and 1. Thus the theoretical curve gave an infinite ordinate,
but finite area at its start.

A laborious method of trial and error was then adopted, and by varying p and y
slightly, as well as y, and the origin of the curve, I sought to improve the fit given
by the rough method (in this case) of moments. The fundamental consideration was
to keep the total areas under £100 value as nearly as possible the same in the
theoretical curve and the statistics. This portion of the curve I treated as prac-
tically referring to homogeneous material. Ultimately I found the following curve :

i 1388°32 gn 690077 Cmeienizs

with the origin as ‘45 unit from zero. Thus the minimum annual valuation was
£4 10s., or, to a weekly valuation, of 1s. 7}d. This would connote probably a weekly
rental of 1s. 8d. to 2s. The total area of this theoretical curve was 5795 in thousands
of houses ; of these 5729 had a valuation under £100 and 66 over £100; the corres-
ponding numbers for the statistics themselves are 5720 and 110. The additional 44
over £100 I assume to be due to the heterogeneity of the statistics—high values
corresponding to blocks of chambers, large hotels and other buildings hardly falling
into the same category as the small house under £100 in value. Unfortunately the
“tail” of the statistics is so defectively recorded that there is no hope of reaching a
separate distribution for this high class property.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 399

Returning now to the curve and statistics, we have the following comparative

results :—
Number of 1000’s of houses.
Value.
Theory. Statistics.
U aaah
nder 10 | 3580 3175 ‘
10-20 | 1045 \ ez 1451 \ oze
20-30 452 4.42
30-40 253 260
40-50 153 151 |
| 50-60 97 90
60-80 102 104
80-100 46 47
Above 100 66 110

The general accordance here is very marked, the chief divergences being accounted
for by the special causes to which we have referred above, 2.e. (i) the crowding of
houses just below the limit of taxation, and (11) the divergent character of the causes
at work determining the frequency of low and high class house property.

The results are depicted, Plate 14, fig. 13.

It will be observed that so far as the observations can be plotted to the theoretical
curve, it leaves little to be desired. The histogram* shows, however, the amount of
deviation at the extremes of the curve.

(81.) Example XI.—Frequency curves of the type considered in Example X. are
so common that it is needful to make a few further remarks with regard to them,
and illustrate them by further examples. Such curves occur in many economical
instances (income tax, house valuation, probate duty), in vital statistics (infantile
mortality), and not uncommonly in botanical statistics of the frequency of variations
in the petals or other characteristics of flowers.

As we have noted, the method of moments developed in this memoir cannot be
directly applied, or only applied to obtain a first approximation to the constants
required. This first approximation, however, will often assist us to obtain with
quite sufficient accuracy the value of the moments of portions of the area, especially
if the position of the initial or asymptotic ordinate is known.

For example, consider the curve of limited range :

y= pe? (b— 2)

where p lies between 0 and 1. Then if « be its area, aw”, = the s** moment about
the asymptotic ordinate of the area up to «:

* Introduced by the writer in his lectures on siatistics as a term for a common form of graphical
representation, 7.e., by columns marking as areas the frequency corresponding to the range of their base.

400 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

“ur

Oy [ yx? (b — x)" dx

1 NY n.mv—1 a \2
= He = | l+s—p
Yo ee Ve i te. fa

Hence, if the range b be large and x be small, this series converges very rapidly,
and we may often take with sufficient approximation even only its first term. Thus

pe hep)
[io 1 = 2—p
Pet en ernie
Bla a oes |
b nearly.
7 = pst
[ho 3 — 4A—»p
ee Yoo" el -»

~_ 1l—p 5)

Now «@ is given by the statistics, and we note that if p has been determined to a
first approximation by the method of moments, we can now improve the values of the
moments of the areas near the asymptotic ordinate by the use of the above
expressions.

For example, if p = ‘5 as a first approximation, we have

and as the area up to a short distance from the asymptotic ordinate is generally a

considerable proportion of the total area, the above values very considerably medify
the calculated moments.

In the case of the curve

Yy = yye Pe",
we have the result

1 ya ih yn }
l+s—p 2+4+s8s—p 1.2.3+s—>p) ;

op’, = yg’ +1? 1

Hence, as before, if y and # be small,

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 401

= cs x’, approximately.*

Results such as the above enable us to approximate fairly rapidly to the constants
of a frequency curve.

As a special example, I take the following. In 1887, Herr H: pr Vries transferred
several plants of Ranunculus bulbosus to his flower garden, and counted the petals
of 222 of their flowers in the following year. He found (‘ Berichte der deutschen
botanischen Gesellschaft,’ Jahrg. 12, pp. 203-4, 1894) :

Petals4 ou ga te: 5 6 eu 8 g 10
Frequency. . . 133 55 23 7 2 yy

Now the series here proceeds by discrete units, and corresponds probably to a hyper-
geometrical series, but remembering how closely the results of tossing ten coins can
be represented by a normal frequency curve, I was not without hope that the areas of
a skew frequency curve would give results close to these numbers. The buttercups
start with 5 petals and run to 10, I therefore took my origin at 4°5 and determined

the constants to a second approximation in the manner above indicated. There
resulted,
Y = 21122547 (73253 — oP,

a curve of Type I., with limited range, the asymptotic ordinate being at 4°5 petals,
or practically a distribution ranging from 5 to 11 petals.
Calculating the areas, there results,

Petals a. ores 5 6 7 9 10 11
F J Theory. 5 6 | ROS 48°5 DRG 9°6 374 8 2,
requency ; i
LObservation . 133 55 23 7 2 2 0

The agreement here is very satisfactory considering the comparative paucity of the
observations.t The results are exhibited by curve and histogram, Plate 15, fig. 14; the
two points on the “observation curve” corresponding to five and six petals are
deduced from the areas given by the statistics by the same percentage reduction as

* Another very serviceable formula is due to Scuuémitcu. It gives the area of the “tail’’ of
y = ye Pe- 7 from g =z to «= ina rapidly converging series, #.c.,

area = Joe Pe” { je ees te = ON L (i+) ax + ke. \ :
1 qe +l (a+ 1 (ye+2) (ye +1) (qe + 2) (ye +8)

9

+ 2048 tosses of 10 shillings at a time gave a mean 3 per cent. deviation between theory and
experiment, 100 tosses gaye avout 9 per cent. The above series corresponds to about 7-2 per cent., and
thus is quite within the range of accuracy of coin-tossing experiments,

MDCCCXCV.— A. 3 F

402 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUUION.

converts the theoretical areas into the ordinates of the theoretical curve. For other
petals, ordinates and areas practically coincide in value.

(32.) Example XII.—Another example of a similar kind may be taken from
Herr DE Vriss’ memoir (oc. cit., p. 202). He cultivated under the name of perwm-
bellatum a race of Trifolium repens, in which the axis is very frequently prolonged
beyond the head of the flower, and bears one to ten blossoms. In the summer of
1892 he had a bed of such clover, produce of a single plant, and in July counted the
extent of this variation on 630 flowers. In 325 cases the axis, according to DE VRIES,
had not grown through the head of the flower, in 83 cases it had grown through and
bore one blossom, in 66 cases two blossoms, and so on. The complete statistics are
as follows :—

High blossoms 0 1 2 8 4 5 6 7 8 9 10
Frequency 6s BRS 83 66 51 36 36 18 7 6 1 1

Taking moments in the manner of the earlier part of this memoir, I found as a first
approximation to the frequency curve :

y = 452842 we 2817 (10-69114 — a) 1528044,

with the origin at °47813 to left of maximum ordinate. This first approximation
seemed to justify three things : (1.) starting at ‘5 to the left of the maximum ordinate;
(ii.) assuming a range, 11, which just covered the whole series of observations, 2.e.,
from ‘5 to 10°5; and (iii.) that the moments of the areas might be found from a value
of p not far from °5.

A second approximation was then made, and taking moments round the asymptotic

ordinate, I found :
ww, = 18680, yp’ = 7°77028,

whence, in the manner of $16, we have:

Xi = 1698182, X2 = 38781526,
and ultimately :
m, = — ‘493118, M, = 1°47797,
and
Yo = 4°65148.

The equation to the frequency curve is therefore :
y= 4°65148 go — 493118 (11 AA x) 147797

The value found for p, 7.e., 493, justifies our calculation of the moments on the
assumption that it was ‘5.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 4038

Placing statistics and theory side by side, we have :

High }
0 1 2 3 4 5 6 7 8 9 10
blossoms

Statistics 325 83 66 ol 36 36 18 7 6 1 1
Theory 303°22 106°12 69°99 49°27 35°23 24°93 17°07 10°96 6:27 2:79 °52

The agreement between theory and observation is here all that could be desired,
except in the case of 0 and 1 high blossoms. Here 22 blossoms have in actual
counting been transferred from the theoretical group of 1 to the theoretical group of
zero high blossom. I consider it highly probable that the theory here gives better
results than the actual statistics ; and this, for the simple reason that it must be
very difficult to distinguish between any one of the low blossoms and a very slightly
extended axis bearing only one blossom, that is to say, the extension of the axis
passes insensibly into one of the low blossoms, or vice ver'sd, and in a certain proportion
of cases it must be difficult to distinguish between the categories 0 and 1. The com-
parison between theory and observation is represented by curve and histogram,
Plate 15, fig. 15.

Examples X. to XII. will suffice to illustrate the application of our theory to
extreme cases of skew distribution.

(33.) Example XIII.—It must not be supposed that in every case of variation by
units (as in the buttercup and clover examples), the curve will be found to be of
Types I. or LI. It is impossible to illustrate, in anything short of a treatise
on statistics, the infinite variety of statistical distributions, but the occurrence of
Type IV. in zoological, as distinguished from botanical measurements, is so persistent
that it seems well to illustrate this for the special case of discontinuous variation.
Professor WELDON has kindly given me the following statistics of dorsal teeth on the
rostrum of 915 d and ? specimens of Palemonetes varians from Saltram Park,
Plymouth.

Teeth. Cases.

NI Ot CO DOR
we)
J
bo

The centroid-vertical here lies *313661 of a tooth beyond 4, ze., at 4°313661 teeth.
The following are the moments about centroid-vertical :—

3 Ff 2

404 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

po = 910906 |
#3 = ‘233908 Swhere the unit = 1 tooth.
ju, = 2°625896

For the normal curve these give

Standard deviation = "9544,
Maximum ordinate = 382°5.

For the skew curve we have

B, = 072222, By = 3164684.
Hence
26, — 38, — 6= 122702,

or, we have a curve of Type IV. The values of 8, and f,, however, show that it will
not differ very widely from the normal type.
Proceeding to determine the other constants we find

— 111°398,
v = — 109047 (v is negative since ps, is positive),
— 716613, m = 56°699,

Distance of origin from centroid-vertical = 7°0149,

log yy = 18°4431056.
Thus

Yy — Yo cost#389 EeaionTe:

t= (166138 tan

give the form of the curve. This curve, the normal curve, and the observations are
drawn, Plate 13, fig. 16. A comparison of the observations and the normal curve shows
an amount of skewness in the tails of the former, which would be very improbable if
the normal curve really expresses the distribution. The skew curve really accounts
for this divergence and is a sensibly better fit. The mean percentage errors in the
ordinates are for the two cases 8°67 and 3°88. The skew curve is thus an excellent fit.

The discontinuity in these teeth probably corresponds to a hypergeometrical polygon,
of which the skew curve is a limiting form.

(84.) Hxample XIV.—Another extremely interesting illustration of skew varia-
tion will be found in the statistics of pauperism for England and Wales, to which my
attention was drawn by Mr. G. U. Yuus, who had plotted the statistics from the raw
material provided in Appendix I. of Mr, Cuartes Booru’s ‘ Aged Poor; Condition’

In Plate 14, fig. 17, we have 632 unions distributed over a range of pauperism varying
from 100 to 850 per 10,000 of the population for the year 1891. The observations

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 405

are at once seen to give a markedly skew distribution. Taking 50 paupers as unit of
variation, we find
Wy = 6°31889, - By = 3060017,
fs = 662.465, B,= 173942.
fog = 122-1815;
Hence
38, — 28, + 6 = -401791,
or the curve is of Type IL.
The other constants were found to be

(— 2 owl Oils.

e = 148°0886,
m, = 20:169714, Oh, = 24:2203
i — te III 00) C—O ot 2
Yo = 99°9065.
Range = 31°4196.
Maximum = ‘60434 to left of centroid vertical.
Skewness = ‘24.
The equation to the curve is thus
2 fe v \ 5:9953 / a 20°1697
y = 99°9065 (1 71993) ( ee ase)
For the normal curve,
Standard deviation = 27514,

Maximum ordinate = 100°301.

Both skew curve and normal curve are drawn on Plate 14, fig. 13. ‘The former is at
once seen to be an excellent fit. We might fairly have simplified our work by taking
zero paupers as the commencement of our range, but preference was given to the more
general results in order to demonstrate that they give no appreciable amount of
“negative pauperism.” The range determines a limit of about 15 per cent. as the
greatest possible amount of pauperism. The normal curve is seen to diverge very
widely from the statistics besides giving an appreciable amount (3 to 4 unions) with
“negative pauperism.” The point-binomial for these statistics is also figured on the
plate. Its constants are p = ‘833, g = ‘167, n = 14°4834, c = 1°70306, the start of
the binomial being 5°81503 to the left of the centroid-vertical: see § 5. The fit isa
very close one, the mean error of ordinate = 5°37, and the suggestiveness of such
results for social problems needs no emphasising.

The case is of peculiar interest, because the statistics of pauperism are known to
give a definite trend to the distribution, «.c., if the statistical curve of pauperism for
1881 be compared with that of 1891, for example, the maximum frequency of the

406 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

earlier will be found at a much higher percentage. ‘The whole frequency curve is
sliding across from right to left. Now it is of interest to notice that in this, as
in other cases where the trend of the variation is known @ priori, the skew curve is
shifted away from the normal curve in the direction in which variation is taking place
with lapse of time. It is not safe at present to extend this to all biological instances,
but the result suggests, for example, that there is a secular progression towards brachy-
cephaly in Bavarian skulls (fig. 8), towards reduced antero-lateral margin in crabs
(fig. 4), towards increased height in St. Louis school-girls (fig. 7), and towards long-
sightedness in Marlborough School boys.* I believe most suggestive and important
results might be obtained for the theory of evolution, if we only had the series of
skew curves for a biological case of progressive variation in the same manner as we
have for pauper percentages.

(35.) Example XV. The theoretical resolution of heterogeneous material into
two components, each having skew variation, is not so hard a problem as might at
first appear, and I propose to deal at length with the subject later. If there be more
than two components, the equations become unmanageable. In this case however, if
the components have rather divergent means, a tentative process will often lead to
practically useful results. To illustrate this I propose to conclude this paper by an
example of a mortality curve resolved into its chief components. By a mortality
curve I understand one in which frequency of death (for 1,000, 10,000, or 100,000
born in the same year) is plotted up to age. I have worked out the resolution for
English males, and for French of both sexes. The generally close accordance of the
results for both cases has given me confidence in their approximate accuracy. The
method adopted was the following: An attempt was made to fit a generalised
frequency curve to the old age portion of the whole mortality curve, the constants of
this curve being determined from the data for four or five selected ages by the method
of least squares; the frequency curve so determined was subtracted from the total
curve, and a frequency curve fitted by the same method to the tail of the remainder.
This second component was again subtracted and the process repeated, until the
remainder left could itself be expressed by a single frequency curve. The com-
ponents thus obtained were added together, and a tentative process adopted of
slightly modifying their constants and position, so that the total areas of the com-
ponents and of the whole mortality curve coincided. It was soon obvious that no
very great change either in the constants or position was permissible, if the sum
of the components was to give the known resultant curve, hence I feel very confident
that whatever be the combination of causes which result in the mortality curve, that
curve is very approximately to be considered as the compound of five types of
mortality centering about five different ages. The allied character of the results
obtained for both French and English statistics confirms this view.

* Dr. Rozerts’ statistics, which I have reduced to skew curves, but have not reproduced in this
memoir.

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 407

Professor Lexis has already suggested that the old age distribution of mortality
is given by a normal curve.* Now, although the rougher French statistics give
a fair approximation to a normal curve, this is not true for English males. The
curve for old age is of Type I., but for all practical purposes it may be treated as one
of Type III. Whatever be the chief causes of old age mortality, they extend very
sensibly through middle life, and less sensibly through youth, only becoming inappre-
ciable in childhood. Hence, if we speak of our first component as the “ mortality of
old age,” the name is to be understood as referring to a group of causes especially
active in old age mortality, but not excluded from other portions of life. The
second and third components I found to be skew curves, but so nearly normal that to
my degree of approximation no stress could be laid on the skewness obtained. The
fourth component was a markedly skew curve, also closely given by a curve of
Type III., and corresponding in general shape to the mortality curves of fevers
peculiarly dangerous in childhood (e.g., diphtheria, scarlet fever, enteric fever, &c.).
These three components I have termed respectively the mortality of middle life, of
youth, and of childhood. I found it impossible to fit the remainder of the original
mortality curve with any type of generalised curve, so long as I supposed the
mortality frequency to commence with birth. Iwas therefore compelled to suppose
the set of causes giving rise to “infantile mortality” extended into the period of
gestation, and I obtained a satisfactory fit for the infantile mortality frequency, when
the range of the curve started about *75 of a year before birth. The form taken by
the curve is the extreme type in which the curve is asymptotic to the ordinate of
maximum frequency (cf. Examples X.-XII.). The five fundamental components of
the mortality curve for English males are the following, the numbers referring to
1000 contemporaries, or persons born in same year :—

(A.) Old Age Mortality.
Total frequency = 484°1.
Centroid-vertical at 67 years.
Maximum mortality = 15°2 at 71°5 years.

The equation ist

: a NUT 2215
y = 152 (1 — 35) ezlbe
the axis of y being the maximum ordinate and the positive direction of « towards
age. The skewness of the curve = ‘345, and its range concludes at 106°5 years.
The corresponding French component = 411, but the maximum mortality (16°4)
occurs at 72°5 years.

* ‘Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft,’ § 46. Freiburg, 1877.
+ Unit of c = 1 year, unit of y = 1 death per year.

408 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

(B.) Mortality of Middle Life.
Total frequency = 173°2.
Centroid-vertical at 41°5 years.
Maximum mortality = 5:4.

The curve is very approximately normal, and has a standard deviation of 12°8
years. The corresponding French component = 180 deaths, standard deviation
12 years, with a maximum of 6 at 45 years.

(C.) Mortality of Youth.
Total frequency = 50°8.
Centroid-vertical at 22°5 years.
Maximum mortality = 2°6.

The curve is very approximately normal, with a standard deviation of 7°8 years.*
The corresponding French component gives a total mortality of 78, standard deviation
of 6 years, and a maximum of 5'2 at 22°5 years.

The greater and more concentrated French mortality of youth is noteworthy.

(D.) Mortality of Childhood.
Total frequency = 46°4.
Centroid-vertical at 6°06 years,
Maximum mortality = 9 at 3 years.

The equation to the curve, the axis of y being maximum ordinate, is
y = 9 (1 + ai) e@7 eet.

Thus the skewness of the curve = ‘87, and the range commences at 2 years.

The French component appears to be shifted further towards youth. It gives a
total of 47 deaths, centroid at 8°75 years, and a maximum of 5°8 at 5°75 years,
skewness = ‘71. Childish mortality is therefore, if these results be correct, more
concentrated, and at an earlier age in England than in France.

(E.) Infantile Mortality.
Total frequency after birth = 245-7.
Maximum frequency after birth occurs in first year and equals 156:2.
The equation to the frequency curve is
y = 236°8 (w + °75)-* e-™,

the origin being at birth, the skewness °707, and the centroid at ‘083 year,= 1 month
neatly, before. birth. Taking the corresponding French component, we have a total
frequency after birth of 284, with 186 deaths in the first year of life. Infantile
mortality is therefore considerably greater in France.

* The mortality of youth would be better expressed by a curve of type y= Yo (i —
§ 13 (v.).

ge \m
: see our

2
ar

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 409

If we investigate the areas of our infantile mortality curve, we have the following
deaths :—

Theory. Statistics. |
Ist yearoflife. . . . 156°2 158°5 |
2nd year of life .. . 53°5 | 51:2 |

After this the mortality of childhood begins to sensibly increase the infantile
mortality. Turning to the “ antenatal” portion of the curve, we have the following
results, of course not verifiable from ordinary mortality statistics :—

(i.) The total “antenatal” deaths for the 9 months preceding birth are 605 for
every 1000 actually born and registered.

(u.) “ Antenatal” deaths for the 6 months immediately preceding birth are 214 for
every 1000 born.

(iii.) ‘‘ Antenatal” deaths for the 3 months immediately preceding birth are 83 for
every 1000 born at the proper period.

The 391 “deaths” of the first three months of pregnancy would not be recorded,
and in many cases possibly pass without notice. The 214 deaths of the remaining
six months would be considered as miscarriages or still-births. The proportion of
1 in 6 of such accidents to births of the normal kind does not appear excessive, On
the average Dr. GALAPIN says such an occurrence is ‘“‘ the experience of every woman
who has borne children and reached the limit of the child-bearing age.” So far then
there appears nothing to contradict our theoretical results in what is known of the
first six months of antenatal life.

For the last. three months we have more definite data. According to our curve
we have 83 deaths (per 1000 born) in the last three months before birth, or 83 in
1083 pregnancies = about 7°7 per cent. Now this percentage must consist of two
factors—still-born children and children who, born before their time, die shortly
after birth, and who would not be recorded in any proper proportions in statistics
based on census returns, nor as a rule in the returns of maternity charities.

For statistics of still-births, I find:

per cent.
Dublin Rotunda Hospital: (1847—54)) es 6
is . (87 t= 7) gen ey ll Selanne
Dra Jeg Diagn for 14,000 births for a large thabernity charity
in St. Paneras. . . 4

Guy’s Hospital Lying-in Clanieys 25, 777 dices, up 127 oe
dead or died within a few hours, 1000 corresponding to
births in the last three months of pregnancy. . . . . 3°84
NewsHoime’s “ Vital Statistics” (no authority cited) . . . 4
MDCCCXCV.—A. 3G

410 MRK. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

It would thus appear that there are 4 to 5 per cent. of still-births, thus leaving
2‘7 to 8°7 per cent. of deaths to be accounted for—if there is any validity in our
analysis—by. deaths of children born before their proper time and dying before
their proper birthdays. Such deaths would not appear in the category of still-born
children in the returns of the maternity charities, nor in any true proportion in the
census returns.

Thus, while it is impossible to assert any validity for the antenatal part of our
curve of infantile mortality, while, indeed, the constants of that curve, and con-
sequently the percentages of antenatal deaths, might be considerably modified had
we surer data of the actual deaths in the first year of life; still there appears to be
nothing wildly impossible in the results obtained, and they may at any rate be
suggestive, if only as to the nature of those statistics of “antenatal” deaths, which
it would be of the greatest interest to procure.

The absolute necessity of skew curves in all questions of vital statistics is sufficiently
evidenced in this resolution of the general mortality curve. A complete picture of the
resolution into components of the mortality curve is given (Plate 16, fig. 18), with
a separate figure on an enlarged scale of infantile mortality. ;

(36.) In conclusion, there are several points on which it seems worth while to insist.
The normal curve of errors connotes three equally important principles :

(i.) An indefinitely great number of “ contributory ” causes.

(ii.) Each contributory cause is in itself equally likely to give rise to a deviation of
the same magnitude in excess and defect.

(ii.) The contributory causes are independent.

The frequency of each possible number of heads in repeatedly throwing several
hundred coins in a group together, practically fulfils all the above three conditions.

Condition (ii.) is not, however, fulfilled if a number of dice be thrown or a number
of teetotums of the same kind be spun together. Condition (iii.) is still fulfilled.

Condition (ii.) is not fulfilled if p cards be drawn out of a pack of n7 cards containing
r equal suits, supposing the p cards to be drawn at one time. Now, it appears to
me that we cannot say @ priori whether the example of tossing, of teetotum-
spinning, or of card-drawing is more likely to fit the proceedings of nature. There
is, I think, now sufficient evidence to show that the conditions (i.) to (ii.) are not
fulfilled, or not exactly fulfilled, in many cases—in economic, in physical, in
zoometric, and botanical statistics. We are, therefore, justified in seeing what results
we shall obtain by supposing one or more of the above conditions which lead to the
normal curve to be suspended. The analogy of teetotums and cards leads us to a
system of skew frequency curves which in this paper have been shown to give a very
close approximation to observed frequency in a wide number of cases——an approxi-
mation quite as close as the writer has himself obtained between theory and
experiment in very wide experiments in tossing, card-drawing, ball-drawing, and

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 411

lotteries. But the introduction of these skew curves leads us to two important
conclusions :—

(i.) Ifa material be heterogeneous we have no right to suppose it must be made up
of groups of homogeneous material each obeying the normal law of distribution. Each
homogeneous group may follow its own skew distribution.

(u.) If material obeys a law of skew distribution, the theory of correlation as
developed by Gatton and Dickson requires very considerable modification,

We may note two points bearing on these two conclusions, which do not seem
without interest for the general problem of evolution. Fever mortality curves are
skew curves. The general mortality curve—frequency of death at different ages—-
is a compound of many diseases, but with sufficient approximation, it can be resolved
into five components; three of these components are markedly skew, the other two
less so. Selection, according to age, is thus distributed with different degrees of
skewness about five stages in life; this at least suggests that selection according to
the size or weight of an organ may be compound, if we take a considerable range of
size, and that the components may have varying degrees of skewness.

The correlation of the ages of husband and wife at marriage is a subject with
regard to which we have a very fair amount of material. For a given age of the
husband, the frequency of marriage with the age of the wife fits very closely a curve
of Type IV., and with sufficient exactness very often a curve of Type III.* The
sections of the surface of frequency are oval curves differing entirely from the ellipses
of the Gatron-Dickson theory, but resembling in general the “oval” polygons
obtained by taking horizontal sections of the frequency polyhedron for the correlation
of cards of the same suit in two players’ hands at whist. Plate 9, fig. 19, shows how
widely these differ from ellipses. There seems therefore to be considerable danger
in assuming in vital statistics, whether in man or the lower animals, that the “ con-
tributory” causes are independent. All the statistics for sizes of organs in animals,
which I have yet analysed, if they are not compound, seem to agree in following a curve
of Type IV., and suggest this kind of inter-dependence of the “ contributory ” causes.
Their correlation surfaces of frequency will thus have for lines of level skew ovals—
what for want of a better name may be termed “whist ovals” as distinguished
from the ellipses which flow from the normal frequency surface. The remarks from
quite a different standpoint of RANKE on skull measurements seem to lead to the
same conclusion. I propose on another occasion to illustrate the resolution of
compound curves into skew components, and further to deal with the main features
of correlation in cases of a skew frequency distribution.

* I have fitted some of Purozzo’s marriage statistics with skew curves, but reserve their discussion
for the present, as they belong properly to the theory of skew correlation.

3 @ ®

412 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

Nove.

Added May 24, 1895.

[Since writing the above memoir my attention has been drawn to a note in
Dr. WesterRGAARD’s “Theorie der Statistik,” referring to Professor T. N. THrete’s
treatment of skew frequency curves. I have procured and read his book, ‘ Forelaes-
ninger over Almindelig lagttagelseslaere, Kj¢benhavn, 1889. It seems to me a. very
valuable work, and is, I think, suggestive of several lines for new advance. It does
not cover any of the essential parts of the present memoir. Dr. THIELE does indeed
suggest the formation of certain “ half-invariants,” which are functions of the higher-
moments of the observation—quantities corresponding to the py— 3p", bs — 10p.p5,
&ec., of the above memoir. He further states (pp. 21-2) that a study of these half-
invariants for any series of observations would provide us with information as to the
nature of the frequency distribution. They are not used, however, to discriminate
between various types of generalised curves, nor to calculate the constants of such
types. A method is given of expressing any frequency distribution by a series of
differences of inverse factorials with arbitrary constants. Thus if

and

AB,, (x) = B,, (x + 4) —_ [st (x te 3)
we can express any law of frequency y = f(x) by

SF (&) = boBn (#2) Fb, AB (@) +.» + bn A"B) (2),

where the constants bo, b,... 0, can be determined numerically when the frequency
of n + 1 chosen derivation-elements is known.

I see a possibility of more than one theoretical development of interest, especially
in relation to compound material, from this development of Dr. TurELE’s, but I doubt
whether it can be of practical statistical service even as an empirical expression for
frequency. Instead of having the 8 to 5 constants of our generalised curves, the full
value of Dr. THrexe’s expression requires as many constants as there are recorded
frequencies, and then expresses the result in functions like A’B, (x), by no means easily
realised or likely to appeal to the practical statistician. It is true the complete series
gives absolutely accurately the frequency of all the points used in the calculation, but
it does not, like the generalised curves, indicate the purely accidental variations of
the frequency. If, on the other hand, we take, as Dr. THIELE suggests, some half-
dozen terms only of the series—which give the really essential character of the

MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 413

frequency—we obtain results which, although more complex in form, are not as satis-
factory as those given by the generalised curve.:
For example, Dr. THIELE gives the following series (p. 12) :—

feebvealucseceiesere NSH ae [ecole Or l/a10y eT) 12
| |

Frequency. . . .| 3 7 30 | 101 | 89) 94

13| 14 | 16) a7 48 19

70 | 46) 30

His “ Faktiske Fejllove ” gives

y = °12218,, (a) + 278 AB,, (x) + -600 A°B,, (x)
+ 216 A%8, (w) + °278 A%B, (w) — 318 AB, (w)
+ +574 A®B, (x) + -596 A7B, (x) + +499 A8B, (x)
+ +259 AB; (a) — 0645 AYB, (x) — 0303 AUB, (a)
— 0088 APB, (2).

He tells us that 6 terms practically suffice, the additional terms merely accounting
for the individual irregularities of this particular 500 observations. Without speci-
fying what the observations are, he tells us that the possible values run from 4 to 28,
or that the range is really limited.

If we fit our generalised curve of Type I., we find for its equation :

8 xv 3°89708 2 1727285
ee (1 te un (1 = icone) ,

the origin is at 11°191, or the range runs from 6°6715 to 31°1202, we., is a range of
24-5487 instead of 25, but is shifted some 2 to 3 units. Considering the small
number of observations, this is not a bad approximation to a marked feature of the
distribution not indicated on the surface by the observations, nor discoverable from
the “ Faktiske Fejllove.”

Comparing our curve (i.) with (i.) the actual statistics—all 13 terms of the
“ Faktiske Fejllove” series, and with (ili.) the first 6 terms of the same series, we
have the following results :—

Values . |

7 8 1) eae 9) | PIB es FS || 1g
Go| TO 22) ON EO) | 2S Ba I eG Tey Il a
(ii.) 3 7A SEENON EO NOL | FO) 2B BOI aia = Bip a
iii.) DT 20 | Be ee GO) 48 eB ee Wes Pa a

The generalised curve here gives slightly the better results in addition to its more
easily realised form, and its fewer constants (iv.).

414. MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION.

On the other hand, there are, I think, some points of first-class theoretical impor-
tance in the mode adopted by Dr. Tuiste for expressing frequency ; it gives us a
means of expanding all varieties of frequency curves in a series of factorial functions
which may Jead to important theorems in the analysis of heterogeneous material. |

PLATES.

The scale of the accompanying figures is not that of the original drawings, and the
clearness and distinctness of the several curves of the same figure have heen, in
several instances, partially lost by the process of reproduction and reduction. In
every case the square element of the figure corresponds to the square centimetre of
the original diagram, and is spoken of both in the text of the memoir and on the
figures themselves as a square centimetre. The scale of actual reduction is indicated
by a fraction placed at the lower right-hand corner of the figure.

ate 7.

y
U

Ae x

Phil. Trans., 1895,

Pearson.

76010 YqIM Pars 1 PUIYIOIL IY] PUD ‘eapije Wolf % 7n0gD
JNO PUuDTs 6LOINGH SIP, MW ‘suUulnypoag) 7uarviffa09
a

A

‘CUUTN]OI JUI1II{909

/
on 249) fo
O7 pajenlpo

ap2qs =d~

jaa 07

uly

Pearson. Phil. Trans., 1895, A, Plate 8.

Fig. 3.
7
= CURVE OF BAROMETRIC HEIGHTS. 4697 OB ERVATIONS
Ri 9 ier eserrtation by Point-Binomial.
5 al Sale FASE
Ey TN ialee Point! Binomial.
SS A ‘ al rt Base-Ure
Le Z Werghted |Ordinates. Ce, 11974 am.
/ \ 86-4 (-04905-4|700/8)°7 > cad bacad =E8I6 C77.
\ = :
; W Lee a Ch, 20712 C7.
82-45 fae +1/064, Peete =7:556
\ WW Frapexia. Ce Z20/7\em.
= g SSF a aoa
Observations : | —~———
Scale ae ency. |) sgcm.=\( 28-304
nite Obderv Li
e at
——— $a

= es
8
ar =,
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Fig. 4.
WELDONS MEASUREMENTS OF THE CARAPACE : RIGHT ANTERO-LATERAL MARGIN OF 999 FEMALE NAPLES CRABS. ( See:BIProc No." 7892)
Sonne
=
|
al

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8

Phil. Trans., 1895, A, Plate 9.

Pearsen.

LSIHM YO4s JOVIYNS
NOILVTSYYOO 40 S3SNIT YNOLNOD

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Pearson. Phil. Trans., 1895, A, Plate 10.
Fig. 6.

CURVE OF BAROMETRIC HEI/GHTS. 4857 OBSERVATIONS. (D2 Venn: Nature” Sept 7% 1867).

NEN
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7

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Fig. 7.
HEIGHTS OF 2192 ST LOUIS SCHOOL-G/RLS, AGED 8 YEARS (WT.Porter) .

la) |
Equation 2 Curve oF f Type FF.
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We 255-3022 _cps2* 5 @ e-F55967 9
Observations : ——-—___
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Theory |: ae es ae 7
Scale of Fi el 1 6g. Crm.=20 girls vi
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Normals, Curve —-—--.—|.- Z|! S
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Pearson. Phil. Trans., 1895, A, Plate 11.

Fig. 8.

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Fig. 12.

DISTRIBUTION OF 109966 DIVORCES ACCORDING TO DURATION OF MARRIAGE. UNITED STATES. 1882-86 (WE Wilcox )
=I 7

pee |
ik Saasane again. b doo Divarveal | [
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cl SUg0 Seoul
3 = peo ane

DUNS S22So00000R0nn0o00005

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o 4 208 4667 6 9 1 HW 2 18 4 15 1% 17 18 19 20 2 &2 2 2 25 26 27 28 29 50 3) 52 35 54 55 56 37 58 59 GO HW F243 44 45 tx hs
Duration of Marriage in Years.

H |_|
A L Hee Ma a
bl OE a i
|_|
EE
Ei

Phil. Trans., 1895, A, Plate 12.

Pearson.

OZ

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=

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(£6-et “peoog psy doszaW) *YFIATS DIMILNI SO SISVI 609 SO NOILNGIYLSIO-JIV

oe a

=

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Pearson.

Phil. Trans. 1895, A, Plate 13.

Fig. 13.
fale fe Sis)
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Fig. 17.
STATISTICS OF PAUPER/SM . ENGLAND AND WALES. DISTRIBUTION OF 652 UNIONS, /89/.

Ey Ho 120 1 160 1 1p0 1 tb3# 10)
Ee wLSES_£7e etl:
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(O77: :Pa r 10,000 of the| po, ‘ton, Unit of x + 50 paupers
Wd 2000 papers [-

Pearson. Phil. Trans., 1895, A, Plate 14.

late I)

tal} scale.

ixon

of | hor

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ur

pas a

Fig. 16.

NUMBER OF DORSAL TEETH ON ROSTRUM OF SE IEE 3 AND (Plymouth, Weldon).
Observations :

No a Ch TVE 5 cp ewe nd encedene

Maximum Ordinate|: 562-5
Standard. Deviation : 9544 i
] | y
Shew urve, Type W: |-----+-
} 4 en je
Bi ton|: 2b7eb3s tan.|\6, 3

y= COS 7.

where 5 log Y. = 8-443,1096-
Origin | to eel Vertical =7-0/45.

|

—

a
Wureber 6 éth:
ai. Z Frege

Phil. Trans , 1895, A, Plate 15.

Pearson.

2
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ae | agrtmatuory
“891481 2/6 tin = pai 200 aly
PIP OF Bujpuddee JOD ae x es
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———

:
scan

Pearson. Phil. Trans., 1895, A, Plate 16.

et
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year.

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Vig 18
ENGLISH MORTALITY. MALES. DEATHS PER ANNUM OF 1000 PERSONS BORN IN THE SAME YEAR. ( Ogle: 1871-1660)
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[ald]

XI. A Determination of the Specific Heat of Water in Terms of the International
Electric Units.

By Artaur Scuuster, /.R.S., Langworthy Professor of Physics at the Owens College,
Manchester, and Witu1aM Gannon, M.A., Exhibition (1851) Scholar, Queen’s
College, Galway.

Received November 13,—Read November 22, 1894.

Tuts research was originally undertaken by Professor ScoustErR and Mr. H. Hapiey
before the authors were aware that Mr. E. H. Grirriras was engaged on a similar
investigation. After a number of preliminary experiments, and just as the final
arrangements for the conduct of the measurements were being definitely made,
Mr. Haptey, on his appointment to the Head Mastership of the School of Science
and Art, Kidderminster, had to leave Manchester. In the meantime Mr. GRIFFITHS’
important research was published ; and we had to consider whether our own work,
which was designed on a smaller scale, could compete with it in accuracy. We
decided to complete the investigation, principally for the reason that, although we
both aimed at determining what is commonly called the mechanical equivalent of
heat through the heating of a certain mass of water by means of an electric current,
the details of the experiments differed very materially, so that our two ways of
dealing with the problem seemed to afford a useful test of the amount of agreement
which may be obtained at present. Our investigation touches only a small part of
that treated by Mr. GRIFFITHS, as we did not attempt to measure the changes in the
specific heat of water due to change of temperature. On the other hand, the more
modest limits within which we have confined ourselves, allowed us to use a much
simpler apparatus. On Mr. Hapiey’s departure, Mr. W. Gannon took his place.
From the former gentleman we received a good deal of help in the devising and
construction of some important parts of the apparatus.

The principle of the method we have used is extremely simple. The electrical

work done in a conductor being measured by [EC dt, where E is the difference of
potential at the ends of the conductor, C the current and ¢ the time, we keep the
electromotive force constant, and measure (c dt directly by a silver voltameter. We

do not therefore require to know the resistance of the wire, and we thus avoid the
difficulty of having to estimate the excess of temperature of the wire over that of
the water in which it is placed. We also gain the advantage of not having to
measure time, and therefore are able to complete the experiment more quickly than
19.7.95.

416 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

we could have safely done if the length of time during which the current passed had
to be measured with great accuracy.

As regards the dimensions of the apparatus, there is not very much choice.
The voltameter limits the current intensity to about one ampére. The calorimeter
must contain at least one litre of water, otherwise the corrections for cooling become
too large ; on the other hand difficulties of stirring appear when the mass of water is
too great ; the calorimeter in our experiments contained about 1500 grams. of water.
In order to measure the rise in temperature of the water with sufficient accuracy,
that rise should not be less than 2°; and it is easily calculated that if the experiment
is to be completed in about ten minutes, the electromotive foree—with the current
and the quantity of water fixed upon—must be about thirty volts. We used Clark
cells as our standard of electromotive force, and a battery of twenty cells was found
sufficient for our purpose. Having fixed on the current and electromotive force, the
resistance of the wire can be determined.

The accuracy which can be obtained altogether depends on the attention given to
small details, and we therefore proceed to describe separately the various parts of the
apparatus used.

The Clark Cells.

As standard of electromotive force we used Clark cells. It was originally intended
to keep one of these cells at a constant temperature of about 25° C. in a thermostat.
This cell (fig. 1), which we shall call the C.T.C. (constant temperature Clark), was
constructed according to a pattern which has proved very useful when it is desirable
to have a cell which can stand without damage a moderate current for a short time.
A small Woutrr’s bottle is taken in which the three openings have stoppers made of
glass ground into the necks. The stopper fitting into the central opening has a
platinum wire fused into it, and the zinc rod is attached to this wire. Of the two
other openings, one carries a bent tube with a mercury trap, and the other a glass
tube which passes to the bottom of the bottle. A platinum wire passes through this
tube and dips into the mercury. The mercury trap is useful in the early history of
the cell, as it is difficult to avoid generation of some gas at first, and the additional
pressure thus produced often damages the joints of the cell. After a time the mercury
may be removed, and the tube sealed off. The cells were set up with the usual
precautions, and have now worked for some years satisfactorily. There is, of course,
the usual difficulty of ascertaining the temperature ; thermometers have been inserted
into some of them, but even then, though they have proved of great utility, they are
not suitable as standards when great accuracy is required, unless placed in an
enclosure of constant temperature.

The comparison of our Clark cells was always made by opposing them and measuring
the difference of their electromotive forces. For this purpose the current from a
Leclanché cell (L, fig. 5, p. 427) was passed through a fixed resistance (R) of 10,000

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 417

Hercury %
trap.”

[Platinum wire
tn glass Lube.

(Saelurated solution
of xinc sulphate

LNW:
————

Mercurous sulphate.

Kine amelgam.

MDCCCXCV,—A.

418 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

ohms and through a resistance box. The difference in the potential at the terminals
of this box was balanced in the usual way by the residual electromotive force of the
two Clark cells. If e,, e,, E be the electromotive forces of the Clarks and the
Leclanché respectively, and 7 the resistance of the box when there is a balance,

APO Ore F

When two Clarks which have approximately the same temperature are compared,
7 would be equal to only a few ohms, and in that case we may neglect the 7 in the
denominator, and in many cases take the electromotive force of the Leclanché equal to
that of the Clark. Care was taken that the Leclanché cell had its normal electro-
motive force, which was measured whenever any change in its value might have
produced an appreciable difference in the experiments.

Large cells can only be used as standards, if they are constructed according to the
principle of Lord RayueicH’s H cell. In the spring of 1891 a cell was set up having
the form of fig. 2. It consists of two glass vessels, one being placed inside the other.
The outer vessel contains the zinc amalgam, the inner vessel the mercury. The vessel
is covered by a wooden lid, through which the electrodes and a thermometer are
passed. The upper part of the outer vessel is paraffined so as to prevent the creeping
of the zinc sulphate over the sides. Very little evaporation takes place, and the lid
is readily removed so that the cell may be refilled when necessary. It was constructed
originally so that the liquid could be stirred, but it was found better not to disturb
the cell. This cell has answered all requirements perfectly, and will be referred to as
the “standard.” The cell, which is not readily moved owing to its weight, stands in
a corner of a small cupboard, and was compared at intervals with the C.T.C. between
November, 1891, and June, 1892. The results are given in Table I. The thermo-
stat, which was not adapted for temperatures as low as 25° C., had to be readjusted
occasionally, hence the small variation in temperature shown in the second column.
The temperature of the standard at different times varied between 11°:2 C. and
18°°3 C., and the experiments afford a good test as to the limits within which a

temperature correction could be safely applied.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 419

TasLe I.—Comparison of Standard Clark Cell with C.T.C. Cell.

1 | 2 8}. 4. 5
Gen = {pais lar
Observe 1
Tere | eee berecune pete difference Calculated
thermostat. standard. | pees LO difference.
1891. e c
Nov. 26 25:26 13:9 — 68 -- 67
ye 25:2 127 — 78 —7
Dec. 11 25:3 13:8 — 68 — 68
eS) 25°4 11:9 — 81 — 82
1892.
Feb. 2 25-08 14-1 | — 63 — 65
SoG | 25-4 12°6 — 76 — 76
xy le 25-4 14:0 — 66 — 66
| = 25°45 14-4 — 65 — 63
March 1 | 25°7 13:2 — 73 — 72
eS 25°52 11-4 =) | =186h |
hy iD 25°65 11:2 — 8&7 — 87
April 2 25°75 13:9 — 69 — 67
ae Vo) 25:7 15-9 — i} — 52
May 9 25°4 16:8 — 46 | — 45
+ LO z 25°8 14-9 = 5S | — 59
., 24 25°32 | 148 — 60 — 60
Jane l 25°46 | 18:3 — 34 — 384
Mean value. . oe 13:99 —663 |

A small correction to the observed numbers is necessary, owing to the small varia-
tions in temperature of the C.T.C. cell. The corrected values of 7 are given in the
fourth column. As the C.1T.C. cell was not quite saturated with zinc sulphate when
placed in the thermostat, the temperature coefficient 0004 was used to reduce its
value to 25°. The corrections are so small that an accurate knowledge of that coef-
ficient is not required. The mean temperature of the standard cell in all these
experiments was 13°99, the mean value of 7 was 66°3. From these data we may
calculate what the value of 7 should have been in each experiment, on the assumption
that the temperature coefficient of the standard was -00081.* The values of 7, thus
deduced, are given in the fifth column. With the exception of the experiment on
May 20, the agreement is quite satisfactory ; and we are justified in concluding that
the changes in the electromotive force of our standard cell may be correctly deduced

* The temperature coefficient determined by Guazeproox and Skinner (‘ Phil. Trans.,’ vol. 183, 1892, A )
is ‘00076 between 0° and 15°—that is, for an average temperature of 7°°5. The temperature coefficient
according to Kaute (‘ Zeitschrift fiir Instramentenkunde,’ August, 1893) is —:000814-—-000007 (t—15),

giving an identical value for t=7°'5.
3H 2

420 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

from the readings of the thermometer placed in it. Recent results of KAHLE agree
with our conclusions, and show that, in the H form of cell, the lag in the change of
the electromotive force with change of temperature is avoided, owing to the fact that
the liquid at both electrodes, being in contact with crystals of zine sulphate, is always
in a state of concentration. We have, after the conclusion of our experiments, set up
a, few cells according to the instructions given in the Third Memorandum of the
Board of Trade. When proper precautions are taken to ensure equality of tempera-
ture, these cells agree within about one part in ten thousand with each other and
our standard cell. Taking account of the determination by GLAzEBROOK and
Skinner of the electromotive force of a Clark cell—1°4342 at 15° C.—and of the
slightly lower value obtained by Kantus, we have adepted 1°4340 as the value of our
standard cell in terms of the international volt. As temperature coefficient, we have
adopted that given by Kau rn (see footnote on preceding page).

Fig. 3.

5

Cupboard Clark Cells.

Standard
ed I a4 7 H a4 YI x IG
Cell.
/ te) 5 6 7 8 9 10 MW fe i

f 15 1 %I7 18 19 20
( To 5 Ta 3’ a 155
Galvanometez
Circuit. ee ,
o Va 2 4 6 8 /0 fe’ 4 16 18 20

Arrangement for Comparison of Clark Cells.

The electromotive force at the ends of the heating coil in our experiments had to
be kept balanced against twenty Clark cells. These cells form part of a battery of
one hundred cells constructed in the year 1890, about eighty of which are still in
good condition. <A set of twenty is mounted in two rows of ten each. The cells are
small, but as we had no means of keeping their temperature constant, their combined
electromotive force had, whenever required, to be determined in terms of the
standard cell. This could be quickly done as follows :—Ten cells of the form shown
in fig. 1 were placed side by side in the same cupboard that contained the standard
cell (fig. 3 and cc., fig. 5). The terminals of these cells—which we shall call the
“Cupboard Clarks ”—were permanently connected to mercury cups numbered 1, 2,
&e. (fig. 3). A board of wood was placed in front of the Clarks and contained a
series of cups 1’, 3’, 5’, &c., permanently connected by copper strips, and a second
series 2’, 4’, 6’, similarly connected. The cups of the two series were placed
respectively opposite the positive and negative poles of the Cupboard Clark cells and

DETERMINATION OF THE SPECIFIC HEAT OF WATER. A421

could be connected to them by means of copper bridges A and B. The standard
cell being inserted and the two bridges being placed as shown in the figure, the
Cell II. is opposed to the standard and the difference of their electromotive force is
measured. Moving the bridges along from one set of cups to the next, the ten
Cupboard Clarks may be rapidly interchanged.

The mounting of the cells also allows of their being rapidly placed in series by
means of copper strips. The figure shows the Cells III., IV., V. thus connected.
The galvanometer used in these comparisons (G, fig. 5) was one of Lord Kertyin’s
High Resistance Astatic Galvanometers. Its resistance was 5600 ohms. It
was placed on paraffin blocks for better insulation, During use its sensitiveness was
such that one scale division corresponded to 7°3 X 107° volt. A carbon resistance
(P, fig. 5) could be thrown into series with the galvanometer when it was necessary
to diminish its sensitiveness. A commutator (K, tig. 5) served to change rapidly the
circuit in which the galvanometer was inserted. This commutator was made of a
paraffin block containing seven mercury cups, but two sets of two were permanently
connected as shown in the figure. Three copper bridges served to connect tem-
porarily the terminals s to g, g to 7 or k, s’ to p or q; when s was connected to g
the Standard Clark was opposed to one of the ten Cupboard Clarks. When the ten
Cupboard Clarks were to be opposed to one half of the battery of twenty cells,
g—Jj and s’—p were connected ; for the other half g—k and s’—q were joined. In
the equivalent experiments when the battery had to be opposed to the electro-
motive force at the end of the heated coil, the three temporary bridges were removed.

The operation of standardising the electromotive force of our battery took about
ten minutes and was carried out as follows :—

1. Reading of the thermometer placed in the Standard Clark, ¢,’.

2. Comparison of the ten Cupboard Clarks separately with the Standard. The
comparison of Cell I. with the Standard gives us a relation of electromotive forces

which may be written
I. — Standard = a,

and the addition of all such relations gives us for the ten cells
(I. + 1. + 111..4+...+ X.) —10 Standards = 4, +0,+...=8,.
3. Comparison once more of the Cell I. with the Standard gives
I. — Standard = a,,

There may be a small difference between @, and a, owing to temperature changes.

4, Reading of the thermometers placed in the Standard, ¢,".

5. Comparison of Sets (1) and (2) of the battery of 20 cells with the 10 Cupboard
Slarks in series, giving by addition the relation

Seui(byee Sct (2) 125 (Ie-eelly Sine tes) FX.) on,

422 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

6. Third comparison of the Cupboard Clark I. with the Standard, the difference
being denoted by as.

7. Reading of the thermometer of the Standard Clark, ¢,*.

From the above measurements we obtain the electromotive forces of our battery in
terms of the Standard, thus :—

Set (1) + Set (2) = 20 Standards + 2 (S, + T,).

After the completion of each experiment for the equivalent, the comparisons are
carried out in the reverse order, and if 8, and T, denote the quantities corresponding
to §,, T, we may take the electromotive force of the battery during the experiment
to be the arithmetical mean of that determined at the beginning and end. The
relation, written as above, would be

Set (1) + Set (2) = 20 Standards + (8, + 8, + T, + T,).

A small correction is necessary owing to the fact that the temperature of the
Cupboard Clarks may not have been the same during their comparison with the
battery as it was while they were being compared with the Standard. We may,
without sensible error, assume that all Cupboard Clarks varied equally, and that,
therefore, the alteration due to temperature changes, for each cell measured in
electromotive force, is expressed by the difference of 3 (a, + a3) and 3 (a, + a).
Hence we correct for the change of the ten cells by adding to 8, the quantity
5 (a;—a,). A similar correction applies to the final comparison, so that the complete
relation of electromotive force is given by

Set (1) + Set (2) = 20 Standards + (8S, + 8, + T, + T,) + 5 (a, — a, + a, — ag).

The temperature of the Standard to which the equation applies is the mean
between 4 (¢,’ + ¢,') and 3(t,°+ ¢,°). The temperatures ¢,, ¢, and ¢,, ¢, were practi-
cally identical in every case, we may take without error $(¢,;-+1,) to be the
temperature of the Standard during the comparisons.

The Silver Voltameter.

The platinum bowl which served as voltameter had a diameter of 9 centims. and a
greatest depth of 4 centims. A 20 per cent. solution of the nitrate of silver was used,
the salt being supplied by Messrs. Jonnson, Marruey, and Co., as thrice recrys-
tallized. The silver plate serving as anode was supplied by the same firm. It was
7 centims. in diameter and 2 millims. thick. The dish rested during the experiments
on tinfoil wrapped round a ving of copper, which rested on a tripod, also covered with
tinfoil (V, fig. 5). The tripod stood on paraftin blocks. The silver plate, protected

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 423

by filter-paper, was suspended from three platinum wires attached to a copper
terminal. The insulation of the voltameter was amply sufficient, and the contacts
were all sufficiently good to allow a perfectly steady current to pass. In order
always to bring back the dish to the same condition, the silver deposit of the previous
experiment was always dissolved away before a new deposit was made. The dish
was washed successively with (1) concentrated nitric acid, (2) a solution of potash,
(3) tap water, (4) distilled water. After drying in air-bath the empty dish was
weighed two or three times with the usual precautions. The silver deposit was treated
in the manner described by Lord RayuercH. Immediately after an experiment the
silver solution was removed from the dish, the deposit washed three times, and left
overnight with distilled water. After washing again next morning, the deposit was
dried in an air-bath, first at 100° C., subsequently the temperature of the bath was
raised for 10 or 15 minutes to 160°C. The dish was then again weighed two or
three times. The distilled water used in washing left no residue on evaporation
from platinum foil, nor gave any visible turbidity with silver nitrate solution. The
voltameter was efficiently protected from dust, which might otherwise have got
entangled in the silver. The deposit always firmly adhered to the dish in charac-
teristic radial lines, and no difficulty was ever experienced in the washing.

Correction of the Weight to Vacuo.

In correcting the weighings to vacuo we must distinguish between the bowl and
the silver. As regards the bowl, it is only the difference in the density of the air
when the two weighings are taken which will affect the result. We found it, there-
fore, most convenient to reduce the weighings to the normal state of the atmosphere
instead of to vacuo. The correction k to vacuo may be written k = wpa, « being
a constant and p = py /yto/hot,, where

Po = density of air at 76 centims. and 15° C.,
h, = height of barometer at time of weighing,
t, = absolute temperature of balance case,

h, = 76 centims.,

ty = 288°.

Representing the changes in barometric pressure and temperature by dh and dt
respectively, we may express the difference in the buoyancy correction from that
which would hold if the temperature was 15° C. and barometric height 76 centims. by

dh = 0 4 dh — hy dt}.
ligt

A424 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

Substituting the values which apply to our platinum bowl weighed against brass
weights, viz.,

the correction becomes

(i) for difference in temperature + °020 (¢ — 15) millim.
(ii) 3 ; pressure + °074(76—/h,) _,,

As regards the silver deposit, the correction amounts to 024 millim. for each gram.
Neither the accuracy of our weighings nor our knowledge of the equivalent of silver
render it necessary to apply so small a correction, which would alter our final result
by only one part in 40,000.

The balance used was one of CERTLING’s long beam balances, and the sensibility was
adjusted so that with a load equal to that of the platinum bowl! 1 millim. corresponded
to one scale division. The bowl was always counterbalanced by the same weights
before and after the deposit, so that any error in these weights would not affect the
result.

To determine the correction, if any, to the weights used in balancing the silver
deposit, a brass weight of nominal value of 1 gram. was standardised by the Board of
Trade, and found to weigh 1:000032 gram. The silver deposit weighing always just
above ‘5 gram., it was sufficient to determine the error of the $-gram. platinum mass
which was used in all the experiments. Four experiments gave for the corrected
mass : 499966, 500020, °500032, -499998, or, as a mean, 500004 gram. It was
therefore sufficient to assume the *5-gram. weight to be correct.

The Heating Coil.

The coil in which the electric energy was converted into heat was made of a length
of 760 centims. of platinoid wire, having a diameter of ‘0345 centims. (29 B.W.G.)
and a resistance of approximately 31 ohms. The coil used during the first few
experiments was wound on a frame made of thin strips of ivory. On determining
the specific heat of that substance we met, however, with a serious difficulty, as it
was found to absorb a considerable quantity of water, which it gave up again on
heating. Thus a fresh strip of ivory was found to lose 10 per cent. of its weight
after heating in an air-bath for two hours. Even coating with shellac will not over-
come the gradual absorption of water. Having had to discard ivory, we fixed on
porcelain, and were supplied through the kindness of the Worcester Manufactory
with strips of that material. The mounting of the frame and wire is seen in fig. 4.

Four strips of porcelain, 14 centims. long and 1 centim. broad, with 30 notches
to keep the wire in position, are mounted by fixing their ends in sockets made of brass
foil, These sockets were connected by stout brass wire. The ends of the platinoid

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 425

wire were fixed to stout copper wire about 5 centims. long wedged into the bottom of
cylindrical pieces of ebonite. The ebonite was held in position by brass supports
soldered to the frame. The upper ends of the copper terminals projected into the
bottom of cups drilled from above in the ebonite; these holes, which were 9 millims.
wide and 15 millims. deep, were filled with mercury, and served to connect the coil

Fig. 4.

ZL DE
Ze
Z\

FS
Wai

S

ey Hey

EDIE

FOV

<— a
\

ELLE
eee
KAO
COI.
Giniinns =

BE EE AES

with the outer circuit. ‘The coil was insulated by a covering of shellac. ‘To obtain a

thin and uniform layer, the frame was immersed in a weak alcoholic solution of the

substance, and afterwards heated for half-an-hour in an air-bath at a temperature of

130° C. This process of immersion and heating was repeated until the insulation

resistance was higher than that required by the conditions of the experiment, and we
MDCCCXCV.— A. 31

426 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

were quite satisfied with the permanence of the covering obtained. The insulation

was tested from time to time and the coil re-covered when necessary. When the coil -

immersed in water was connected to one terminal of the battery, the second terminal
being a bare wire, the resistance was generally found to be over 40,000 ohms, the
electromotive force being 30 volts. That an insulation resistance equal to that
amount is amply sufficient will be seen if it is remembered that leakage can only
cause error in so far as the water is decomposed. If the whole of the current were to:
pass through the water instead of through the coil, about 1 volt would be lost, so that
an error of 3 per cent. only would result. Considering the small diameter of the wire
and the high resistance of distilled water, it will appear that, even if our wire had been
completely uncovered, the error introduced would not have been great, and even an
insulation resistance of 1000 ohms would have made it inappreciable.

The Stirring.

The stirrer is shown in figs. 4 and 5. It consisted of a piece of brass foil cut to a
half-moon shape. The upper surface was soldered to fine brass tubing, 17 centims.
long. Two pieces of glass tubing fixed to the frame of the coil passed through
circular holes cut into the stirrer and served as guides. The stirrer was moved up
and down by a wheel and crank W (fig. 5) driven by an electromotor. A piece of
brass tubing, of the same kind as that attached to the stirrer, was fixed to the
crank, and the motion was transmitted by a flexible joint made of several layers of
thin unvulcanised india-rubber, firmly tied to each of the two parts of the brass
tubing. This joint, devised by Mr. Hapiey, worked very satisfactorily, and allowed
sufficient lateral play to facilitate the adjustment of the calorimeter and coil below
the driving wheel of the stirring apparatus.

Some Questions concerning Thermometry.

The method of using mercury thermometers in accurate work has undergone
considerable change in the last twenty years. In measuring a temperature, the
interval between 0° and 100° used to be determined by plunging the thermometer
first into a mixture of ice and water, and then into boiling water. If the two readings
are Ty, Tyo), the temperature ¢ corresponding. to an intermediate reading, T; would be

t= 100 (I. — T/L ee

Owing to certain properties of the glass envelope, analogous in their effects to
elastic fatigue, a thermometer when exposed to a constant temperature will not,
however, take up its final indication for a time which may be considerable, and this
set of the glass affects especially the zero point, the apparent zero as at, first observed

J. Sa ale be

427

SPECIFIC HEAT OF WATER.

DETERMINATION OF THE

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3) TY

428 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

being dependent on the temperature to which the thermometer was previously
exposed. It is found, however, that consistent results can be obtained by referring
the reading of a thermometer not to a fixed zero, but to the position of the mercury
thread, observed when the thermometer is plunged into ice directly after being
exposed to the temperature to be measured. Calling T,/ the zero, as thus determined,
after exposure to the temperature ¢, that temperature measured in the mercury
thermometer is now defined as

ESC es

The two definitions of temperature indicated by (1) and (2) are identical if the
so-called depression of the zero T,° — T;’ is proportional to the temperature ¢, as with
thermometers made of the Jena, or French standard glass. Writing in this case

Ty? — Ty! == @ (T; — Ty’)
or
1

T, — Ti =~ (1 — 1,9),

and similarly
. i
Tyo — T= iene (Tyo ne T.),

we obtain by substitution in (2)

t = 100 (T, aE Ty) /(T roo — T,%),

which is identical with (1), if the zero in that equation is meant to signify the
position which the thermometer would take up if plunged into ice for a considerable
time.

If the observations are made with English glass of recent manufacture, the
identity of equations (1) and (2) does not hold, as the depressions of the zero are
nearly proportional to the squares of the temperatures. It then becomes of import-
ance to define clearly how a temperature is taken. Thus Wrese finds that ther-
mometers made of English glass read /ower than the air thermometer by as much as
0°:047 at 40°, while Rowxanp states that a// thermometers examined by him,
including those of English manufacture, read higher than the air thermometer. The
two statements are not contradictory; the discrepancy is explained by the fact that
Wiese refers all temperatures to the zero observed directly after each reading, while
at the time Rowianp’s work was done, this practice, which alone converts the
thermometer into an instrument fit for scientific research, and is now uniformly
adopted, had not yet come into use.

It is an essential point in thermometric measurements that the work done by
different observers should be comparable, and some uniform scale should be adopted.

430 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

may introduce errors into a calorimetric measurement. With French or German
standard glass the depression of the zero, corresponding to a certain interval, is less
than the thousandth part of that interval. If the thermometer has been, before the
experiment, sufficiently long in the calorimeter to take up its permanent position,
and if the rise of temperature is then made to take place, the position of the zero
in the final period must lie between its original value and that corresponding to
permanent immersion in the final temperature. The error made by either assumption
cannot exceed one part in a thousand, and we may form a sufficiently good estimate
as to the actual zero value to reduce considerably the limits of possible mistake.
But the slow set of the glass envelope which shows itself in the shifting zero, may
affect our results in another way. The correction due to loss of heat by radiation and
conduction is generally determined by observing the temperature of the calorimeter
at the beginning and conclusion of the experiment. But even if there is no loss in
the final stage, the thermometer will apparently fall slowly, owing to the imperfect
behaviour of the glass envelope. Let the rate of fall be 8; if the calorimetric
observations are conducted in the usual way we should over-estimate that loss
by the quantity 8. If the time during which the calorimeter has been rising in
temperature is 7, we may correct for the error made in this way by adding 4r to the
final temperature, or deducting $¢ from the zero. This is equivalent to saying that we
may correct for the set of the glass envelope in a calorimetric measurement by taking
for the zero during the final stage the zero shown by the thermometer after immersion
in the final temperature during a period equal to half the length of time it has taken
the thermometer to rise from its initial to its final value. In our experiments this
would be between four and five minutes.

To obtain some clearer information as to time taken by our thermometers to arrive
at this permanent zero a series of experiments were carried out. We had a thermo-
meter (Baudin, 12773) which in all respects was as nearly as possible like the one
used in our calorimeter experiments (12772). The former was placed in water of
about 22°, and kept there for over four hours, the latter was kept during the same
time at a temperature of from 10° to 12°, and then suddenly raised to the higher
temperature and placed side by side with No. 12773. The two thermometers were
read alternately every quarter of a minute for about a quarter of an hour, so as to
obtain a good comparison. After the lapse of another hour a similar set of readings
were taken at the same temperature. As the mercury threads stand between the
same divisions in the two cases, a systematic difference in the reading cannot be due
to any calibration errors. The following Table III. gives. the results of the com-
parisons. The times are given in minutes reckoned from the moment that 12772
was placed beside 12773. The column headed A denotes the difference between the
indications of the two thermometers, 12772 always reading higher.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 429

For the present we cannot do better than use thermometers made either of standard
Jena or French glass, as their behaviours have been thoroughly studied. By making
use of the published investigation, we may. then refer our measurements. to the
thermometers of Berlin or Sévres.

In calorimetric researches it is often irmaselila or inadvisable to dgaunine the
zero after each measurement. The behaviour of standard glass is so regular that,
after the thermometer has been in air for a few years, we may predict with consider-
able accuracy the position of the zero from a knowledge of the temperature to which
the instrument has been exposed. The following Table will illustrate this point.

TABLE I],
1. Dee war oS ee 5. @
-| | E | |
Observed zero | | :
Date ore Duet | Ae reduced to Caleulated Difference.
‘ | : observed. 760 millims. Zero. Was
1893. ° : oats | ssi
Dee. 19 | 12°47 | 0167 0194. | 0198 |; +:0001
sp ee SLPS: 0194. | 0183 | 0193 - —-0010
oy 2 | 13°28 | 0162, || ‘0185 | _ 0186 —-0001
ny 14-14 0150 ‘0187 | ‘0178 +-:0009
ry ES | -0080 | 0104 - | 0102 _ - +:0002
pe. 1} 22°46 “0086 | ‘0123 ‘0101 | +:0022
ny lS BPRS | ~ -0085 | 0115 | “0100 +0015

The second column gives the temperature to which our standard thermometer had
been exposed previous to the zero determination; the third column gives the
observed zero, measured by an eye-piece micrometer, the fourth place of decimals
having no significance; the fourth column gives the observed zero corrected for
change due to the varying pressure on the bulb. According to (GUILLAUME, the zero
of a thermometer after exposure to a temperature t, should be capable of expression
in the form z — 000092 (t° — 15°) where z is the zero corresponding to the tempera-
ture of 15°. The fifth column gives the zero reading calculated according to this
formula, taking for z the value 0°0170; the sixth column shows the difference
between the calculated and the observed reduced values.

The agreement is satisfactory, especially for the lower temperatures. The experi-
ment on December 12 was made after exposure of the thermometer to the tempe-
rature of 22° during four hours, and the zero is seen to be exactly that calculated
from the formula. In the two last observations the thermometer had only been kept
in the water for about two and a half hours; and we conclude from the observations
that the time was not quite sufficient to lower the zero through its full amount.

A little consideration is necessary to decide how far the uncertainty of the zero

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 431

TABLE III.
Date. November 2. | November 6. | November 8. | November 13. Mean.
| Temperature previous . , : : ;
to comparison. . . 10-4 13:2 1B) > 2 10:0 114
Temperature during | |
comparison. . . . 21:2 21:2 21:3 21:2 | 21:2

me |} 5 m EB m 5 m. | e m 5

2:5 | 0:0128 | 23} 0:0108 | 2:0 | 0:0137 | 1:5 | 0-0097 | 2-1 | 0:0118
65 | 0113 | 55 | :0118 |} 65] -0132| 70) -0116] 64] -0120
78:0 | -0104 | 69:0 | -0092 | 89:0 | :0125 | 65:0 | -0098 | 75:2 | -0105

It appears from the table that the thermometer suddenly plunged into water at a
temperature of about 10° higher than that to which it was previously exposed, will,
during the first hour show a gradual lowering of its indications, corresponding to the
lowering of its zero point, amounting to about 0°-0012. Even after the first hour
the change will not be complete, as is seen from Table III. ; the experiments made on
Dec. 13 and 19 showing that after two hours and a half, the zero is still too high by
about 00018. The first indications of the thermometer must have been too low
therefore by about 0:004. As the total change of zero corresponding to the rise from
11°-4 to 21°-2 is 0°009, it follows that about half the depression takes place in the
first few minutes,

In view of these experiments we conclude that the zero of a thermometer of
French glass used in calorimetric determinations may after the lapse of a few minutes
be assumed to have a position half-way between those corresponding to the lower and
the higher temperatures. The extreme uncertainty of this range is less than one
patt in two thousand, but it is practically certain that an error of more than one
part in five thousand cannot be introduced by the assumption made.

The Thermometers.

We used as primary standard a thermometer made by Tonnexor (No. 4929). A
complete calibration and examination of this instrument was made for us by the
“ Bureau International des Poids et Mesures” at Paris. The thermometer is divided
into tenths of a degree, the length of each degree being 0°58 centim. The divisions
are beautifully sharp and can be read both in front and behind the mercury thread.
The stem is cylindrical and has a diameter of -45 centim. The bulb has a length of
4°8 centims. and a diameter very nearly equal to that of the stem.

432 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

A thermometer plunged into a calorimeter can only be read with convenience when
the thread is a few inches above the level of the water; and if the length of a degree
is short, the correction for the emergent stem becomes serious. It is important that
this correction should be small, as it cannot be ascertained with great accuracy. ©
Hence it is better for calorimetric measurements to use a thermometer with an open
seale so that nearly the whole thread may be immersed. The open scale has the
further advantage of being more easily read. It is generally supposed that the
accuracy of thermometer measurements is increased by using a thermometer in which
the length of a degree is made very large, and the manufacture of such thermometers
has been pushed to ridiculous extremes. Our experience confirms the conclusion drawn
by GuitLAumE (“ Thermométrie,” p. 180), that the uncertainties in the indications
of a thermometer measured in degrees increase with an increase in the length of the
degree, and that, therefore, apart from the convenience of reading, the advantage
altogether is in favour of a short degree. When the whole thermometer can be
plunged in water and the temperature of the water is kept sufficiently steady to
allow a careful reading, a thermometer such as that of TonnELor, divided into tenths
of a degree, the divisions being half a millimetre apart, allows as accurate a deter-
mination of temperature as any mercury thermometer can give us at present.

It was the uncertainty of the correction of the emergent stem which finally
decided us to use in our calorimeter a thermometer with an open scale ; but it was
essential that it should be made of the same glass as the standard. We chose one
by Baupin (No. 12772), having a length of degree of 3°1 centims. approximately,
and being divided into fiftieths. It contained according to the statement of the
maker 33°0 grams. of mercury. It could be read at the freezing-point and between
12° and 23°. The stem was shortened by an expansion in the glass above the zero
point insuch a way that the distance from the division which marked 12° to the
centre of the main bulb was only 8°1 centims. The radius of the bore can be
calculated from the weight of mercury, and is thus found to be 0°0061 centim.
From experiments made under varying pressures, the thickness of the glass bulb can
be roughly estimated as ‘066 centim. In order to allow us to use the thermometer
for our purpose it was necessary (1) to calibrate the thermometer, (2) to compare it
with the standard, (3) to determine carefully the pressure coetticient, as the comparison
had to be conducted with the thermometer in a horizontal position.

The Calibration.

The calibration was conducted according to the method of THrEssEN, as described by
GuimtaumE. Threads were broken off, having a length of very nearly one, two, &c., up
to ten degrees, and these threads were pushed forward from degree to degree. Their
lengths were measured on the thermometer in the usual way, an estimate of the over-
lapping of the mercury to one-hundredth part of a division being made by the eye,

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 433

looking through a telescope of small magnifying power, but without a micrometer.
The observations with every thread were repeated more than once, often by different
observers. The final result is given in Table IV., in which the second column gives
the calibration correction in thousandth parts of one division. The reductions are
easily made by the method of least squares in the manner indicated by THIESSEN.
The probable error of a single observation®* was calculated to be ‘020 division, and the
probable error in the final correction at each point is ‘008 division, or, as the thermo-
meter was divided into fiftieths, the probable error in the calibration correction is
0°00016.

TABLE IV.
A = F Calibration correction Calibration correction |
a aee ebcetree deduced from observa- deduced from observa- |
Ps totals atch beeen ere er

sion = 0°-00002. ee ‘| measurements. 1894. |
12 0 —— —
13 77 88 75
14 184 186 172

15 22 30 15 |
16 272 283 246
17 253 265 257
18 45 41 38
19 83 82 122
20 291 286 314
21 75 86 50
22 80 103 88

23 0 — — |

We conclude from this that it is extremely unlikely that our calibration is wrong
by 0°:0008 at any point. In order to see how far the eye without micrometer may be
trusted to carry out a calibration by means of one thread (Gay-Lussac’s method), we
give in the third column of Table IV. the calibration corrections deduced from the
observations of the thread of one degree. At the conclusion of our experiments it
seemed more satisfactory to make certain that no appreciable change had taken place
in the thermometer. The calibrations were, therefore, repeated, but this time only
with one thread, according to Gay-Lussac’s method, and the readings were taken
with a micrometer. The results are given in the fourth column. The greatest
difference between the corrections found in 1892 and 1894 amounts to about ‘04
division, or 0°:0008; the average difference amounts to less than half that value.

The observations made at the conclusion of our experiments were only intended as
a check, and we feel justified in concluding that no change has taken place in the

* By a single observation here is meant the measurement of the mercury thread in one of its positions.
Several measurements in the same position are taken, and their mean value counts in the reduction as
one observation.

MDCCCXCV.—A. omer

434 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

thermometer, and that our calibration in 1892 was satisfactory. The numbers
obtained from the single thread by Gay-Lussac’s method are practically identical
with those obtained by the more complete method.

The temperatures for which the corrections have been obtained being too far apart
to allow us to interpolate safely for the intermediate points, a thread of 2°°5 was
broken off, and by means of it the corrections for every half-degree could be deduced.
The divisions of the thermometer were not equidistant, but the maker had attempted
to correct for inequality of bore. This method, much in use at one time, causes a
good deal of unnecessary labour, as already pointed out by GuiLLAUME, whenever the
instrument is to be used for accurate work; its subsequent calibration cannot be
dispensed with, and the lengths of the divisions must be measured one by one, as
there is no clue where a sudden change in the length may occur. We give in an
appendix the method adopted to deduce the final corrections for each division of the
thermometer.

Pressure Corrections.

The reservoir of a thermometer is generally subjected to an internal pressure due
to the column of mercury forming the thread, and this pressure causes quite an
appreciable increase in volume. If the thermometer is always used in the vertical
position, no error is caused in assuming uniformity of bore; the effect of internal
pressure will only be a shortening of the distance between the fundamental points.
Even in this case, however, care must be taken that the range for which the
thermometer is used does not include bulbs like those which are placed above the
freezing point in calorimetric thermometers.

A comparison between two thermometers is more easily conducted in a horizontal
than in a vertical position ; and in that case, of course, the effect of pressure must be
taken account of.

The effects of external pressure are easily measured by suspending the thermometer
in a vessel in which the pressure can be quickly changed from the atmospheric
pressure to one of a few centimetres only.

We have used a method which is a slight modification of that given in GUILLAUME’S
book. It is unnecessary to enter into long details, as the method will be described in
another communication. Three experiments were made on March 21, 1892. The
change of pressure was a sudden diminution from the atmospheric pressure to one of
27 centims. The observations, when reduced, give

0°:002088
0°:002085
0°-002080

Mean . . 0°:002084

as the effect due to 1 centim. of mercury at 0° C. at the latitude of Manchester.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 435

The experiments were repeated two years later, on February 22, 1894, when two

different determinations gave
0°002096

0:002072
Mean . . 0:002084

It is seen that the changes in atmospheric pressure, which may amount to several
centimetres, may produce a change in the indications of a delicate thermometer which
cannot be neglected.

From the effect of external pressure we may easily deduce that of internal
pressure. If Pa is the diminution of volume due to an increase of pressure P applied
externally, and P the increase in volume of the same pressure is applied internally,
then the diminution in volume due to a simultaneous increase of pressure P inside
and outside is P(«# — 8), and this must also be equal to P/x, where « is the
compressibility of the walls of the thermometer bulb. Hence

a — B= 1/k.*

The reading apparently is diminished when the thermometer is raised from the
horizontal to the vertical position, not only because the glass bulb expands, but also
because the mercury is compressed. If x«’ is the resistance to compression of mercury,
a pressure P will have the same effect as an increase of volume P/«’ of the reservoir.
Hence, if 8 now denotes the complete effect of unit increase of pressure applied
internally on the reading in degrees of the thermometer, we obtain

1 1
Sait shee ay aa
K K
1 ae. . oF) 076 c :
—; —— is the relative compressibility of mercury and glass, which is known.
K K

AMAGAT, whose measurements doubtless are the most accurate at our disposal, finds
for glass of medium hardness the relative compressibility to be 1°707 x 107°, and
for lead glass (cristal) 1°512 x 10~® (‘Annales de Chimie et de Physique,’ vol. 22,
1891). For the French thermometer glass the coefficient will not differ much from
the larger of these values,

The numbers given refer to the atmosphere as unit pressure. It is more convenient

* This relation is quite general and independent of the shape of the bulb, which need not be of the
same thickness throughout, provided it is of homogeneous material. The relation in Gutttaumn’s book
is proved in an elaborate manner for spheres and cylinders, and is then said to hold ‘no doubt only
approximately ” for thermometer bulbs.

[Since the above was written, Mr. Curun has published a paper (‘ Phil. Mag.,’ October, 1894), in
which a proof of the relation between the internal and external pressure coefficients practically identical
with the above has been given.—June, 1895. |

a ix 8

436 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

for our purpose to take as unit pressure that due to a column of mercury 1 centim.
long, and for unit change of volume that corresponding to an increase in temperature
of one degree. The relative coefficient of thermal expansion of glass and mercury
between 10° and 20° C. being 1°598 x 1074, the apparent compressibility of
mercury reduced to the new units will be found by dividing the above number. by
76 X 15598 x 10~*. The relation between B and « then becomes

B=a-+0°'000141.

The number used by the Bureau International des Poids et Mesures, founded on
some older determinations, is 0°000154, and the uncertainty of this term might be
raised as an objection to the use of a thermometer in the horizontal position. But
the whole term being of little importance, it does not matter much which of the
different possible values we adopt. Thus the difference between GUILLAUME’S
internal pressure correction and ours would produce a difference in the measured
temperature range of our Baudin thermometer of one part in 25,000, and in the
Tonnelot standard it would be equal to only the sixth part of that value. For the
sake of uniformity we have continued to use GUILLAUME’S number, and therefore
take for the Baudin 12,772,

a = 0°002084
B = 0:002238,

where « and 6 measure in degrees the changes in the apparent temperature due to
a change of pressure of 1 centim. of mercury applied to the ontside or inside
respectively.

A small correction was necessary to allow for the fact that the mercury in that
part of the stem which is not immersed in the calorimeter is not necessarily at the same
temperature as the water. To ascertain this correction two small thermometers were
used, one placed in the space between the calorimeter and the disc (D, fig. 5) which
covered the water jacket, while the other was placed above this disc about half-way
between it and the upper end of the thread. We found that in the last period when
the calorimeter had risen about 2°, that part of thread below the dise D could be
assumed to be at a temperature 1° above that of the air, while that part of the
thread which was above the disc had not appreciably changed its temperature. The
correction was always small, as the whole rise was only 2° and only a few degrees of
the stem were exposed to the air.

The thermometer was always read by means cf a cathetometer telescope, the
cathetometer stand being very convenient to move the telescope parallel to itself.
The avoidance of parallax is of importance and can be easily secured in this way,
provided the thread is always read when in the middle of the field.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 437

Comparison of Thermometers.

Having found the calibration correction of a thermometer, it remains to determine
its range. The calibration of our calorimetric thermometer was carried out between
the points marked 12° and 23° respectively, and in order to find the interval between
those points according to some fixed scale, it would seem most natural to compare the
thermometer near the extreme points of its range with a standard. This we attempted
to do at first, but found that the results of different comparisons were not as con-
cordant as we could have wished. Two thermometers, however, carefully calibrated,
will show differences when compared with each other amounting to a few thousandths
of a degree, and there seems little doubt that local irregularities, either in the width
of the bore, or in the nature of the surface affecting the capillary constant, render the
readings of a mercury thermometer uncertain to that extent. These irregularities are
more likely to occur near the ends of the scale where the tube had to be blown out
into a bulb or joined to the reservoir. We decided therefore to compare the Baudin
and Tonnelot along the whole scale in order to obtain as accurate a value for the
Baudin as possible.

The comparisons were carried out in a horizontal bath with a slowly rising tempe-
rature. It is unnecessary here to enter into the details of the construction of the
apparatus and method of comparison, as these will be furnished in another communi-
cation. Table V. shows the result. Column II. gives the reading T, of the Baudin
thermometer, corrected for calibration and division errors and reduced to the vertical
position. The third column gives the correction y which has to be applied to the
Baudin thermometer in order to reduce it to the readings of the standard mercury
thermometer made of French glass. The values of y are those obtained by experiment.
Calling t, the reading of the Baudin thermometer, we require to express y as a linear
function of the temperature in the form

VY == a) + biies
Reducing the observations by the method of least squares, we found

a= + 0:0194
b = — 0:00089 + 0:000047.

Calling y’ the value of y calculated with the help of these data, y — y = A will
express the difference between the calculated and observed corrections.to the Baudin
thermometer. The fourth column of the table in which A is entered shows that the
agreement is satisfactory. The residual differences are accounted for by errors of
observation, by remaining errors of calibration of the two thermometers and by irre-
gularities in the capillary phenomena. The probable error of a single comparison is
found to be 9°-00096, that is about one thousandth of a degree, and the probable
error of the interval is about one part in 20,000.

438 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A
TABLE V.
1. ilk, IQUE, | IV.
| |
Comparison. Ty. : of A.
1 | 12-585 +0:0072 +0:0010
| 2 | 12-643 | +0:0068 +0:0014.
| 3 | 12-885 | +0:0073 +0:0006
4 12-923 | +0:0051 | +0-0028
5 13-068 | +0:0068 +0:0010
6 13315 | +0:0099 —0-0014
7 13-393 +0°:0088 —0-0013
8 13 687 +0:0071 +0-0001
9 14-023 | +0:0075 —0-0006
10 14-108 +0:0096 —0:0027
| 11 14-171 | +0:0074. —0-0006
12 14-184 +0:0075 —0:0007
| 13 14590 + 0:0067 —0-0008
14. 15:132 | +0:0076 —0:0017
15 15°194 + 0:0065 —0:0006
16 15°538 +0:0052 +0-0004
17 15-981 +0:0057 —0:0005
18 16:018 +0:0035 +0-0017
| 19 16534 | +0:0037 +0-0010
| 20 17-226 | +0:0062 —0-0021
| 21 17:322 +.0:0037 +.0:0030
99 17-964 | +0:0035 —0-0001
93 17:997 | —0-0005 +0:0039
24 18-032 +0:0026 +0:0008 |
| 25 18°593 +0:0032 —0-:0003 |
26 18-999 +0:0026 —0:0001 ||
27 19°107 | +.0:0023 +0:0001 |
28 19-464. +0:0015 + 00006 |
29 19:997 | +0:0041 —0-0025 |
30 20-011 | +0:0006 +0:0010
31 20-055 | +.0:0021 —0-0005
32 20-545 | + 0:0006 | +0:0005
33 21-065 | -+0.0028 —0:0021
3 21-103 +0:0005 | +0:0001
35 21-485 | +.0:0006 —0:0003
36 21:501 +0:0008 | —0-0005 |
| 37 92-054 +.0:0004. | —0-0006 |
| 38 29-145 —0-0036 +0:0033
| 39 99-451 —0-0010 +.0:0004

40 22-831 | —0-0011 +0:0002

In the comparison of the calorimetric and standard thermometers, the two were
always treated exactly in the same manner, and exposed simultaneously to the same
temperatures ; hence we may assume that their zeros varied equally, and, as the zero
of the standard was assumed that corresponding to the steady state of the thermo-
meter after it has been exposed for a sufficiently long time to the temperature of
comparison, the correction found for the Baudin applies to the ultimate reading of
that thermometer at any temperature. As it has been shown that we must in our
experiments take the zero to be halfway between its initial and final positions, the

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 439

corrections under the condition of our experiments have to be diminished by 0°00046 ;
hence, if ¢ is any interval of temperature on the standard thermometer, and ¢, that on
the Baudin thermometer, we find finally

t = ty (1 — ‘00135).

We have made a few observations which check the correction (:00046) we have
made to eliminate the error due to the fact that, in the actual equivalent experiment,
the zero of our Baudin had not reached its final state. The Baudin was placed in
water at a temperature 10° above that at which it had previously been kept, and was
compared after the lapse of about ten minutes with the standard. The latter instru-
ment had been immersed in the warm water for several hours, and its zero was
determined at the conclusion of the comparison. The corrections thus found on three
different days for the Baudin were — 0°:0059, — 0°:0069, — 0°:0053, or — 0°-0060
in the average, at a mean temperature of 22°°6. ‘Taking the correction at 12° to be
that found above, viz., 0°°0082, we should get an interval correction of — 0°-60142,
holding for the conditions of the experiment closely resembling those of the equivalent
experiments. The difference between this number and the one adopted (—0:00135)
is less than one part in a thousand.

The Calorimeter and Water-equvalents.

The calorimeter consisted of a copper vessel, heavily gilt outside and inside, the
weight of gold deposited being about 1°6 grms. The copper vessel was of the usual
cylindrical form, and had the following dimensions :—-

ileteht? = Tavlos: eas es Pall7-9¥centims:
Diameter owsection: ss eee) L10 4.
itincknesstomwallsW (ies are. 0°0295 centim.
Total weight of calorimeter . 161°3 orms.

The following data will show the agreement between different determinations of
the specific heat of copper :—

TaBLE VI.
Range of tempera- Mean | ipa Wepa ae
Observer. Specific heat. | ture through which | temperature of Be im eS
copper was cooled. | of copper. | ok
fo} (e) ° fe) Ap
Reenautt (Naccari)* 0933 100-17 59 17
| ToMLINSON . . . . 0938 100 — 20 60 20
POGSt aa, Cee te ae meee 0933 100-15 58 | 20
JOULES irae et 0921 40- 8 24. 7
| TOMMINSON 9 > ' 2-2 0926 60 — 20 40 20

* REGNAULT gives a higher value, based apparently on a wrongly-assumed value of the specific heat
of lead. The above value is that which Naccari has recalculated from RErGNAULT’s observations,
correcting for the error.

440 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

The mean of the first set of three observations gives ‘0935 for the specific heat of
copper at 59°, and the mean of the last two :0924 for the specific heat at 32°. The
average temperature at which our observations were made was 19°, and, assuming
the specific heat to be a linear function, we may with sufficient accuracy adopt for its
value -0918. The water-equivalent of the calorimeter, taking account of the small
quantity of gold on it, is thus found to be 14°71. An error of 1 per cent. in this value
would change our result by one part in ten thousand, and we may certainly trust the
assumed specific heat of copper to that degree of accuracy. Our heating coil and
frame were made of brass, porcelain, glass, platinoid, and shellac. After the conclu-
sion of our experiments the whole of the heating frame, coil, and stirrer was broken
up and enclosed in a cage of copper gauze, and its water-equivalent determined, with
the following result :—

TasLe VII.
‘ . Water Mean temperature |
Experiment. - | 1
equivalent. of copper.
|
| : |
|

1 9°62 | 27

2 9°72 29

3 9°68 27

4 9:96 57

5 9°95 58

6 9:98 58

From these figures we calculate the water-equivalent at 19° to be 9°59.

We had originally intended to calculate the water-equivalent of our frame and coil
by adding the equivalents of its parts, and we had for this purpose made some
experiments on the specific heat of porcelain and platinoid. The experiments were not
quite satisfactory, in the first place, because they related to a temperature higher than
the one used in our experiments, and secondly because when they were made we had
not quite realised what serious errors may be introduced, even with the best thermo-
meters when the temperature during the last period is falling. Our values, for this
reason, were no doubt too high, Although we trust entirely to the water-equivalent
9°59, which was directly determined with all precautions, and with a thermometer
rising during the whole course of the experiments, we nevertheless give as a check
the equivalents calculated from that of its parts.

ia
mt

‘ee

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 441

TasiE VIII.
| |
| Material. | Weight. Specific heat. | Water-equivalent.
IZOrCe lara ye | 23°32 196 4°59
Plabinoi dey Fis, ees ee 5°76 102 D9
Glasses Se ge oo eet or 5°58 “190 1-06
prass ge VAs CATS 42°55 090 3°82
Copper terminals. . . 2°04 | 092 ‘19
| otal ae 10-25

This refers to a temperature of about 60°, and agrees sufficiently well with the
equivalent 9°96 which was directly determined, if we remember that the specific
heats of porcelain and platinoid are, for the reasons given, too high, and that the
values for the specific heat of brass and glass were assumed to be those usually
given.

We must add 0°34 to the water-equivalent belonging to a silver disc covered with
gold foil, which was kept floating on the surface of the water in order to prevent
evaporation as far as possible,

As regards the thermometer, we calculated the specific heat from the data inscribed
on it by the maker, according to which the weights were as follows :—

IWerehtioftmercugvie.)0) (lal et nO OReTAIMNSs
Weichtiofjclassi bulbs: 1-oss5isnie 62. ol Sorerams:
Wierchiioteclasspnistemun sien aey as te ee 2OnOe at

Taking the specific heat of mercury to be 0°033, and that of glass 0°19, we calculate
that the water-equivalent up to the point marked 12° was 2°05. An experiment made
to determine directly the equivalent of the thermometer, showed that we could trust
the figures given by the maker, the value found being identical with that calculated
from his data. We may add 2:05 permanently to the water-equivalents, and in the
separate experiments correct for the additional length of the stem immersed, which
was slightly different on different occasions. The correction is determined by the fact
that the water-equivalent corresponding to a length of 1° of the stem is 0°34. We
may take, therefore, as the equivalents which were the same in all experiments :—

@alonmetervic tic jan ie eae wee mn cite timate le pil
Heatme coil, frameand Shirteray ee) oe 9209
StveridisGs ico. S~ taeseere ee pe pe RE hal afk VOLE
ierinometer as tay, as; market: Wee ne 2205
Parts surrounding calorimeter. . . .. . . 0°33

27°02

ise)
i

MDCCCXCY.—A.

442 PROFESSOR A. SCHUSTER AND MR, W. GANNON ON A

The reason for the last item will be given in connexion with the discussion of the
cooling correction.

The Total Mass of Water.

The calorimeter contained approximately 1514 grams. of distilled water in each
experiment. The mass of water was determined by volume and by weight. In the
estimation by volume a carefully calibrated 500 cub. centims. flask and burette were
used. The weighings were taken on a balance, allowing, to estimate accurately,
0°1 gram. The buoyancy correction amounts to 1°58 gram.

As our calorimeter was not completely covered, a certain amount of evaporation
took place, the mass of water during the experiment differing by about a decigram
from that which was put in. <A few experiments give a fairly consistent rate of 11
gram. per hour of evaporation under the conditions of our experiment. As a check
the water was nearly always weighed both before and after each experiment, and the
mass during the experiment was then found by interpolation.

The Cooling Correction.

The interchange of heat between the calorimeter and its surroundings depends on
conduction and radiation. If the water of the calorimeter is exposed to the
air, evaporation may sensibly lower the temperature, but for the present we may dis-
regard the effects of evaporation. The loss of heat to the outside is usually corrected
for in a well-known manner. The correction depends on the assumption that the loss
of heat is proportional to the difference in temperature between the calorimeter and
its enclosure, and if the loss of heat is small, the assumption is generally justified. In
a well-disposed experiment the temperature (w) of the calorimeter alters slowly and
regularly during the preliminary period. If ” observations are made at regular
intervals of time T, they should be expressible with sufficient accuracy in an expression
of the form u=v-+ kT. It is usual to obtain the two constants of this equation v
and k by graphical means; we have employed instead the method of least squares,
not for the reason that we believe to have obtained a greater degree of accuracy in
this way, but simply as a matter of convenience. ‘The process of calculation takes
less time than the graphical method, and the results are quite free from personal bias.
The observations themselves give a series of equations,

Uy =v+kT
Uy = 0 + 2kT
wy, =v + nkT.

It is required in the first place to calculate v and &. The most probable values of
v and k are

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 443

gn (n — 1)v = (2n + 1) A — 3B
gu(n— 1) (n+ 1)kT = 2B— (n+ 1)A,
where
A=u,+tut...+ um
B= u,+ 2uy +... + nu,

The last observation being taken, the second period—in which the heat to be
measured is allowed to enter the calorimeter—begins after a further interval T, and
it is required to calculate, in addition to the rate of heating &T, the most probable
value w,,, of the temperature at the beginning of the second period. The above
equations give

Une. = U+ (nm + 1)kT
6B —2(u + 2)A
n(n — 1)

In our case, where the rise in temperature was always small and regular, ten or
twelve observations were considered sufficient to determine the constants, and in
that case the labour of reduction is small.

After an experiment the change in temperature of the calorimeter had to be
observed once more, and a value k’ corresponding to k was again determined in a
similar manner. From the two values k and k’ the loss of heat of the calorimeter
during the whole of the experiment could easily be calculated, for the rise in
temperature during the actual heating was uniform. If the current passed during m
intervals, each equal to T, and if — k and —F’ denote the rates of cooling during the
first and last periods, the loss of heat during the m intervals was $m(k+ kh’). A
small correction was necessary owing to the fact that the observed values of & and k’
did not correspond to the temperature of the calorimeter at the beginning and end of
the second period.

We have now to examine shortly how far errors in the estimation of the cooling
correction may arise. Nrwton’s law of cooling is known to be approximate only. If
we had to deal simply with radiation, we should obtain greater accuracy by adopting
the law of STEFAN, according to which radiation varies as the fourth power of the
absolute temperature. We have calculated that the difference introduced by STEFAN’S
law in the final value of the equivalent amounts to about one part in sixty thousand,
and considering that the combined effect of radiation and conduction seems to follow
Newton's law more closely than the effect of radiation alone, we are justified in
taking that law as correct. In order that the usual cooling correction should apply,
it is not necessary that the different parts of the enclosure should all be at the same
temperature, nor is it always necessary that the temperature of the surrounding
bodies should be constant. If, as in our case, the calorimeter receives its heat at a
constant rate, the temperature of the enclosure may vary as a linear function of the

3L2

444 PROFESSOR A, SCHUSTER AND MR. W. GANNON ON A

time during the same time without vitiating the experiment, for as long as we assume
Newron’s law, it does not matter whether the calorimeter rises uniformly or the
enclosure falls uniformly or whether they both vary together. This is an important
consideration, for unless we take very elaborate precautions, the enclosure must to a
certain extent follow the temperature of the calorimeter. All that is requisite for a
correct estimate of the cooling is that the rates should be accurately known at the
beginning and ending of the second period. The change in temperature of our water
jacket in the actual experiments was very small and sometimes inappreciable.

When the temperature of our calorimeter was raised 1° above that of the water
jacket, the cooling amounted to about 0°-0025 per minute; the cooling surface was
about 725 sq. centims. ; the amount of water in the calorimeter, 1500 grams. Hence
there was a loss of heat for each square centimetre of surface of 0:0052 unit per
minute. In Mr. E. H. Grirrirus’ determination, where the pressure of the sur-
rounding space was reduced to about one-hundredth atmosphere, the corresponding
number was between 0'0028 and 0°0026, taking 300 sq. centims. as the exposed
surface. On the other hand, his total amount of water was always less than one-
quarter of that used by us; so that the actual cooling in his experiments for one
degree difference was about double ours. It is interesting also to compare our
number with that corresponding to the ioss from a cylindrical rod suspended -
horizontally in the air and quite unprotected. Mr. Less (‘ Phil. Trans.,’ Vol. 183,
p- 490) finds for a nickel-plated rod of about 2 centims. diameter, 0°011 gramme-degree
per square centimetre per minute, or about twice our number. In the latter case, the
conditions of the experiment are most favourable for great loss of heat by convection ;
and Mr. GRIFFITHS’ experiments show that by reduction of pressure to about one-third
of a millimetre the loss is only reduced to about one-quarter of what it is in that
case, and one-half of what it may easily be reduced to in a calorimetric experiment at
atmospheric pressure. It ought to be possible by properly disposed diaphragms
to reduce considerably the effects of convection currents at atmospheric pressure and
SO gain in a simple way the same advantage as is done by removing the air surrounding
the calorimeter.

We may calculate approximately that part of the loss which is due to conduction
irrespective of convection, Taking the thermal conductivity of air to be 0°000055,
and the distance between the calorimeter and the enclosure as 3°8 centims., we find
that thermal conductivity alone would account for a loss of roughly 0:001 gramme-
degree, or about one-fifth only of the actual loss. As in Mr. GRiFFrTHs’ experiments
the enclosure was at a greater distance from his calorimeter than ours, his observed
loss by radiation and conduction is also about five times that due to conduction of
air alone.

Evaporation will produce a certain amount of cooling of the calorimeter, if that is
not perfectly enclosed; but unless the rate of evaporation changes with the
temperature, the effect will only be a lowering of temperature by a constant quantity.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 445

The rate of cooling can only be affected by evaporation in so far as it increases with
the temperature, and since for small changes it would vary as a linear function of the
temperature, any error due to evaporisation is eliminated by the cooling correction.

Some Corrections to the Water-equivalents.

1. Correction for Surrounding Air.—The usual method of finding the value of
the correction depends on the assumption that the loss of heat is proportional to the
excess of temperature, and as regards radiation this will hold whenever the variation
is small. When however an appreciable quantity of heat is carried away by
conduction, an error may be introduced by taking as the excess of temperature the
difference observed between that inside the calorimeter and that of its jacket, for
the temperature gradient in that case will not be uniform during the whole course of
the experiment. Consider, for instance, a calorimeter placed on a more or less
conducting material like wood or cork. If the calorimeter is suddenly heated,
the temperature gradient at the surface will be large and will then slowly diminish.
The cooling observed, as usual, after the lapse of a few minutes, will underrate the
heat lost during the first few minutes. It is easy to see that when conduction
comes into play, the amount of heat lost or gained will depend on the distribution of
heat in the conducting body, and that will depend on the previous history of the
calorimeter. Thus, when a calorimeter is kept heated until all the surrounding
parts have reached a steady temperature, and observations are then made on the
rate of cooling, we are not justified in applying the rate thus formed to the period in
which heat is communicated to the calorimeter. An estimate may be made of the
error introduced if the correction is applied in the usual way. We take the case of
a calorimeter placed on a non-conducting slab of thickness c. At the beginning of
the experiment everything is to be at temperature zero. At the time ¢ = 0, the
temperature (%) of the calorimeter is to be gradually and uniformly raised so
that we may take wu = pt. Finally, at a time T, the temperature is kept constant
and equal to pT. It is required to find the rate at which heat is given up by the
calorimeter at any moment, and the total amount of heat which passed through its
surface.

Taking the flow to be linear, the differential equation to be satisfied is

du/ot = a? 0*u/dx?.

Here a = x/s, where « represents the conductivity and s the heat capacity per unit
volume. We introduce the conditions

yu = 0 if t = 0 for all values of a.
— ¢ (t) for 7 = 0.
u = 0 for x = ¢ for all values of t.

446 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

Also ¢$(t) = pt between ¢ = 0 andt=T, and ¢(t) = pT itt>T
The solution of the differential equation can be put into the form

7 Qn=n 7] ’ + » 2 2 = 0
u=$(t)" oa = > sin et + SES

. IT Dh aes
3) GS — ae | Bae MINI GS ON GDN:
T n=1 1 C T n=1 ¢ 0
where £ is written for az/e.

The first term is often omitted as it vanishes for all finite values of x But as we
shall have to consider the value of du/ox for « = 0, it is retamed here. To perform
the integration we must distinguish two cases, according as ¢ is smaller or greater
than T. Taking ¢(A) = pd, and performing the integration with respect to A
we find

C—2 2p 2 il

NTL
y= (1 — e-”*") sin
C TB? na 8 c

U = pt

(1)

For larger values of t we have to divide the integral into two parts as the value of
¢ (A) has a discontinuity for ¢ = T.

The final equation for u then becomes

(tonto

Dn fo}
mee 2p 1 pant et (pn2per oe MUTT
epi — — F =e" (e*PT — 1) sin —-
L c TB? na 12 ( ) c

Writing (du/ox), for the value of du/ox at the plane « = 0, the quantity of heat
passing out of the calorimeter up to the time T will depend on

T T
aa \ 2 dt = = | jer AR 2p i) spl — gory de
CX /0 -) np?
0 0

T eT 5 2 » N= oO 1
ne Pp oe pe i 30> ae 2pe S e
2¢ 302 «AB at le an WE

— RT

We also obtain ift > T

t
Ou T be ne Qn 2 I i ie
~\) dt 7 (2t =D) ag ee Se (cr)
\OL /o aC

3a Ta* y= 1 n*
0

The application of these formule is easy when ft is so large that e~*¢~”
may be neglected. The heat H which has passed through unit surface of the

calorimeter up to the time ¢ is obtained by multiplying the right-hand side of the
last equation by k = a’s.

Neglecting the last term this becomes

ee

= (2t a T) + ue

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 447
and the rate at which heat is given up at the time ¢ is
dH /dt = pkT/c.

If the cooling correction is applied in the usual way, the rate at which heat is lost
would, during the period of heating, be taken as half that corresponding to the final

period, or in other words we should take loss of heat as Sa T during the period of

: AT ;
heating, and as — (¢ — T) from the time that the temperature of the calorimeter has

become steady. It is seen that in this way of calculating, the term 4 (pest) is

neglected. This term represents the amount of heat which is necessary to raise
a thickness 3 of the material through which the heat is conducted to the final
temperature of the calorimeter.

We see from this investigation that a certain amount of the air surrounding the
calorimeter should be added to the water-equivalent. For air a? is about 0°26, and
in our experiments the walls of the enclosure were 3°8 centims. from the calorimeter.
We may, without sensible error, neglect the error due to the curvature of the sides
of the calorimeter and substitute 3°8 for c. The value of f? then becomes
0:2672/(3°8)? = 0°18.

As several minutes always intervened between the time at which the temperature
of the calorimeter had become constant and the observations for the cooling
correction, 6?(t — T) was always greater than 10 and e~®“—” was therefore quite
negligible. We may in this case then simply calculate the water-equivalent of a
quantity of air surrounding the calorimeter, and having a thickness of ¢/3 or
1°3centims. ‘The total effective surface of the calorimeter being 724 sq. centims., the
quantity to be added to the water-equivalent becomes. 0°28.

2. Correction for Thermometer.—In taking the water-equivalent of the thermo-
meter, it is usual to consider only that part which is plunged into the water, but this
requires justitication, as it is clear that those parts of the thermometer which are close
to, but not actually in contact with the water, must be heated also. The following
calculation will give an estimate of the error which may be thus introduced. We
may assume, in the first instance, that the thermometer which is surrounded by air
rising from the calorimeter will not give up any appreciable heat to the outside, so
that we may apply the same differential equation for the flow of heat as that used in
the former problem. We may treat the thermometer as a glass rod of indefinite
extent, having the temperature of its surface in contact with the water raised at a
uniform rate pt until t = T when it is kept constant at the temperature pT.

The solution of the equation applied to this case gives us :—

448 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

—(%) = 2p /t fort < T
IZ] o a. T

ole) D_ (fi — /t —T) fort > T

a

T/Ow pt”
ee = Ae
(es eS: An/ 7

|

In our experiments the average time ¢ during which the rate of cooling was
observed was with sufficient accuracy equal to 2T, reckoned from the moment the
heating began. In that case, the above formule show that the total amount of heat
which has passed into the thermometer, denoting by A the area of its cross-section, is

An ApT*”
3a,/7 [2 V2 ine 1];

while the heat lost to the calorimeter, calculated by means of the cooling during the
last. period, is
Se Apie

ar/ ly 3 = Wh

The quantity to be added to the water-equivalent is obtained by dividing the
difference of these values by pT, and becomes therefore

Nhe Far Ness YEE
= wie (5 — /2)=12——
a 7

oa 7

Substituting for @ in terms of the conductivity «, the capacity for heat of unit
volume of glass s, this becomes 1:2 A ,/(«sT/z).

Putting in the numerical values corresponding to our experiments « = 00021,
T = 540, s =°5, A = -21, the correction is found to be 0°12.

3. Correction for Leads.—On the other hand, the water-equivalent of the coil was
slightly over-estimated as the wires serving as leads were reckoned in, although.
part of them protruded out of the water. The length which was outside the water
was 2°8 centims., but about 8 millims. of this was in close contact with stout copper
rods, the temperature of which would not rise appreciably during the experiment.
From the previous investigation, which is applicable to this case, it would appear
that one-third or 0:7 centim. of the part surrounded by non-conductors should have
been taken into the water-equivalent instead of the whole. The error committed in the
heat capacity of 2:1 centims. of copper wire, weighing ‘22 grams. per centim., that is 08,

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 449

should be subtracted from our water-equivalents, as there were two such wires.
The heat produced by the current in the leads (No. 14, I.W.G.) would, if entirely
used to raise the temperature of the leads, produce a rise of 0°°2 in the time of the
experiment. If the whole of this heat is imagined to enter the calorimeter it would
produce a difference of 1 part in 150,000 in the total rise. No error can therefore
arise through the heating of the leads.

4. Correction for the parts of the Calorimeter not in contact with Water.—The
water in our calorimeter reached to about 1°5 centims. from the top of the vessel,
but a rough estimate of the error introduced will show that we were justified in
taking the whole of the calorimeter into the water-equivalent. The cooling which took
place when the temperature of the calorimeter was at 1° above that of the sur-
roundings amounted to 3°5 gramme-degree units per minute. If we assume that the
heat lost was the same at every part of the calorimeter, we find that the loss due to
radiation and convection of the part of the outside surface above the level of the
water amounted nearly to one quarter-unit. The loss of heat towards the inside of
the part not filled with water must have been small, but in order to over-estimate
the loss we may assume that the part of the calorimeter which was above the water
lost 0°5 heat unit per minute for a difference in temperature of 1°. This will allow us to
calculate the temperature gradient along the copper close to the water surface. If « is
the conductivity of the copper, A the area of the section of the calorimeter, ¢ the time,

KtA du/dx = °5,

and since « is nearly unity and A = 83, du/dx is found to be nearly ‘01. The
calculated temperature gradient of +35 of a degree per centim. must have exceeded
considerably the actual one, and must diminish with the distance from the water
surface, but assuming it to be uniform all over the upper part of the calorimeter, the
average temperature of the copper would be 0°:007 below the temperature of the
water. The heat capacity of that part of the calorimeter is approximately unity, and
therefore the error in the water-equivalent, considerably over-estimated, is 007, a
negligible quantity.

5. Correction for Cork Supports.—It only remains to discuss whether the cork
supports on which the calorimeter stood added in any appreciable way to the water-
equivalents. It is not possible here to estimate the effect by calculation, as the
contact between the calorimeter and the cork is irregularly distributed over the cork.

We therefore made a few experiments in which the change in temperature of the
cork was directly measured by means of thermo-junctions, the calorimeter being
treated exactly as during an experiment on the heat-equivalent. We found in this
way that the heat which entered the three corks during the whole duration of the
experiment is only ‘08 unit as against 3300 units which have entered the water in
the calorimeter, and as the greater part of this heat is allowed for in the cooling
correction, no addition need be made to the water-equivalents on this account.

MDCCCXCV.—A. 3M

450 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

The sum of the various small corrections to the water-equivalent amounts to 0°33,
or about 2 parts in 10,000 of the whole water-equivalent.

The Auxiliary Current.

In the first two series of our experiments, the thermometer was generally rising
during the first, but falling during the last period. It is known that a falling
thermometer will somewhat lag behind the real temperature, but we had hoped to
eliminate this by applying a constant correction. Special experiments made for the
purpose did not, however, give us sufficiently consistent results, and it appeared that
the lag was too variable to be allowed for. Hence we decided to work only with a
rising thermometer. We might have achieved this by raising sufficiently the tem-
perature of the surrounding water-jacket, but this would have made the gain by
radiation and conduction in the first period greater than we thought could be correctly
measured. The plan we adopted consisted in sending through our coil, in the final
period, a weak current (about 0°1 ampere) which just overbalanced the cooling. The
current—which we call the auxiliary current—could be measured with sufticient
accuracy to calculate the rate of heating which was due to it alone, and as the rise in
temperature was observed, the loss by radiation could be deduced.

Fig. 6.

resistances.

Astatic

galvanometer.

The auxiliary current was derived from two storage cells and was measured by one
of Lord KeExvin’s magnetostatic centiamperemeter balances placed in circuit with
the coil and cells. In order to avoid any error that might arise from a possible
change in the constant of the instrument due to a change in the value of the earth’s

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 451

magnetism, we took the precaution of calibrating the instrument immediately after
each equivalent experiment. This was done as follows :—

The current from two storage cells passed in succession through the current meter,
a coil of manganin wire and a set of adjustable resistances (see fig. 6), The
terminals of the manganin coil were connected up through the astatic galvanometer
with our Standard Clark cell, so as to oppose the E.M.F. at the terminals of the
manganin coil due to the passage of the current from the storage cells to the E.M.F.
of the Clark cell. If the galvanometer shows no deflection on both circuits being
closed, then e = zr, where e = E.M.F. of the Clark, 7 = current in the current meter,
7 = the resistance of the manganin coil.

A coil of manganin wire was chosen, since this material has a very small tem-
perature coefficient ; it was supplied by Messrs. Exxiorr, having a composition of
copper 84 per cent., manganese 12 per cent., nickel 4 per cent.; its resistance value
was nearly 14 true ohms. An example will explain the calculation of the value of the
current. On May 20 the current meter read 48°34 divisions (a short focus lens
enabled us to read the divisions to hundredths). Temperature of the Clark
cell 17°12 C. Hence the current is equal to 1°4827/14 = 0°10234 ampére; and
therefore 1 division = 0°00212 ampére. The instrument remained very constant
throughout the equivalent experiments, as may be seen from the following table :—

TABLE IX.

Wate Value in amperes of
; 1 division.

WER ANON Gs We Sg. es 0:00213
ode SSD W eS 2, See HERP ee 0:00212
© ey slideu aren ptpascme S 000212
HD) ( nse code oes 0:00212

afin)" § Wie) 6. oboe 000212
EGP Ko) hehe eae, Bene 0:00212
SLi Lis f ives <a Soar nalce 0:00212

As a check upon this method of calibrating the current meter, it was also
calibrated on one occasion by measuring the current passing through it by the
silver voltameter. Its constant as thus determined was 0°00212. The sensibility of
the current meter was such that its readings were accurate to 1 in 400. Hence the
cooling correction to be applied is accurate to 1 in 200, and from the data already
given it appears that an error of that amount only affects the accuracy of the
equivalent to 1 in 200,000. Knowing the value of the auxiliary current, the rise
in temperature (#) per minute of the total mass of water is calculated from the
formula 6 = (C°R x 60)/(J x M), R being the resistance of the heating coil.
The mean of several determinations of R with an Elliott P.O. box—which had been

3M 2

452 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

sent to Messrs. Exuiorr for careful examination—gave a value of 31°32 B.A. units at
the mean temperature of the equivalent experiments, or 30°90 true ohms, if
1 B.A. unit = ‘9866 true ohm. It is clear that an approximate value of J will
be sufficient in this part of the calculations. Any error in the value of J will affect
the cooling correction to half its value, and as that correction amounts to 1 per cent.
of the equivalent, an error of 1 per cent. in the assumed value of J would involve an
error of 1 part in 20,000 of the final value. The reductions had naturally to be
made before we knew what our own value of J was going to be, so we applied
provisionally Mr. Grirrrrys’ value of 4194 xX 107, and although our own value
is slightly lower it would have made no appreciable difference if our value had been
taken instead.

The Temporary Coil.

The only part of the arrangement which has not so far been described is a coil of
platinoid equal in resistance to the one in the calorimeter, in series with a resistance
approximately equal to that of the silver voltameter.

This coil and resistance served for a preliminary adjustment of the circuit. It was
necessary, in order to secure sufficient accuracy, that a balance of electromotive force
should be obtained soon after the beginning of each experiment, and this could be
done by means of this coil, which, for distinction, we shall call the temporary coil.
The keys which serve to change currents were all made of paraffin blocks, and of very
simple construction. The blocks had six holes filled with mercury, and copper con-
nectors completed the circuit. The two ways in which connection could be made may
be seen in the key marked 4, (fig. 5), where the holes are numbered. In the position
of the key which we shall call a, the cups 1 and 8 were connected, as well as 2 and 4;
while, in the position b, 1 was connected to 5 and 2 to 6. The keys k, and k, were
exactly similar, and we shall speak of the positions a and b of the keys when the
corresponding connections were made. Thus, k; (a), k, (b) means that the key k; was
in position a, and key #, in position b, The key &; served to short-circuit the silver
voltameter in the final period ; a copper connector could be placed for this purpose
either at @ or b.

Method of Maintaining a Constant Difference of Potential at the Terminals
of the Heating Coil.

The difference of potential at the terminals of the heating coil was kept constant
by balancing it against the battery of twenty Clark cells in the well-known way. The
success of this method, when the potential difference had to be kept constant for some
minutes, depends on the ability of the operator in altering the total resistance of the
circuit through which the current is passing by small variable amounts. The current
—which, in our experiments on the heat-equivalent, was about 0°9 ampére-—tends to

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 453

diminish in value, owing to (1) change in the values of the different resistances in cir-
cuit, due to change of temperature produced by the passage of the current ; (2) change
of the resistance of the silver voltameter ; (3) running down of the electromotive
force of the storage cells. In order to counteract the effects of these changes, a
number of separate resistances, W,, W., W3, and two switches, s, and s, (fig. 5), were
placed in series with the remainder of the circuit. W, consisted of coils of platinoid
wire; W, and W, were platinoid wires of different resistance-values, any number of
which could be connected in series by means of mercury cups and copper bridges.
The resistances W,, W., W, enabled the current to be adjusted to the proper value
when running through the temporary circuit; W, or W, enabled us to make any
necessary change at the moment of sending the current through the heating coil.
The switches s, and s, were used to keep the spot of light in the zero position during
the nine or ten minutes the current was passing through the heating coil. They
consisted of a stone base, on which were arranged eleven brass studs (shown in figure)
along a semicircle, having binding screws (not shown) attached to their ends. Over
these studs slides a movable contact piece attached to an insulating handle. The
movable arm consists of a number of thin brass plates, jointed together only at the
centre, and so fitting that they form independent springs which press edgewise on
the brass studs, thus ensuring good uniform contact. The resistances to be inserted
are placed in the binding screws attached to the studs (soldered to ensure better
contact). One switch had platinoid wires of 0°008 ohm, and the other platinoid wires
of 0006 ohm. These switches gave a much greater range than was found necessary
in any experiment. When the spot of light was observed to move from the zero
position, a movement of the arms of these switches brought it back. The spot of
light was never as much as five small divisions from its position of rest, but even a
deviation of ten divisions during the whole time of the experiment would have
produced no appreciable difference in the value of the equivalent.

The current was only switched on to the principal circuit when it was found to be
running with fair steadiness through the temporary circuit. After some little trouble,
caused by leakage, we were able to keep the current constant without any con-
siderable change in the value of the total resistance of the circuit.

The electromotive force that is thus measured is the difference of potential at the
terminals of the heated coil, provided there is no leakage in the wires connecting
these terminals to the galvanometer. The insulation of these wires was found to be
7 X 10° ohms, so that the electromotive force at the galvanometer is practically equal
to the electromotive force at the terminals of the coil.

Method of carrying out an Experiment.

Two observers were required to carry out an experiment ; one (A) kept the electro-
motive force at the ends of the coil constant and compared the Clark cells; the other
(B) took all the temperature observations,

454 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

- A weighed and measured quantity of water having been placed in the calorimeter,
the platinum dish (after being weighed several times) was filled with 120 cub. centims.
of the silver nitrate solution. The water in the jacket of the calorimeter was raised
about 1° C. above the temperature of the water in the calorimeter, so as to secure a
convenient rise before the heating of the coil commenced. The observations are
conveniently divided into three periods. The reference to the connections will be
understood with the help of fig. 5.

Preliminary Period.

A, being the main battery, the key Q was open at first, and the connections in the
other keys were as follows: k, (a), k, (a), k, (a). The observer (A) compared the
Clark cells with the help of the key &,, and at the conclusion of the comparisons
which took about 8 minutes—the temporary bridges of k, were removed. (A) then
closed the main circuit at @, and the connections were such that the current was

flowing through the temporary coil and could be adjusted till a balance was obtained
against the 20 Clarks C.B. The observer (B) in the meantime observed every minute
the thermometer which was plunged into the calorimeter, The rise was roughly about
0°-002 per minute, and so regular that more frequent observations would have been of
no value. (B) also observed the auxiliary thermometers.

Everything being ready, a signal was given 10 seconds before the current was to be
sent through the principal coil. (B) now broke connections at k, and joined k; (a).

Main Period.

(B) changed the connection /, (a) to k, (b), and the main current thus passed through
the coil in the calorimeter. A signal being given that this was done, (A) makes
connections k, (b), and thereby opposed the Clark battery to the electromotive force
at the terminals of the principal coil. If the preliminary adjustment was perfect (as
it was on two occasions), the spot of light remained at rest ; but generally it moved
slightly to one side, and then a slight readjustment of the resistances brought it back
to its position of rest. (A) called out when he had obtained a satisfactory balance, and
this was generally three seconds after the main current was complete. As the
experiment lasted nine or ten minutes, and as the electromotive force was never as
much as two in a thousand out during the first three seconds, no error in the final
result can be introduced in this short period. During the heating of the coil (B) did
not take any temperature observations except when half the proposed time of heating
had elapsed. The object of this observation is to be able to point the telescope very
near the division of the thermometer which the mercury thread would reach at the
conclusion of the experiment.

Final Period.

Ten seconds before the main current was interrupted, the connection at k, was
broken, the balance being always so steady that it could be trusted to be maintained
during that interval. (B) now broke &, (a), and three seconds after connected ks (0).

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 455

(A) in the meantime had changed f; from a to b, k, being still at b. The circuit is now
seen to be such that the small battery A, sends a current through the magnetostatic
meter M and the calorimeter coil. In this final period (B) observed the thermometer
and the magnetostatic meter, and also made observations on the auxiliary thermo-
meters placed near the stem of the Baudin, in order to introduce the stem correction.
(A) once more compared the Clarks.

The Results.

We divide our experiments into three series, but only attach any value to the
third, as during the first two sets the thermometer was falling in the last period.
We had hoped, at first, to be able to apply a small correction, to eliminate the error
which is due to the fact that a falling thermometer will read too high, and we made
a large number of experiments to determine the correction. We arrived, however, at
the result that the indications of a falling thermometer are so irregular that no
correction is possible. Consequently in our third series the thermometer was rising
during the whole course of each experiment.

We think it worth while to put on record an impression that the behaviour of our
Baudin thermometer has altered since we received it from the maker. As soon as it
came some preliminary experiments were made, to see if we could work with the ther-
mometer while it was falling, and the observations seemed to show that the fall was
sufficiently uniform. Our first three experiments gave results which were very con-
sistent, and a minute after the current was broken the temperature seemed to fall
already in a perfectly regular manner. But as we continued our work, the behaviour
of the instrument seemed to deteriorate. Thus in our experiment of March 8th the
thermometer had hardly fallen three minutes after the current had stopped. It is
possible that this was due to accidental circumstances, for it is well known that
different places in the bore of a capillary tube behave very differently. We wish
therefore to express no opinion at present as to the probability of an actual change
in the behaviour of the thermometer, but only to draw the attention of other
experimenters to this point which seems worth keeping in mind.

The results of the first three experiments which constitute the first series are con-
sistent, but no value is attached to the equivalent as deduced from them, owing to
the uncertainty of the water equivalent. The coil, as has been mentioned, was then
wound on an ivory frame. When Mr. HApiey, who then assisted in the work, began
to experiment on the specific heat of ivory, he met with serious difficulties. The
ivory contained water to begin with, as was shown by the diminution in the weight
of fresh ivory when heated up ; it absorbed again when placed in water ; the results
were consequently not to be trusted. Even when coated with shellac, the substance
did not behave in a consistent manner. There were other imperfections in our
calorimeter at that time which make it impossible for us to know the water equivalent
with sufficient accuracy.

456 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

In the second series of experiments, the coil was wound on porcelain strips, aud we
were quite satisfied that the water equivalent was known with sufficient accuracy.
Nevertheless the agreement of the results in this series is not satisfactory.

In experiments 4 and 6 the thermometer was falling both in the first and last
period, and the cooling correction was consequently somewhat large; on the other
hand the lag of the falling thermometer would affect both the first and last period,
and, therefore, be partly eliminated in the result.

Experiment 5 is rendered a little uncertain by the fact that the thermometer at
the beginning of the first period fell slightly, and then remained perfectly stationary ;
it is therefore probable that the temperature was really increasing at the beginning of
the experiment. The cooling correction, calculated on the assumption of no rise,
would be too large, hence the calculated equivalent too small. The result of March 8th
is anomalous, and does not seem altogether accounted for by the sticking of the
thermometer at the end. There was on that day an exceptionally large difference
in the amount of water, as measured by weight and by volume. We took, as
usual, the mass as determined by weight ; had we taken the latter, the calculated
equivalent would have been 4181. A final revision of our calibration correction
showed a small error, which may have affected some of the results in series I. and
II., by about one part in two thousand. As we do not attach any value to the
numbers obtained, we have not recalculated the numbers.

The results of our third series are as consistent as could be hoped for. We thought
it useless to multiply the experiments, as it did not seem to us that our results could
be materially improved by repetition. Their good agreement shows that our results
are correct to more than one part in a thousand, provided that we have avoided
systematic errors. The difference between our results and that of Mr. GRrrrriTHs
must be due, on the one side or other, to errors which a multiplication of experiments
could not eliminate.

We give the results of our experiments in the form of Tables.

Column I. gives the number of the experiment.

Column II. gives the date.

Columns III. and IV. state whether in the first and last period respectively the
thermometer was falling or rising.

Column V. gives the value of the equivalent calculated, the temperature scale being
that of a mercury thermometer made of French hard glass.

Columns VI. and VIL. give the same equivalent, reduced to the nitrogen and
hydrogen scale of the Bureau International des Poids et Mesures.

Column VIII. gives the temperature range of the experiment.

DETERMINATION OF THE SPECIFIC HEAT OF WATER.

TABLE X.
Series I,
IT. IIT. IV. We VI. VIL. VIII.
1892. | 5 3
1 April2 | Rising | Falling | 4164x107 | 4175x107 | 4177x107 | 15:2—17-2
2 ars - id 4168 4178 4180 16-8—18'8
3 | June 9 os 4169 4177 4:178 19:9—21-9
Mean . 4:167 4¢177 4-179 17:3—19'3
TABLE XI.
Series IT.
| E i
II. III. IV. V. VI. VII. VIII.
|
| 1892.
4 | July 5 | Falling Falling | 4188x107 | 4197x107 | 4198x107 | 182—20-1
5 se ? id 4177 4-187 4:189 16:-4—18'4
1893.
6 | Feb.11 | Falling | . 4:192 4.203 4205 15-4—17°6
7 » 22 | Rising | a 4185 4196 4198 149-171
8 | Mar. 1 | i 4186 4:198 4200 143-165
aigeress +o sey itaeet 4169 4179 4181 16-4—18'6
| |
Mean 4-183 4193 4195 159-181
TABLE XII.
Series ITT,
[ich eae | : l ai
1. eet] rte TV [et Ayaan | Be eeval VII. VIL.
1893. | | Et is
10 | May 13 | Rising | Rising | 41824x107 | 4:1927x107 | 4:1940x107 | 17-4—19°6
ll ey is i 41807 4°1910 41923 17:2—19:-4
12 20 io a 4:1807 41910 4.1923 17-3—19°7
Saal ances i i 4/1804 41902 4:1916 17-9—2071
14 i * - 41776 41872 41884 18:°2—20°4
15 es se) eee 4 41822 4:1908 41919 20°2—22-4
Mean of firstfour. . . .| 41810 41912 41934 17-4—19-7
» lasttwo. . . .| 41799 41890 41901 19:-2—21-4.
eemserics (hh. 41804 41905 4 LOL7 18:0—20°3
|
=i) : z £3 Teue

MDCCCXCV.—-A. 3 N

458 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A
Our final value is

4'1804 on the mercury scale of hard French glass,
J = 107 X < 4:1905 on the nitrogen scale,
4:1917 on the hydrogen scale,

at a temperature of 19°'1.
This result depends on the assumption that the electrochemical equivalent of silver
is 0'001118, and that our standard Clark cell had an electromotive force of

1°4340 (1 — at — 15) volts,

where « = ‘000814 + ‘000007 (¢ — 15) as given by Kau eE (‘ Zeitschrift fiir Instru-
mentenkunde,’ vol. 13, p. 310, 1893). GLAZEBROOK and SKINNER’S coefficient refers
to a mean temperature of 7°°5, and is identical with the above at that temperature.

Discussion of Results.

The comparison of the results of different observers will be facilitated by Table XIII.,
in which we compare ergs with the foot-pound at Greenwich and the kilogram-metre
at Paris.

Tape XIII.

| i Foot-pounds at Kilogram-metres at
Ergs x 107. Gee, is Paris.
4-160 772°83 424-07
4-165 773°76 424:58
4-170 77468 4.25°09
41765 77561 425°60
| 4-180 77654 426711
| 4-185 | W747 4.26°62
4-190 77840 427:13
4-195 779:33 427-64
4-200 780 °25 428:°15
4-205 78119 4.28°66
4210 78214 429°17

This table has been calculated on the assumption that g at Paris is equal to 980:96,
and at Greenwich equal to 981:24.

We have prepared another table (XIV.) which will give at any temperature the
correction of an interval measured on our mercury thermometer to an interval measured
on the nitrogen and hydrogen thermometers. This table has been calculated with the
help of the equation given by Cuappurs for the correction to the thermometer made
of French hard glass.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 459

TABLE XIV.
| 10°. 12 14°, 16°. 18°. 20°. Oe. 24°.
| |
Correction to nitrogen |
thermometer. . . .|—000369 | -00337 | -00305 | -00275 | -00247 | -00220 | -00194 | -00170 |
| |
| | | |
| Correction to hydrogen |
thermometer. . . .| —0°:00418 | 00381 | 00345 | -00313 | :00280 | :00249 | -:00219 | -00190
|

In comparing our results with those of other observers, we have in the first place to
consider the value which Mr. Grirrirus has obtained in his very excellent series of
measurements. His final result (‘ Proc. Roy. Soc.,’ vol. 55, p. 26; Phil. Trans., vol. 184,
1893, A., p. 361), is

J = 4:1982 (1 — 000266 6 — 15) x 107.

This refers to the nitrogen thermometer. At a temperature of 19°1 the value
would be reduced to 4°1936, which corresponds to our 41905 at the same tempera-
ture. GRIFFITHS’ value is to be increased slightly owing to the fact that he really
measures the difference between the specific heat of water and of air. This would
increase the value of J by ‘0011 about, so that the value of J at 19°1 would be
raised to 4:1947 Xx 10’, which is exactly one part in a thousand larger than ours.
The difference is smali, but must be due to some systematic error, as both GRIFFITHS’
value and our own agree so well with each other, that ordinary observational errors
and accidental disturbance could not have produced so large a difference in ‘our
result. The least satisfactory part of a calorimetric measurement must always be
the cooling correction, and we have considered it of great importance to reduce that
correction as much as possible. The uncertainty of the cooling correction does not
necessarily depend on its value; thus, we can much diminish it by starting, as we
have done in our last series, with the initial temperature of the calorimeter about as
much below that of the water-jacket as the final temperature is above it. Yet the
uncertainty of the correction does not seem to us to be diminished by that process.
We may reasonably estimate the uncertainty due to the cooling correction by calcu-
lating what the error in the observed rate of cooling, either at the beginning or end
of the experiment, must have been in order to produce a difference of one part in a
thousand in the final result. We find in our own experiments that the error must
have amounted to more than 15 per cent. We consider it unlikely that so large an
error occurred always in the same direction. Apart from the cooling correction,
however, it is difficult to see how a difference of one-tenth per cent. is produced
unless by accumulation of a number of small errors.

3N 2

460 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

The weak point of Mr. Grirrirus’ determination is the small quantity of water he
uses, his result depending on the introduction of about 120 grams. into his calorimeter.
The highest water equivalent with which he werked was about 350 grams., of which
85 are due to the calorimeter itself. The chief objection to the use of such small
quantities lies in the great cooling correction. In the experiment quoted by him on
p- 482, the loss of heat due to radiation and conduction at the end of his experiment
amounts to about 9 per cent. of his heat supply. If such loss has been wrongly
estimated to 1 per cent., an error of 745 per cent. would result in the final value. The
consistency of Mr. GrirritHs’ results shows that if an error occurred due to that
cause, it must have been systematic, and we may point out how, with such large
cooling correction, serious errors may arise. In applying the cooling correction it is
always assumed that the loss of heat depends only on the difference of temperature
between the calorimeter and enclosure ; but, as has been already pointed out, this is
not the case as regards conduction. Mr, Grirritus’ calorimeter was suspended by
three stout glass tubes, through one of which the stirrer was passing. The exhaustion
in the space surrounding the calorimeter was never sufficient to do away with the con-
duction of air, so that we may take the larger part of the cooling to be due to
conduction and convection. The loss of heat in that case must to some extent
depend not only on the temperature, but on the rate of change of temperature.
Whether the part which depends on the rate of change is sufficient to produce a
sensible difference in the result, it is not easy to say, but the error produced would
with different currents and quantities of water be the same in all cases, and could
not, therefore, be detected by the inconsistencies thereby introduced into the results.

The difference between our value of the equivalent and that of Mr. GRIFFITHS is,
however, of smaller importance than the difference which exists between them and the
equivalent, as determined directly by Joute, Rowxianp, and Micunescu. JOuLE’s
latest value, which is the only one which needs consideration, is 772°65 foot-pounds
at 61°°7 Fahrenheit. The number refers to the degree as measured by JOULE’s
mercury thermometer. RowLAND adds to this a correction to the air thermometer of
about 38, and another small correction for a change in the heat capacity of the
apparatus, which brings the value up to about 776. ‘The correction to the air ther-
mometer has been obtained by means of a comparison made by JouLE himself with
one of Rowianp’s thermometers. JouLE’s original thermometers have been tem-
porarily placed by Mr. B. A. Joute in the hands of Professor ScHusTER, in order that
an accurate comparison may be instituted between them and modern thermometers.
A full description of the comparisons made will be given on another occasion. The
result arrived at shows that the correction is less than that assumed by RowLanp,
and would bring his value up to only 775 at the temperature indicated.

GRIFFITHS compares his result with that deduced by RowLanp from Joue’s obser-
vations. RowLaNp combined the different values obtained by JouLe in his various
investigations, attaching weights according to his judgment as to their relative

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 461

merits. GRIFFITHS finds in this way that the difference between himself and JouLE
amounts to one part in 350, but, if equal weights are attached to all Joutr’s results,
the difference is reduced to one part in 4281. Little value can be attached, however,
to a combination of JouLE’s results which gives equal weights to that obtained in
1847 and that deduced from his latest and most careful work. There is, moreover, in
Row anp’s table a misprint or error in the reduction of JouLe’s 1847 result from
foot-pounds to kilogram-metres, which lowers the value as given by GrirritHs from
779°2 to about 778. It does not seem to us advisable to go beyond JouLz’s 1878
results, and the value assigned by him in this latest research should be taken as
giving his final judgment on the matter. Reducing to the nitrogen thermometer of
the Bureau International, JouLE’s result is 775 foot-pounds at Greenwich, at a tem-
perature of 16°°5 C. At the same temperature GRIFFITHS’ number is 779°8.

Great weight must be attached to Row zanp’s determination, which, at the
temperature to which JouLE’s number applies, is 777°6, and at 19°°1, 776:1, corre-
sponding to our 778°5. RowLanp’s value is, therefore, just halfway between our
own and JovuLe’s result. But it must be taken into consideration that if the
comparison between RowLanp’s and Joue’s thermometers, as made by the latter, is
to be trusted, RowLanp’s value referred to the “ Paris” nitrogen thermometer
would be slightly reduced. At any rate, it seems probable that if his value is
in error, it is rather in the direction of being too high. We have, therefore, a
difference of at least three parts in a thousand to account for between our result and
that of RowLanp, and of nearly four parts in a thousand between GRIFFITHS’ and
Rowanp’s at a temperature of 19°1. These results are summarised into the
following table :-—

Taste XV.—Equivalent in foot-pounds at Greenwich, at 19°°1, referred to “ Paris”
nitrogen thermometer. -

ScHUSTER and

|
Joute. RowLanb. GRIFFITHS. (Su SSraeN

774 7761 779-1 778'5

We now turn to an investigation by Micutescu (‘Annales de Chimie et de
Physique,’ vol. 27, 1892) in which the mechanical equivalent of heat is measured
directly by what seems an excellently devised series of experiments. His result
is 4°1857 X 107. He does not state the exact temperature to which this applies,
but all his experiments seem to have been made between 10° and 13°, so that we
may assume 11°°5 to be the mean temperature of his experiments. RRowLAND’s
value at that temperature is 4199 X 107. We must draw attention to one point in
MicuLescu’s work, which requires clearing up before we can give to it any decisive

462 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

value. verything in the experiments depended on the measurement of a couple,
the arm of the couple being the distance between two knife-edges, one of which had
to support a weight of more than 43 kilos. The distance between the knife-edges is
said to have been 28 centims. in all experiments. Very insufficient information is
however given how that distance was measured, and it would almost seem as if the
author had trusted to the maker in adjusting the central knife-edge to the zero
point of its scale. If the apparatus is still in existence it might be well to make
sure that no error has been introduced through a wrong estimate of the length of
the lever arm.

In order to compare Micunescu’s value with that of others we must apply a
temperature correction which is somewhat doubtful, but taking the mean of Row-
LAND’S and GRIFFITHS’ values as the most probable at present, we obtain at 15° the
following values :—

TasLe X VI.—Equivalents in foot-pounds at Greenwich, at 15°, referred to the
“ Paris ” nitrogen thermometer.

ScHUSTER and

LE. ROWLAND. MIcULESCU. GRIFFITHS.
Jou D GANNON.

775 778:3 7766 780°2 779-7

If we remember that RowLanp’s number referred to the “ Paris” nitrogen
thermometer would probably be smaller by one unit, we are struck with the fair
agreement there is on one hand between the results of JouLE, Rownanp, and
Micuxescu, and, on the other hand, between GRIFFITHS and ourselves. As far as
we can draw any conclusions from the comparison, it seems to point to a difference in
the value obtained by the electrical and direct methods. Whether this method is
due to some remaining error in the electrical units or to some undiscovered flaw in
the method adopted by Mr. Grirrirus and ourselves remains to be decided by
further investigations.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 463

APPENDIX,

We give the observations and the calculation of the result of the experiment on
20th May, which is typical of the other experiments. The symbols used are the same
as those on pp. 421 and 422.

(1.) Lhe Electromotive Force.—Comparison of the Clark cells.

Before the experiment After the experiment
Time: 11 43m Time: 12) 16™
Go ie 0G ts = 177-23
| I—Standard = —3:2 (a) I.—Standard = — 40 (ag)
Wen hc aa 46 Nene eee ees
| Te ee Se Ube 6 eee este OS
Ve a ee i= » = - O8
Vvi— (zc) V— 5 = = Id)
Vii ee aes S07 Wie 5 SS Te
VII— — sg = SO: Vi— = 3 -= e708
VIll.— 55 = —01 VIIl.-— . ed:
Ix.— eS ee oe Ix.— pS oe
x.— eo) x.— » = + Ie
5 = —09 s& = —101
I.—Standard = — 4:0 (4,) I.—Standard = — 4:0 (a;)
po = UPA (2
[Ser tea (ies Were eX i= 14-0) etl == (Ie Mee Xe = 15-0
| Set 2.—(. +I. +...4K)= +20] Set2.—(.—I.+...4+K)= +132
I.—Standard= — 3:2 (a) I.—Standard = — 4:1 (a)
te = 172-12 | tg = 17°17
Time: 11! 53" | Time: 11 06™

The observations in the column headed “ After the experiment” were made from-
below upwards, the interval between 11" 53™ and 12" 06™ being taken up by the
experiment on the equivalent. The correction due to temperature change here is

5 X (a3 — a, + a, — a.) = 05.
Hence
Set (1) + Set (2) = 20 standards + 6°6 (see p. 422).

As the total resistance of the circuit differed very little from 10,000 ohms, and the
electromotive force of the LecLANCHE used was 1°45 volts, the correction to the
battery of Clark’s becomes 6°6 X 1:45 X 107-* = 0:0010 volt.

464 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

The average temperature of the Clark cells during the above experiment was 17%5.
Hence the electromotive force calculates out as follows :—

2 0iClaxkecelistatw5 4Cn ee hee 28°6800 volts.
Correction to 17°°15, taking the change ot erie

each cell to be 0°00115 volt per degree a
Correction of battery to standard . . . + 00010

32

Electromotive force of battery. . . 28°6317 ,, (E).

(2.) Total Water Equivalent.

Weights.
@alorimeter/+-\coil 52-55 5 eee eee ee Ome onarns:
Calorimeter + coil+-water ... . . . . 41781°54 ~,,
(At 12 45.)
Hence

iWatenan Gs i cepts ob co ee AO

Evaporation correction = 05

Buoyancy 55 = 1°58

Equivalents eri SG

Total water . . . 1540°39 (W).

The equivalents include 27°02, the constant value throughout all the experiments
(see p. 441), and 0°34 for the part of the thermometer stem above 12°, which was
immersed in the water.

(3.) Weaght of Silver Deposit.

| | thts Ser | |
Observed | | eae | eatometes 3
Date of ‘oht | Lempera-| Baro- oes correction | Corrected | jroo Ditfer-
Weighing.| WSS" ture. meter, | Ccrrechon | in milli- | weight. i ence.
=P) @eGhein, | | in milli- seep e
| grams. o ; |
| |
lt ze | | |
May 19 | 64263487 17:0 749°7 +:040 +076 64263603 | 263612 |
» 20 263510 169 | 749:9 +038 | +074 263622 | ~~ 62034.
» 23 | -*883859 169 | 7582 +°038 +013 "883910 | .eon9n3 | :
ye 8} 883943 | 17-0 758°2 +040 +013 883996 ; |

The silver deposit was thus 0°62034 gram. (W).

DETERMINATION

The weighings are supposed to be correct to *1 mmillim., and in the mean of any two

OF THE SPECIFIC HEAT OF WATER.

observations the second decimal may be retained as having some significance.

temperature and pressure corrections were calculated for safety to 001 millim., and
it was found more convenieut to carry out the calculations to that place, cutting off

the unnecessary figure at the end.

THE temperature was measured by subdividing a thermometer division of 0°02 to

(4.) Temperature Observations.

the 100th part by the eye; each reading is probably right to 0°-0004.

Time. Temperature. Time. Temperature.
h. m. h. |
11 48 17: 2200 12 11 | Main cirenit broken
9 30 Auxiliary circuit made
50 one 12 19-7512
1 2312
| : 3 24,
2 60
: 4, 56
3 96 5 80
4 24.32 6 9
BY 80 f
: 7 7616
6 2516
8 40
7 60 9 76
8 2604
20 96
2 2 1 | 7712
12 00 86
1 Circuit made 2 | 36
si 3 56
4 | 80
|

By the methed of least squares, we obtain from the preceding observations :—

Mean rate of rise per minute in the first period

Temperature at 12" 1™

Mean rate of rise per minute in ie ‘third Daried
Temperature at 12512 .

0°:00406
17-2722

0°'00227
19°°7508

The readings of the centiampere balance at equal intervals of time were

or a mean reading of 61°26.
MDCCCXCV.—A.

62°06
61°86
61°46
60°56

60°36,

3 0

466 PROFESSOR A. SCHUSTER AND MR. W. GANNON ON A

The calibration of the balance immediately after the experiment showed that 1 divi-
sion = 0°00212 ampere, so that the mean value of the current flowing through the
measuring coil in the final period was equal to 0°12987 ampere. From this and the
data: resistance of coil = 31°32 B.A. units, 1 B.A. unit = ‘9866 x 10° C.G.S. unit,
J. (assumed) = 4194 X 107, total water = 1540°50 grams. ; we easily obtain that the
rise per minute due to auxiliary current = 0°°00484. As the observed rise per minute
was 0°-00227, the cooling per minute in the final period was equal to 0°:00257.

We require to know the temperature at 12 h. 11m. Since the cooling per minute
at a mean temperature of the calorimeter of 17°°25 was — 0°:00406, and at a mean
temperature of 19°76 was + 0°:00257, a slight calculation will show that the cooling
per minute at 17°27 was equal to — 0°-00401, and at 19°°75 was + 0°'00254.

We are now able to calculate the temperature rise.

Temperature at 12 h. 12 m. 5 = LEO
Rise in temperature during 55 seconds due to
piallipia AMES SMS os a eon) a love "0044
Coolinestors minutes sme a) ee ae 0025
Therefore temperature at 12h, llm.. . . . = 19°7489
Calibration correction at this pomt. . . . =— 0°0054
Therefore corrected temperature at 12 be 11m. = OrAag
ANeanoseauins ais WAIN I 5 gg a 5, ee IY
Calibration correction at this pont. . . . = — 0°0050
Therefore corrected temperature at 12 it ima: =p eZ OMe
Difference of these temperatures. . . = RAoe
To this difference we must add the following corrections :—
(a) For the cooling during the time the main cir-
cuit was closed, 10 x 3 (:00254—00401) = — 0°:00735
(b) To correct for the wrong interval of the
Baudin thermometer — 0°00135 xX 2°47 . = — 0°:00333
(c)Ror thetemercent stem.) 3 3) 5 e c——OmOOlZG
Ka) n(0) ta(C)is a raenns | ee ae ee =— 0°:0094
Therefore corrected rise in temperature = 27-4669()

J = wK/(001118 We) = 4°1807.

DETERMINATION OF THE SPECIFIC HEAT OF WATER. 467

Tue following Table includes the Values of the Quantities necessary for the Final
Calculation of the Heat Equivalent in the Experiments of the Third Series.

| Date of Wet oe BIGao- Total water | Temperature Welle aii di nileni
. eposit in motive oe ne on mercury | temperature
| experiment. im grams. change.
| | grams. force. 2 2 thermometer.| of water.
| 13th May . 0755938 28°6349 | 1543-07 2:2200 41824 x 107 18°3
| Lith ,, ‘ 55881 286330 | 154032 2°2224, 41807 11-2
20th ,, : “62034 28°6317 1540°39 2:4669 4:1807 185
| Sth June . 55684 | 286050 | 1540-41 2°2125 41804 19:0
9th ,, 3 55780 285878 153434 2°2251- | 41776 19:3
15th ,, : 55952 285418 | 1539-91 2°2180 41822 | 21°3

ON,

[ 469 |]

XII. The Oscillations of a Rotating Ellipsoidal Shell containing Fluid.
By 8. 8. Hoven, B.A., St. John’s College, Cambridge.
Communicated by Sir Ropert S. Baur, F.R.S.

Received January 18,—Read February 7,—Revised March 28, 1895.

Introduction.

Ty a paper published in ‘ Acta Mathematica,’ vol. 16, M. Fonie announces the fact
that the latitude of places on the earth’s surface is undergoing periodic changes in a
period considerably in excess of that which theory has hitherto been supposed to
require. This result has been confirmed in a remarkable manner by Dr. S. C.
CHANDLER in America (vide ‘ Astronomical Journal,’ vols. 11, 12), who, as the result of
an exhaustive examination of almost all the available records of latitude observations
for the last half-century, has assigned 427 days as the true period in which the
changes are taking place.

The old theory, based on the assumption that the earth was rigid throughout, led
to a period of 305 days, and M. Foute proposes to account for the extension of this
period by attributing a certain amount of freedom to the internal portions of the
earth. The earth he supposes to be composed of “a solid shell moving more or less
freely on a nucleus consisting of fluid at least at its surface.” The argument advanced
by M. Fouts in favour of this constitution of the earth, namely, the independence of
the motions of the shell and the nucleus, appeared to me to be unsatisfactory, and I
therefore proposed to myself to test the validity of it by examining a particular case
which lent itself to mathematical analysis, namely, that in which the internal surface
of the shell is ellipsoidal and the nucleus consists entirely of homogeneous fluid.

The principal axes of the shell and of the cavity occupied by fluid are assumed to
be coincident, and the oscillations are considered about a state of steady motion in
which the axis of rotation coincides with one of these axes. It is clear that a steady
motion will be possible in this case, and that such a motion will be secularly stable
in the event of the axis of rotation being the axis of greatest moment for both the
shell and the cavity.

The problem was originally treated by the analysis used by PorncaRE in his

memoir on the stability of the fluid ellipsoid with a free surface (‘ Acta Mathematica,’
25.1095:

470 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A

vol. 7). This analysis reduces the determination of the motion of the fluid to the
problem of finding a single function ¥, subject to certain boundary conditions, which
in our case take a very simple form. In the case where the surface of the fluid is
ellipsoidal, it is found that, when the system is oscillating in one of its normal modes,
w will be expressible as the sum of a series of Lamé products of a single order 7 only.

When n is different from 2, the types of oscillation are such that no disturbance of
the shell is involved, and a period equation for the oscillations of the fluid may be
deduced in a manner similar to that given by Porncarn.

The types of oscillation corresponding to n = 2 demand exceptional treatment, in
consequence of the motion communicated to the shell when they exist. The fluid
motion, however, is found to be such that the molecular rotation is everywhere the
same. Mr. Bryan has suggested to me that this circumstance may be made use of
in order to treat the oscillations which involve motions of the shell by a simple
analysis previously employed by GREENHILL (‘ Proc. Camb. Phil. Soc.,’ vol. 4, p. 4)
which does not involve Lamé functions. To facilitate the reading of the paper, the
results are first deduced by this method, and the Lamé analysis by which they were
originally obtained is reserved for an appendix.

The oscillations under consideration are found to be of two types. One of these
corresponds to an oscillation previously discussed by Hopkins in his “‘ Researches in
Physical Geology” (‘ Phil. Trans. 1839). This exists only in consequence of the
contained fluid, and in it the oscillations of the sheil are similar in character to the
“forced” nutations of the earth produced by the action of the sun and moon. In
the other type the motion of the shell is closely analogous to the motion of a rigid
body when slightly disturbed from a motion of pure rotation about a principal axis,
and, in fact, identifies itself with such an oscillation in the event of the inertia of the
fluid becoming negligible.

On applying the problem to the case of the earth, the latter mode is that on which
the variations of latitude depend. The period, however, is found to be shorter than
it would be if the fluid were solidified, and thus, in this particular case, M. Forte's
results are contradicted. It appears to me to be highly probable that any such
freedom in the interior of the earth as that supposed by M. Foie, provided the
surface does not undergo deformation, would have the effect of reducing, instead of
extending, the period, and the true explanation of the phenomenon is probably that
given by Newcomps (‘ Monthly Notices of the Royal Astronomical Society,’ March,
1892), who shows that the elasticity of the earth, as a whole, would have the effect
of prolonging the period.

§1. The Period Equation.

Let us refer to rectangular axes coincident with the principal axes of the ellipsoidal
cavity.

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 471

Let a, 8, y be the principal semi-axes of this cavity; A, B, C the principal
moments of inertia of the shell.

Suppose the motion of the fluid at any instant consists of a rigid body rotation
with angular velocities & y, € about the axes of the ellipsoid, compounded with the
irrotational motion consequent on giving the shell additional angular velocities
GeO, Ox.

The velocity-potential of the irrotational motion will be

Be
Bare oe

cea ca
e+ Be”

Y yz 5 200, + -

The velocity-components will therefore be

EN Vises GH mace end aril
US ee a raging Ostrard Saty Zn |
Bg P=
cama s+ ar ee eRe (1).
pee poeta =, — ay + yé |
B+ ese ie

Hence, if hy, hy, h, be the components of angular momentum, and M denote the
mass of the fluid, p, its density,

’ 1
=A(O) + 4) + [[[orde dy dz (wy — v2) =A (0, + £) $y |
+ 3M (6° +) & !
hy = B(Q,+ 7) + [|r de dy de (uz — wx) = B(O, + 9) + # = Og (2)
+ 3M (7° + 2’) », |
bs : ae sé e (2 — By
hs = C(O; + f) + [ [fox de dy dz(vx — wy) = C (9, + €)+ 5M e+ Os |
!
+ IM (2 + B)L j
where
p= (eowr), vse og) 6 6 ies ss (OO)

If the system be disturbed from a motion of pure rotation, with angular velocity a,
about the axis of z; & 7, 0), Q,, Og, will all be small quantities, while ¢ will be
approximately equal to w, and hence, on omitting small quantities of the second order
and putting ¢= w» in small terms, the equations of angular momentum, viz. :—

hy — her +-heq = 0 | [ p =O+¢
hy — hep + hyr = 0 iga) qg=O+7
hs — Ing + hor = 0 r=O,+¢

472, MR. S. 8S. HOUGH ON THE OSCILLATIONS OF A

become

A() +405 =A pn +1M(#+ y)é

= [BOQ +n) +H FIM (+7) 9 [oF (M-+7)[C+ MM (e+ 6 )]o=0

~ =o

= (+ Sibi 70, + 3M (8+) é]o=0

B (Qs +) + wey Gs + AM (9 $0) 7

C(O, +) + eM Go 0, + IM (2 +

HELMHOLTz’s equations of vortex motion are

Qa? 28?

Hr er eee E= 0.

Hence, if we put &, 7), 0), Q:, Q;, € — w each proportional to e”, and introduce,
for brevity, the notation A’=3M (6? + y’), &

s[atreet)a ra tard )

@
Tests each ala

ise is Be -/
lc $O AWE =| 0, (4).
By 7a NOH caeeila col
+(C+0'-A-a)£-“[(B 4p 5=%) 0, + (B+ B)n] =0,
qa Sg Me a ae
ae ar tee Oa eg ee J
03, = 0 C=o.
Eliminating 0,, ©), € y, the period equation is
| AL B—» | Ate DY ae? we , Rel yoy. Dy
pe [at+oS-]. CHO —B—p =, M(A+A), C4+C—B-B |
| —— fa\ sibert —M Cees E Vous) A EEIAU, =
Re Apo = (ees C40'=A=A', (B4B’) LE
Qo? nM =i
| 0, top? Bs > 0,
| — 28? ri
B+? 0, 0, ay

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 473.

On expanding and arranging according to powers o, X, this determinant
reduces to

MTA (B° + y*) + v (8 — 7°) [Ble + 7?) +e (2 — 7°)
— ot? (a? + y*) (BP + 7’) (B — C — v) (A — C — p) + 4028? (A + v) (B+ B)
ey (Be Cea Ane 13]
=o {4028? (B—'C — yp) (A —€ = a) 05 ks Sete ee Se I):

§ 2. Case of Shell without Inertia.

If the shell be so thin that we may neglect its inertia compared with that of the
fluid, we may put A = B = C= 0, and equation (5) then becomes

(22 — yf) (B= 7) X= wR? fy — 3 (2 +B) YP + dB") + dole’ = 0 (6);

when the system is symmetrical about the axis of rotation «? = 6, and this equation
reduces to
AM (a2 — y2)? — wd? (a2 — y?) (5a? — 2) + 4o!a2B? = 0,

a lea ala i ee ess eet rt)

These are the same as the values obtained by Bryan (‘ Phil. Trans.,’ 1889, A,
p- 208), for the case of a spheroid whose surface is free. As is there indicated, the
modes of oscillation corresponding to these periods are such that the surface of the
spheroid maintains its shape, but changes its position. Such oscillations wiil,
of course, not be affected by supposing the fluid contained in a rigid shell without
inertia, and we might have expected to obtain the same values for the periods, when
the figure of the shell agrees with a possible figure of equilibrium of the fluid rotating
freely. :

From (7) we see that the roots, if real, are positive; in order that they may be
real, we require that 9a” — y? and a — y? must have the same sign.

Hence a necessary condition for ordinary stability is

the roots of which are

vy > 9a" Nor “V7 <a
1.€., y must not lie between « and 3a.

Returning to the case where « + £?, in order that the roots may be real and
positive, we must have

CHG = Gai 82) > 0.

(2) y* — 3 (a? + B’) y’ + 5a°P? > 0.

eet) yt 08 Bem Gar By: a?) (ye 8) Os
MDCOCKCV.—A. 3 P

474 MR. 8. S. HOUGH ON THE OSCILLATIONS OF A

The 1st condition requires that y? should not lie between a? and £?.
Now
yi — 8 (0? + B) 7? + 5028" = (7? — 3a?) (y* — 88") — 40%?
= (3a — y’) (88? — y’) — 402°.

The 1st form shows that condition (2) is certainly satisfied if
ye > ba” and also.) >) 582

The 2nd shows that it is satisfied if y? < a and < f”.
Lastly,

{yt — 8 (02 + B’) 7° + 5028}? — 16258" (9° — 02) (7° — B)
= (y? foe a”) (y? aan B’) fy! — & (a? + B?) y + 9a°B?} + 4 (a? pt 8’)? y4
(y? — a2) (9° — B) {(y? — 502) (y* — 5B") — 16028" + 4 (02 — BY 4
=, or

(a? — y*) (B® — y?) {(5a? -- y*) (58? —y?) — 160787} + 4 (a? — 6)?

Hence condition (3) will certainly be satisfied if y? > 9a? and also > 98%, or if
y? < @ and also < B’.
Thus the roots of (6) will both be real and positive if

y<a andalso <8,
or if
y>3a andalso > 3p.

These conditions are sufficient, but not necessary, to ensure stability; the neces-
sary conditions are given by the inequalities (1), (2), (8).

The analytical conditions here discussed are approximately realised in the case of a
liquid gyrostat (vide ‘ Nature,’ vol. 15, p. 297) mounted on gimbals in such a way that
the centre of gravity is held at rest. The inertia of the gimbal-rings will be unim-
portant when the rotation is rapid, and, if we may also neglect the mertia of the case
compared with that of the fluid, the gyrostat will be stable when set rotating about
its least axis; it will also be stable when set rotating about its greatest axis when
this axis is, at least, three times as great as either of the others. It will, however,
certainly be unstable when set rotating about its mean axis.

§ 3. Approximate Solution of the Period Equation.

Let us for the future suppose that the cavity which contains fluid is approximately

spherical, so that ~— » Bea
Y

ave small quantities.

en

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. AT5

Suppose

Merve Bay
=— €1,
wf Y

= €9.
From (3) we have
vp (a? — y*) =n (8° — y’);

therefore, if we neglect squares of €,, &,
B/e, = v/e, = gC say.

In the case where the thickness of the shell is finite compared with its linear
dimensions g will be a finite quantity; when the shell is thin g will be large, and
when the fluid nucleus is small compared with the dimensions of the whole system q¢
will be small, the densities of the fluid and of the crust being supposed comparable
with one another. In all cases qg will be positive.

If e, « are each equal to zero, the equation (5) becomes

ABM —[(C — A)(C — B) + AB] No? + (C — A\(C — B) ot = 0,
or
(2 — w) [AB — (C — A)(C — B) o?] = 0.

Thus we obtain as a first approximation to the roots

SOLAN Es
Ye es c He B) w.

Next let us retain first powers of €,, €, in (5); this equation then becomes

MAB(1 +e, + «)
= a2[(C — A) (C —B) (1+ 4 +4) + AB(1+ 24 + 26) + g(ACe + BCe)]
+ ow (1 + 2e, + 2e,)(C — A + qe) (C — B+ gCe) = 0,
or
02 =a?) (AB — OC —AC— Ba?)
+ «, [ABA — wd? {(C — A)(C — B) 4+ 2AB 4 qAC}
+ w*(C — B) {2(C — A) + gC} }
+ «, [AB — wd? {(C — A) (C — B) + 2AB + qBC}
+ of(C—A)(2(C—B)+gC3]=0 . (8);
dividing by ABh* — (C — A)(C — B)o”’, and putting \*? = o? in the terms which

contain €, or €, as a factor, we obtain as a closer approximation to the root \* = o’,
3) Pw j

476 MR. S. 8. HOUGH ON THE OSCILLATIONS OF A

ee (Ce Jue BEE C (Cl Biv)

2 = ow./1 —

o*| a —(C— A) —B) }
/ See VB) = ABH Oa Bae)
2 — (CA) (Ci) ia
—— oS (Ei) as es) (lg) a? (ll > 2K) saves 1) ey i een)
therefore
A= +o0(1 + E).

(CAC)
AB
terms, an approximate value of the second root, correct to first powers of €, €, is

given by

Again, dividing by \? — ? in (8), and putting \? = #* in the small

gc(C — B) — gA

(C — A)(C — B)
AB

«(C= A= B)
2 9 AB
ABW — (C — A)(C — B) w& = — ea?

—1

(C= a) = pe ae)

— €0~ (© — A)(C —B) a ?
AB
or
a SC Say ces G = Craw
Oak Cap
J pe pen aa ee 8 (a)

to the same order of approximation.

This approximation involves the assumption that ¢,, €, are small compared with
GC =A Cr-=B.

; the approximate value of the root will, however, be the same if we

iNew ts B
C—A C—B
suppose —~— , —=,— to be small quantities of the same order as «,, &.
pp A B q i
Let us put
OESROS, CE
Ara Se aS aon?

Retaining only finite terms in (5), we obtain as a first approximation to the roots
? = w and dh? = 0; also, the independent term in (5) is a small quantity of the
second order in kj, kg, €, € Thus the root which approximates to \* = 0 will be of
the second order. Regarding )* as of the second order, and retaining only terms of
this order in (5), we get

2, [4ABa2B?] — w?. 4028. {Bey + Ce} (Ax, + gCe} = 0,

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. A477

or

= ow. (kK; + Ge) (Ky + Je)

to the same order, and this is the value obtained above (10).

§ 4. Application to the Case of the Earth.

The nature of the two types of oscillation will be found fully discussed in the
Appendix. It is there shown that the oscillation corresponding to the root w (1 + E)
is that previously examined by Horxtns in his ‘ Researches in Physical Geology,’
whereas the second type is analogous to the motion of a rigid body when disturbed
from a motion of rotation about a principal axis.

If the Earth could be regarded as a system such as we have been considering, we
see that in addition to the ordinary Solar and Lunar Nutations, which would be of
the same nature as when the Earth is supposed solid throughout, there might exist
certain free nutations the amplitude of which could only be determined by observa-
tion. If the amplitudes were sufficiently large, the oscillations corresponding to the
root \ = w (1 + E) would render themselves visible in the same way as the Solar and
Lunar Nutations, namely, by small periodic displacements common to all stars. The
period of these displacements would be 1/E sidereal days, and a knowledge of it would
enable us to determine EH, a quantity which depends on the form of the internal
surface and the thiokness of the crust.

The oscillations which correspond to the root \ = w/{(K, + qe) (kK, + Ge)}
would manifest themselves in a different manner. They are, in fact, similar to the
“Eulerian” nutation (vide TissERAND, ‘ Mécanique Céleste,’ vol. 2, p. 494), and will
involve a small periodic change in the latitude of places on the Earth’s surface, as
found by meridian observations of a circumpolar star, this change taking place in a
period of {(k, + qe) (Ky + qe) }~* sidereal days.

Now it appears probable that in oscillations of long period, such as Precession, the
effects of fluid friction would be to make the internal fluid move with the crust
as if rigidly connected to it (TisszRAND, ‘ Mécanique Céleste,’ vol. 2, p. 480, or
Lord Ketytn, ‘Popular Lectures and Addresses,’ vol. 2, p. 244). Hence, if A,
A, €& be the principal moments of inertia for the Earth as a whole, supposed
symmetrical about its axis of rotation, the Theory of Precession will still enable us

to determine the value of es aS go5-

cy
But, if we put x, = k,, €, = «,, and denote by M the mass of the fluid,

C€=C+2M2=C {14+ q(1 + 24)},
A=A+G5M(?+y)=A+4qC(1 +).

478 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A

Therefore,
G-A_ CHAt+qy _mt+ae
G ~ Cat+q+2%e)” 144

very nearly.
Therefore the period in which the latitude variations will take place is

sidereal days =

€ Dy crt f
eee aT ee sidereal days ;

when the Earth is supposed solid throughout, this period is

ea sidereal days.

We thus see that if the Earth consisted of a rigid shell containing a homogeneous
fluid nucleus, the theoretical period of 305 days, calculated on the assumption of the
Earth’s rigidity throughout, would be diminished in the ratio 1: 1 -+ qg, where gq is
an essentially positive quantity, whose magnitude increases with the size of the
nucleus.

In order to form some idea of the magnitude of this effect, let us suppose that the
fluid and the crust have the same density p, and that 7, 7, are the mean radii of the
fluid nucleus, and of the Earth as a whole.

We then have approximately

p=v= ampre, and C = ap (7° — 7”).

Therefore,
pall iy havent AN 2
Le €,C iH Tae
7? 1 / » 5
1 as ——— = —(—]),
pu Tee I 0) : ()

and the period will be diminished by les i xX 305 days.
»)
Taking the mean radius of the Earth as 4000 miles, we obtain the following table,
where the first line gives the thickness of the crust in miles, and the second the

diminution of the period in sidereal days :—

Thickness of crust in miles . 2000 1000 500 250 | 100

Diminution of period in days .

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 479

Now, although in the light of Professor Newcoms’s work (‘ Astron. Soc. Monthly
Notices, March, 1892), it appears probable that this effect would be modified by the
elasticity of the Crust, it could scarcely be reversed if the fluid nucleus were of any
considerable extent. We must, therefore, conclude that the observations on Jatitude-
variation, so far from establishing the existence of a fluid interior, as supposed by
M. Forts, rather tend to confirm the views hitherto maintained by physicists on
other grounds, that there can be no internal fluid mass of any considerable extent.

APPENDIX.

TREATMENT OF THE PROBLEM BY LAMé& ANALYSIS.
§ 1. Equations of Motion of Flud.

Let us refer to rectangular axes rotating with angular velocity w about the
axis of z. The fluid is supposed to have no motion relatively to these axes other
than that due to the small oscillations with which we are dealing.

Let u, v, w, be the velocity-components at any point 2, y, 2 relatively to these
axes : we shall, as is usual in small-oscillation problems, neglect squares and products
of the small quantities u, v, w.

The actual velocity-components parallel to the instantaneous positions of the moving

axes will be
U—wy, V+oxr, w,

and the differential equations of motion of the fluid are therefore (Basset, ‘ Hydro-
dynamics,’ p. 22)

ee ca al -+),
ie MO Vv, if
ot w(u — ay) + on = a - +)

: Be Hie zi)

at By ea
where V, is the gravitation-potential of the forces to which the fluid is subject, p the
fluid-pressure, and p, the density.

Putting
eV Anineee(sbo) oe as ae

the above equations reduce to
du/ot — 2ov = oys/0x
Bless Wo — MEN oo Se eo eo 8 0 (2)
ow/ot = 0y/ 02

480 | MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A
We have, in addition, the equation of continuity
Ot 0x 4-500) 04 OW) 02z-— 10) ay. hae uy Eee)

Equations (2), (3) are sufficient to determine u, v, w, p, subject to certain boundary
conditions.

From (2) we obtain

we oh, eee ov
|e ee | Pi rr an Oe
e el, ¢¥ Ow
ap +- 10°| v erah a 2 A b (4).
ES ae |
ot? ~ oveé J)

> OW 0
= EOF ae = (Vth); where = tite
or, by the third of equations (2)
9 Opp oe D)
de a + ap (Vb) = 0 st 2 5 Selah TERRE aes

This is Porncar®’s differential equation for the oscillations of a mass of fluid about
a steady motion of pure rotation.
Let us now suppose that the system is executing one of its component harmonic
vibrations.
Assume that
ens v= v,e™, W i= Wier

y= We.

and

Putting these values in (4), (5), and dividing out by the time factor, we get

eotece, - OWT ov
i PER. {id oe + 20 ~ |

oy
Lf ove oe
= N= — 20 —= eS oll ee 6
Ui pepe {in ay on r (6),
1 ah |
WW), = = ae
% in O82 J

while y, satisfies the equation

tn 4 Oy do?) Oy
met ga +(1- ) ao). 2 a

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 481

§ 2. The Boundary Conditions.

The position of the shell at any instant may be defined by means of three coordi-
nates, 6,, 8, 3, which denote the small angular displacements, about the axes of
reference, of the shell from the position it would occupy in the steady motion.

The displacements parallel to the coordinate axes of the point of the shell, whose
coordinates are (a, y, 2), are

— yO, + 265, — 26, + «6s, — «0, + y0).

If cosa, cos, cosy be the direction cosines of the normal to the undisturbed
surface, the normal distance between this surface and the displaced surface will be

(— 8; + 20.) cos a + (— 26, + «6;) cos B + (— x8, + y,) cosy
= 6, (y cosy — zcos B) + 0, (z cosa — xcos y) + 4; (wcos B — y cos a).

The condition to be satisfied at the boundary is that the rate of increase of this
length must be equal to the component velocity of the fluid, relative to the moving
axes, in the direction of the normal to the undisturbed surface. Now as these rela-
tive velocities are all small quantities whose squares we are neglecting, it is
unnecessary to distinguish between the velocities at the disturbed and undisturbed
surfaces ; thus, at the latter surface we require

ucosa+vcosB+weosy = 4, (y cos y — z cos B)
+ A, (2 cos a — x cosy) + 6, (« cos B — y cos 2).

Putting 0, = @4e™, &c., and omitting the exponential factor, we obtain

u, cosa + v, cos B + w, cosy = 1A [ 0, (y cos y — 2 cos B)
+ 6, (zcosa — «cos y) + &, («cos B — ycos «)];

or, putting in the values of u,, v,, w,, W, from (6),

r Wy ow Ory 4a*\
aC ee cosa + By CE a0 ee “08 y ( |

rn
2a 0
eee cos a — cos

= [9 (y cosy — zcos B) + 0, (z cos a — x cosy)

10/5 (a COS) B'—YICOs &)I| “MEI Se Bt AES BITES iE AE Vig:
Let us now put
Ae :
eS aie,

MDCCCXCV.— A. 3 Q

482 MR. 8. 8S. HOUGH ON THE OSCILLATIONS. OF A

Corresponding to any series of points whose coordinates are denoted by (a, y, 2),
we shall obtain a new series whose coordinates are (a, y, 2’), which will be real or
imaginary according as )? is greater or less than 4w°. We will take as the standard
case that in which \?> 407.

If the point (a, y, z) trace out any surface whose equation is f(x, y, z) = 0, ee
corresponding point(«,¥,2’) will trace out a new surface whose equation is f(«,y,72') =
The part of this latter surface which corresponds to the real part of the nae
SF (&, y; 2) = 0 will, however, be purely imaginary if )? < 4?.

If (cos a, cos B, cos y), (cos @’, cos 8’, cos y’) be the direction-cosines of the normals
to the two surfaces, we have

cos « : cos B’ : cosy’ = of/ ox : of / dy : of / oz’
= of / dx : of / dy : z (of / dz)
= cos a : cos 8 : 7 cos y.
Substituting in equations (7), (8), the differential equation for yp, takes the form
O°, Oa? 4 O's, Oy? + Oru Oz> = Oke 1. 4e) seu:

while if f (a, y ,z) = 0 be the equation to the undisturbed boundary of the fluid, y,
must satisfy the equation

11 cos a! ae cos 8’ + cos 7’ | — 20i {F* c0s a! — WF cos 6}

he Gs cos y’ — 72’ cos B')

a cee + 6, (72! cos a! — = cos ¥) |

_+ 6,' (w cos B’ — y cos @’)

(10)

at the surface f(a, y, z’) = 0.
The problem of finding the motion of the fluid is thus reduced to that of obtaining
solutions of equation (9) consistent with the boundary condition (10) at the surface

J Gh Oh C2) = ©
§ 3. Case of Ellipsoidal Surface.

Hitherto, no assumption has been made as to the form of the surface of the fluid.
Let us now suppose that it is given by the equation

a oP ee eee

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 483

that is to say, that it is an ellipsoid whose principal axes coincide with the axes of
reference.
We will take as the standard case, that in which

: po > & 1b S10.
Put
poesia)

The equation to the auxiliary surface f(a, y, 72’) = 0 becomes

x AE ae
aN a a eta hae (EO)

a?
S55
p

Let us now introduce two sets of elliptic coordinates (p, , v), (p’; »’, v’), connected
with (x, y, 2) (x, y, 2’) respectively by the equations

2B yy _V@=P)F=*) ee ESE =e)
oi Meson UCD Ves = ~Veam 9 ve
& pv’ y es VJ (uw == b) (8 ize y’) Pa a Vv (6? za pb?) (c? 7S y’)

p’ => be’? /(p2 — 0?) ne by/ (2 a: b) ’ J (p” os c’) ES VEL (12),

p’ will be equal to p for points which lie on the surfaces (A) (A’), but not otherwise.
Let us also put

X=alp, Yayo —2), Z=2/Mp?— 2) =2/V/(e? — ©), « (13)
for points on these surfaces; so that X, Y, Z are subject to the relation

pee 1 Dee Bee eels. (15),

X, Y, Z may therefore be regarded as the coordinates of a point lying on a sphere
of unit radius.
Denote by R, M, N three conjugate Lamé functions of the elliptic coordinates
p, », v, and by R’, M’, N’ three similar functions of the coordinates p’, p’, v’.
A form of solution of equation (9) convenient for satisfying boundary conditions at
the surface (A’) is
Ui SARIN frie tt tue.-lcceeh. toed. Giemsa (4)

The effect of the fluid on the motion of the shell will depend only on the fluid
pressure over the surface, and this by (1) will involve the value of y, at the surface.
3Q 2

484 MR. S. 8. HOUGH ON THE OSCILLATIONS OF A

To find the value of y, at the surface (A), we may transform the expression (14) for
ws, first to the surface (B) and then from (B) to (A).

Now, by a known property of Lamé products (vide Heme, ‘ Kugelfunctionen,’ vol. 1,
§ 89), if M, N be two conjugate functions of order 7, the product MN at the surface
(A) will transform into a surface harmonic of order » at the surface (B); and, con-
versely, any surface harmonic of order 7 at the surface (B), when transformed to the
surface (A), can be expanded in a series consisting of Lamé products with constant
coefficients, each of which products will be of the n™ order.

The same conclusions will hold for the surface (A’) and the sphere (B).

We can thus express the value of , at the surface (A) in terms of a series of
Lamé products, in which each term will be of the same order as that from which it
arises in (14).

The couples on the shell due to fluid pressure are

[[p do (y cosy — zcos £), {|p do (z cos y — « cos f), [|p do(w cos B — y cos y),

where do is an element of the surface and the integrals are taken over the whole
surface.
If P denote the perpendicular from the centre on the tangent plane to the ellipsoid

P
A) Cc d 1 = = =
( pan pr/ (p? = b?) (p? = c’)

~ G2) =P)

3

y cos y — 2008 8 = Py: | 1 1 | Pyz (c? — 02)

pP—e p? ap

and Pyz is proportional to

l/ (yw? — BP) (2 — 2) / (2? — *) (2 — ”) = IMN,,

where M,, N, are two conjugate Lamé functions of the second order. But, if MN be
any two conjugate Lamé functions different from M,N,, //MNM,N,do=0. For, if
we transform to the surface of the sphere (B), /do is equal to the corresponding
element of the spherical surface, and MN, M,N, transform into two different surface
harmonies.

Thus the only term in ys, which can give rise to any couple about the axis of « will
be the term involving the Lamé product M,N,.

Similarly the terms which can give rise to couples about the other axes will be of
the second order. These, as we have seen above, all arise from terms of the second
order in (14), and, in order to evaluate these couples, it will be unnecessary for us to
calculate any coefficients in y, other than those of terms of the second order.

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 485

§ 4. Transformation of Boundary Equations.

Let us now transform our boundary conditions to the surface of the sphere (B).
We can at once express the right-hand member of equation (10) in terms of
3 YQ CARS GI

, Ria: PX
costa — = ===,
p p
; Py Py
Coe a eP—F — /(—— #8)
Yai PZ
cae — /(p? — &)

where P’ has the same signification with reference to the ellipsoid (A’) as P has with

reference to the ellipsoid (A).
The right-hand member therefore becomes

= 8 r Ge YZ Po 0’ b? |
we. P | Se Se Wea "| C8)

Consider next a single term of order n in yy, say f= R’M’N’. We have seen
that M’N’ is expressible in the form ¢S,, where € is some quantity which does not
vary over the surface of the sphere (B) and §, is a spherical harmonic function of
degree n in X, Y, Z.

If dv’ denote an element of the normal to the surface (A’), we have P’ dn’ = p’ dp’,
and therefore,

a Ov OW Ov __ PY oy,
COS @ eee cos 8’ + -7 cos y' = Bie amen Oa:

Now M’, N’ are independent of p’. Therefore, when f, = R’M'N’,

a Sabiaill Wy ROR, / pa APs
cos a + = cos B’ “ee Ay cos y' = ry Ay ee mee Gp’: os 1) (iG):

Next let ds be an element of a line through (a, y, z’) whose direction-cosines are
( meg COS ces 0) , and which, therefore, lies in the surface (A’).

sin 7” sin y'’

Then

ae Ov, ae

Ox

and when y, = R’M’N’ = R’S,,

a :
é

aii 8
i — — (Rd .8, + Be (17).

486 MR. S. S. HOUGH ON THE OSCILLATIONS OF A

Now, the element ds lies entirely in the surface (A’), and corresponding to every
point of it there will be a point X, Y, Z which lies on the sphere (B). Hence, as
R’, « do not vary over the surface of the sphere, they will remain constant as we
pass along the element ds. Thus we have

0 ,
ay (R’e) = 0
and, therefore, from (17)
Ovi. Sh ey (eS OX) OS el aseneZ
oe oe Sle ae aU plas ae

But from (13) we see that

Cg ( COSIE\ = = Ee cosec vy’ on ) Gases
as Oi Tf any) p (p> — b) 1 pJ/ PB) uy
ONY 1 Yi A UTR (= =)= Pz , cosee PX , cosee ;
8 S(p—B) Os — /(p? 8) \sin 9] — p?/(p? — eae NES) %
OZ il Oza IE
SP (Cane?) mae
Therefore,
dy AY SEAR alll GiB ates 1 seein
0s pr/(p? — 2°) {x ay mek peosee Me
and
= — ae — ! oa — life Re | OS, |
cos a’ cos B' = sin y’ ~. = GaP) | aw Yay - (18).

From (15), (16), (18) we see that the boundary equation, on the assumption of the
form (14) for w,, takes the form

” 124’ 5, cS. }- Bui ZA’ = u waz ws ye)

oY ox
2 — 2) ee) ze
= = 946 Gp V0 + Oo ga IK + 0, }
VEGA AT Tg aA Ts em *Yy 0)
Now the function Xa a —Y = is itself a spherical harmonic function of order x,

OSn OSn . .
and both 8, and X = a7 Yi ax may be expressed as linear functions of the 2n + 1

independent harmonics of the nth order.

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 487

Omitting for the present the terms of the second order, if we equate to zero the
coefiicients of the 27 + 1 independent harmonics, we shall obtain a series of 27 + 1
linear equations connecting the 27 + 1 quantities A’ which occur with Lamé products
of order xn. These equations show that all the quantities A’ vanish except for certain
values of \ which satisfy the determinantal equation obtained by eliminating them.
The roots of this equation will determine the possible periods of free oscillation, and
when the system is oscillating in the mode corresponding to any one of these roots,
Lamé products of one order (7) only will appear in y,.

These modes of oscillation do not involve any motion of the shell, and it is evident
that they could not be generated or destroyed by any disturbance communicated to
the shell, if the fluid be free from viscosity.

We proceed now to examine more closely the modes which depend on terms of the
second order. As we have seen above, terms of different orders correspond to different
fundamental modes; and therefore we may for the future suppose that the second
order terms alone exist in Wj.

§ 5. Lamé Functions of Second Order.

A Lamé function of order 7 is a function R of one of the four forms

R = Es R = V/ p* Zee b? 0 P20; R = Vp" —¢ 0 lee R = J (p° a b°) (p> Ta, c’) . Psy

where P,, denotes a rational, integral, algebraic function of p of degree n, and R
satisfies the differential equation
PR

9 9 9 dh E 9
ap? see os ie) re el ep 1)p?>—B]R. (20),

(2° — *) (pe)

where B is a suitably chosen constant.
The Lamé functions of the second order are, therefore, the three functions

Ee PEC 5 (FO) Boe 2 (eA)
together with two functions of the form p? +8... ... .. +--+ + (22).

To find these latter functions, substitute in equation (20) with n = 2; we obtain
2 (p? — B) (p? — 2) + 2p? . (2p? — B — 2) = (6p? — B) (p? + A).
Equating coefficients of p®, and the terms independent of p, we get

—4(2+¢)=68—B, 26%? = — BB.

488 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A
Eliminating B, the values of 6 are given by
IP +2P+eAYB+R O=0....... . ap
Let us now apply the formule (16), (18), to the different forms of R’; take first

RB = pl/(p? —B).

At the surface

WN! = p'/ (un? — B). 0. / (8 — v2) = eo, xy = Dee’ ,/ (c? — B). XY.

Therefore, when y, = RMN’,

from (16)
ots cos « + 2 = cos 8’ ave os TCOStyA==ae es b?c’ ,/ (ce? —b*). xy |
|
from (18) + (24).
Be cos of — VF cos f= PP /(c®—V) (|

Similarly, when R’ = p’,/ (p” — c”),

M’N’ = __ be? ,/(c? — b?) XZ_ at the surface,

and

a cos a’ + a cos [sy a os cos y = fp’ es be! 4/ (62 ah 0?) XZ,

|
op (25) ;
cos! — SP cos p= P A/& —3(— YZ) |

and when R’ = V/ (p? — b”) (p? — c?),

M'N’ = be’ (c? — 6?) YZ,

MH eos a! + WP cos pi + PICOSLy a= eae 2iphiio Oier 1a a’ (c? — 0°) YZ, |
VF — BF) (e — (26)
Bp cos a! — SP cos p= PME) (c’? — b*) XZ i

Take, now, the form (22).
When

=(p*+ 8), RMN = (p? + B) (x + B)(’ + 8);

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 489

but p*, pw, v° are the three roots of the equation in «

therefore,

(2 — p*) (4 — p*) (a —-v?) =a(a— b*) (a — c?) — a? (a — b*) (2 — c?)
—ya(e—c) —#a(a — b*);
putting 2 = — @ in this identity, we obtain

RMN = (8 + p*) (B+ ) (8 +) =B(B + L*)(B +c’)
+ «(8 + 0°) (B+ &) + ¥B(B+ &) + 2B (B + 0b’),

and, therefore, at the surface

RMN = (X? + Y? + 22) B(B + 8°) (8 + &) + p?X?.(B +B) (B+)
+ (p? =P) VY. B(B +c) + (p? — &) 2.B(B +B)
=(pP + B)[(B+ (B+ e)X +8 (B+e)V +88 +2) 2),

or, since by (23) (8 +- 8) (8+ ¢*) = — B(B +’) — B(B + 0b’),
RMN = (p’ + B)[B (8 + ©) (Y° — X*) + B(B + B*) (2 — X*)],
therefore, when R’ = p? + f’,
MN’ =6(8' +.)(V—X)+ 6 (6 +0)(2—%),
and if p, = R/M’N’
OY cos a! ae ! cos B’ $+ Mh cosy

== AE ES Se G4) (VO) ee (Sse OCA 2) (2)

Cit gee ON Ny a p b2
7 8 ‘ cos B = EG ) 2XY {28 (6 qr @ ap (8 (8 ap Oks

or since f’ satisfies an equation similar to (23),

Oy Si Ca ator OY p> + B’ 2 1\ 7.2 fe
7 OnE = 7 cos B = Ea oy eee + B’)b?} . . (28).

Let us denote by f’,, B’z, the two values of @’, and assume that
MDCCCXCV.—A. 3 R

490 MR. S. S. HOUGH ON THE OSCILLATIONS OF A

yy, = Ay (p® SIF By)(e° ate By)(v? + 8) + Ay (p” a B's) (p? = B's) (v? + B's)
+ nO V0? Ba! (uw? — BM — 9")

B, / ph hp) , yp) f LO fh)
eee J (p? — 6”). pw! / (6? — pe”). (ce? — v”)

F be’ (ce ar ) V(e" Ne =e): V (pu? b*) (c” — p”). J (% —v"’)c*® —y"),

From equations (24) . . . (28), we see that (19) now takes the form

2A, {8 (8 + ¢%)(Y? — X*) + 61 (B1 + 8) (2 — &)} ‘
y.| + 2A2 (Ba (Bs + 07) (Y? — a + Bs (6, + 2) Gs > X2)}

2p?
i Be NOt Ie

YZ

ae a DGaH

~ 2A,(B +o) (p+ BY)KY—2A3 (B's + 6?)(p? +.B) XY
+ Bipv p? — b? (XK? — Y’) — B.pV/p?— e2 YZ

u +B, V(p?— 8) (pe =e) XZ_

Bagi GNy e—b - (ny. ; P |
= Ol) 5 YZ + Os Fag ZK + Op ee XY] (29),

pa
2o1

~ pa/(p? — B)

§ 6. Calculation of Coefficients in ,.
Equating coeflicients of Y? — X*, Z? — X? in the two members of (29)
A,B) (By + ©”) + A2B’, (B'2 +c”) + B, =0 | (30)
A,B’, (B', + 0) + AsB's (B's +P) =0|

Multiply the first of these by 2 and add to the second. Reducing by means of
(23) we obtain

62 = Aui(e2-b Ba) Aa(eo-b Bees 3 = =0. (31).

Multiply by = and subtract from the first of equations (30) ; then

A (p+ Bi) (C7 + Bi) + As (p° +.B) (? +83) + F(1-F)B =o.

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 491

But if we equate coefficients of XY in (29) we obtain

) 9 4 19, , , 19, , 9.91997
B, (2p? =) ay wt >. [Ai (p? + B’ i) (eC? + 8B) + As (p?-F B’,) (c? ++ B'.)) = — 77070’.
Hence
B, (2p? — 0°) +5 — 2p”) = — N°76',0%,
or
B, (2p? — 6°) 7? = — N?7?6'50°,
or
r20? ,
B,=- ae Pron OS = FPG WGN ID cae saath eh BON

Again, equating coefficients of XZ, YZ in (29), we have

ITT PEON a
B, i 2 1 2 B = h* 26 0) = DGG
~pia/ (oe? = ce) Nisei? TN? pa/(p? — &)
Debt USE wtp V(p 2 = 2297 Cn
(7D) 7 Be Tap * °0 9 9 Q\ 9
Os 7ip— Bye) tx Be 7ge TVG =P) = 4)
or, since p® — c? = 7 (p? — ¢”)
wi
B, (29* — ¢) — SB, (p? — 0") = NiO |
(33).

B, (2p? — b? — c*) + = B, (p? — 2) = — Wr’, ab) |

Now, as we have seen above,

Ay (p? + B4)(#? + Bi) (0? + BY) + Aa(p? +B) (x? + B's)? + Bs)
= ALB (Bi +0) (Bs+e2) +22 (B40) (Bite%) +98 (B +e?) +2°8 (Bi th}
+ Asf B's (840%) (B40?) +0" (B+0*) (Bote?) +B (Bete) 42°83 (Bat V)}

which by (30) is equal to
A, B'?.(B+0")+ AoB’,? (6. + b)4 ac? {A, (B+ 02) +A,(6,+0)} +9 { —_= =F}

— A, (By ~- b?) f— 2 (Bb? =e ce’) Bi - 1h2¢'2} en A, (8 at b) _ 2 (24 c) B’, a 1P%¢ 2}
+73 (@—/),

co
a]
bo

492 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A

and this by means of (30) and (31) reduces to
{— 40? +(e —y')} —B.
Hence the complete value of y, is

amet f— 40? 4+ 2 — yy} + Byry + Bowe’ + Boyz’

= Bi [—Wep oy} + Bay +2 wef Eye ape, (32!)
where B,, B,, B; are given in terms of 6’), 6’, 6’; by equations (32), (33).

From equations (6), (34) it will be seen that, in the motions with which we are
dealing, w, v, w are linear functions of x, y, z. Hence the components of molecular
rotation of the fluid, which involve first differential coefficients of w, v, w, will be inde-
pendent of x, y, z. This justifies the assumption made in § 1 of the paper.

§ 7. Calculation of Couples on the Shell due to Fluid Pressure.

At any point of the fluid the pressure is given by (1); we have, viz. :—
P = pilV, + 30° (2 + y')} — pil

Let us now refer to a new set of rectangular axes, Ox,, Oy,, Oz,, coincident with
the principal axes of the ellipsoid in its displaced position. The direction-cosines of
one set of axes relatively to the other are given by the scheme

mH | Y 21 |
i if —6, 0, |
= (35).
| y 0; 1 —6,
= | |
| Zz vere 6, 6, | 1 |
| |

v= XL, — Y,9, + 2%,
Y= 9, — HO, + 24s,
2% — ©O,+ WF)

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 493
and, neglecting squares of 6,, , 03, we obtain
P= PLY, + 3° (@? +H’) — o7y,2,9 + 07229] — pp. . . (36),

where in the small term # we may replace a, y, z by 2, y, 2}.

If L, M, N denote the couples on the shell about the axes Ox,, Oy,, Oz,

Py,z Pye CB
— [| do} ie EL i =@-A@-a ({ Ppy,2z, do,

ey Poe
ve (|p doy ~ ma = <5 [{Ppa.e, do,
N= he ie = Sel Te a 2) it Ppxy, do,

where do is an element of the surface of the displaced ellipsoid, and the integrals are
taken over the whole surface.

Let us now consider separately the parts of these couples introduced by the
different terms in the expression (36) for p.

(a) Take p = p, Vj.

The pressure at every point is the same as if the fluid were at rest under a
potential V,.

V, will, in general, consist of three parts due respectively to («) the attraction of the
shell; (8) the mutual attraction of the fluid particles ; (y) any external attracting
system.

If the part («) gave rise to any couple, it would be exactly counterbalanced by the
couple on the shell due to the attraction of the fluid, since the attractions of the shell
on the fluid and of the fluid on the shell are equal and opposite.

The system of forces (8) also form a system in equilibrium, and, therefore, can
give rise to no resultant couple on the shell. Thus no couple can arise from the
mutual attractions of the parts of the system.

The pressure at any point due to the part (y) is the same as if the fluid were at
rest. Thus the couples due to any external attracting system will be the same as if
the fluid were supposed to be solidified. If we add to these couples, due to the
attraction of the external system on the fluid, the parts due to the direct attraction
on the shell, we see that the total couples due to any external system will be the
same as if our system were solid throughout.

(b.) Take

P= 30'p, (UP + IY") — © py (1, — @9,).

Integrating over the surface of the ellipsoid

494 MR. 8S. 8. HOUGH ON THE OSCILLATIONS OF A

we have

({P Ax, Yyi2, — 0, [ | Pidaapec—105

\) Pdo yy" = ys mp(p> —_b°) (p? — c*J, &e.
Therefore,

[[pP do ye, = — oO,p, ate mp (p? — 2) (p? — 2),
and the corresponding part of L is
— y's 7p1- p (p” — b*)* (p* — e*)* (c? — 6") w°O,.
Similarly the parts of M, N arising from this part of p are
+ sap. p(p? — BY. (p? = 2) (— c2) o% and 0.
(c.) Lastly, if

aa hod ; B, B
p= pipe a B, {a — y? — 30°?} + Byyy, + a Tae AF a ne | >

C — is 9 9 9 9\2 9 9 B. in
c 9 9 9\2 B, 4
—3@ 8 ies 20 do = + y's 7p,C°p (p* — 6°) (p® — oP = e™,
b? 9 9 19,2 9 2 5
(pe —B) {|Pp yx do = — 485 7p,b*p (p* — b*)} (p* — ce”)? Bie™.

Collecting the different parts, we obtain for the couples, provided there be no
external disturbing force,

: 9 9\2 9 9 B, iAt
=) 35 Tp P(p’ — 0") (po ee — Bb), {08 + Be \

9 9\,2 i) 9\2 9 By a 9
M = + vfs mpi. p(p? — b) (p? — et) e®. |e — 06,

N = — +57 p,- p (p? — 0”)? (p? — &)' 0. Bye™

= (u — ») Bye™ J

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 495

where, for brevity, we have put
v=smp)-p (p'—b*)* (p> — c°) (c? — B'), w= smi. p(p°—L*) (p?— cc? . (38).

The terms in ” arising from ()) are due to the centrifugal force of the fluid, and
occur in consequence of the axis of rotation of the shell not accurately coinciding with
that of the fluid, while the terms (c) are due to the effective inertia of the fluid.

§ 8. Dynamical Equations of Motion of the Shell.

Let A, B,C be the principal moments of inertia of the shell; p, g, 7 the angular
velocities about the principal axes.
The position of the shell at time ¢ + 6¢ may be found from its a, at time ¢ by
dé, “
le O° ay OF

giving it a small rotation w d¢ about Oz,

about the positions of the axes Ow, Oy, Oz at time ¢ + dé.
The direction-cosines of these latter axes referred to their position at time ¢ are

(i, W800). ae U(Groty 10)s 5 #(OrNO". 1)

Hence, resolving the rotations in the directions of the axes Ox, Oy, Oz at time ¢,
the component angular displacements are

Oe Gh (ae O85,
and the angular velocities about the axes Ox, Oy, Oz are
b,, 6,, o + 5.
Resolving these about the axes Ox,, Oy,, Oz, we see from the scheme (35) that
p=6,—ah,. g=6,+ a6, r=a+6,. .,. .. (39):
EULER’s equations of motion are
Ap —(B—C)qr=L
Bg — (C — A)rp = M,
Cr —(A — B)pg=N

where, if the system be subject to no external disturbing force, L, M, N have the

496 MR. 8. S. HOUGH ON THE OSCILLATIONS OF A

values given in (37). If there be any external attracting system we must add to the
right-hand members the couples due to this system, estimated as though the system
were rigid throughout. In dealing with the “free” oscillations, however, we may
omit these terms.
Introducing the values of p, q, 7 from (39) and omitting small quantities of the
second order .
AG, — (B — C) a6, — of, (A + B— C0) =L,
BO, + (C — A) a, + of (A + B— C)=M,

C6; =.

Hence, on replacing L, M, N by their values (37), putting 6, = @',e™, &, and
omitting the time factor, we obtain

6, {AN + (B—C) 0%} + ro’, (A+ B—C) —» {e+ Bel a 0 |
0°, {BN + (A — C) w?} — cho’, (A + B—C) — ps {ar, s 2m oh \ . (40)
0,{0N%} —(n—r)B, =0
from (32)
B= ae 6,

Hence the freedom defined by the coordinate @; is neutral, and a disturbance,
which causes the coordinate 0, to vary, will not give rise to an oscillatory motion.
From (38) the values of B,/z, B,/7 are given by
Bs (o,¢ — gy — 208 Bh
T hr
2nt B,

T ws

° 9 9.9 7 a)
(p? — ¢?) —NC? W, = 0 |

Weg (A),
(pf? — 2?) + (2 = B) OL = oy

Eliminating 6’,, 6’, B,/7, B,/7 from (40), (41) by means of a determinant, the
periods of free oscillation are given by

AN+(B—C—») a%, Ne AL =O), 0, =
SF No (A-EB =O) BE (AE=C-= 1) aie emo 0
0, —d2c?, 2p?—c”, — 2 (ppc) =e
8 (e&—B%), 0, “2 (p—c%), 2p Pc?

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 497

§ 9. Reduction of Period Equation.

Expanding out this determinant, we obtain
[{AW — (C — B+ rv) o*} {BY — (C —A +2) 0} — od’ (A + B— C)’]
9 19 2 by SO 22
x | (2p — 09) (2p? — BF — 0) — FE = 07]

+ per? {Ad — (C — B + v) a} (2p? — 0? — c”)
+ v(e —b?) V {BM — (C — A + p) w*} (2p? — &”)
— 2w°d? (p> — ce”) (A + B — C) fu (e — b?) + v0}
SP UUCH Cha ON Oe Rh Mi Sue. 55 Sy Sul me een (ee

Now since

=)

= p(p? — 1) + (p+ p=) (6? — 02) + (p?— oF (1 —

1 9.9 9 9 9 9 9 9 f9 2\9
repel Pe (2k oes) tes Pees) (Ore Caste (Pa)

=. * (2p — c*) (2p? — b? diay 4ex*p* (p* — b*)5 (43).
itt 9 9
BOC aerccn i (2 fae etl, eae)
if ) ) 2 2% 9 9 ONG
= 272 {? (2p? == Ge) 4a” (p° a b’)§

and

9 19 1 9.9 9 9 1 9 9 9 2.9
2p? — c% = —.{rp® + (p® = ©) 5 = ag. M (2p? — &) — daip?}

> YS

Hence substituting in (42) we obtain the following cubic for )? :

[ {Ad — (C — B+ v) 07} {BY — (C — A+ pz) 0} — wd? (A + B—C)’]
{d? (2p? — b? — c®) (2p? — c2) — 4e%p? (p? — 2)}
+ porn’. fAXW — (C — B + v) w} {d? (2p? — b? — c) — 40° (p? — b*)}
+ v(c? — b?) {BNW — (C — A + p) w} fd? (2p? — c) — 4a*p§
— 2u?d4(p? — 2) (A + B —C) {u (c? — 8) + ve%}
+ py (V — 407) 7 (e — F)=
MDCCCXCV.—A. 38

498 MR. 8. 8S. HOUGH ON THE OSCILLATIONS OF A

Let us now change our notation, replacing p’,

p — b*, p?—c by a’, B, y*; the
period equation may then be written

[fA + (B — C—») 0%} (B24 (A — Op) a} — o2(A + B— C)]

x [8 (8 + )(B + 7) — 40°
+ ple — y)X [AM + (B— C — ») 0%) 22 (8 + 7) — do
+0 (6? — 72)? {BY + (A — C—p) 0%} (2 (2 +) — 40%}
— 2M. (A + B— 0) {n(B—y) +(e — y)}

+ port (X= 4o2) (2 — ¥*) (8 — 7) =0

ey

(44).
If we put \” = @’, the left-hand member of (44) becomes

DPIC BC») (A+ B=
’)

—#)—(A + B—C)] (e+) (B + 77) — 4088)
+ OMT) (a eve y

pane fy? — 8B}
+ of ( — 7) {A+ B— C —p} fy? — 30}
— 207 (A+ BC) {u(B =) + (8 = ')} — Spee! (2 =) (B = 7)
— oF (A+B—-C)| p {(a'-+y’) (P+y’) — 4088+ (2) (yy — 88") —2y"(¥'—B)5 |
_Fvf(C4+P)\(B+7)—48 B+ (~—B)(P— 302) — 27 (~P—2)5_|
+ pve! se ey (8? ey) = AaB: iy oye Bil

fe A IB Vy 302) eB me) ae eon le
therefore \” = w° is always one root of (44).

Arranging (44) according to powers of \*, we have

S| AB (a? -+ y*) (B+ y°) + pA (B? + y’) (2? — y?) + vB (oe?
Bate UO ry) (Bo ye) =|

~o rt! (2+y) (@+y) (A+B—C)?—A(A—C—p)—B(B—C—»)} + 4A Bah? |

=i Cr = Fe eS 5 CS — Op) bayer

— v(B— y’) {(@ + 7’) (A — C — p) — 4Ba*}

ap Ay (AS BC) iS? 7) on (a

_+ 4py (a? — y*)(B’ — ’) a
+ oth®. (a? + 7°) (8 + vy?) (B—C —») (A—€ — 4) |
a aes (A BC) A (SC) BBC), |
= su Be? — y)\(B — © — ») — Avan y) (Aaa
— of (4026? (B—C —v)(A—C—»)}.

+7) (B= 7)

Dividing out by the factor \* — o, we are left with

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 499

Mt. [A (B? + 7”) + 7 (8 — 7°) I[B (e’ + 7’) + pw (? — y’)]
— oe + 9) (B+ ¥?)(B—C— (A —C~ p)
Hi 2((4 + BC) (ae) n(B C=) (BC) cae
elie (o 98) (BEG aye ipa (7) (es =) i
+o. (402° (B — C—v)(A—C—yp)} =0,
or
NS LAS (Soe) (8 77) BGs.) (ae,
— oe + PB + 7)(B- C=) (A—C~ p) + He (A+) (BH HY)
Sone Op ie a ie) |
+ off 40°8?(B—C—r)(A—C—p)}=0... . . (45).

In order that the system may satisfy the criteria for “ ordinary ” stability the roots
of this equation in )* must be real and positive.

The period equation (45) agrees with the equation (5) (§1), and the solution of it,
in the case in which the ellipsoid differs but slightly from a sphere is given in § 3.

§ 10. Nature of the Oscillations.

From equations (40), (41), (48) we see that the equations giving the ratios of the
quantities @’,, 65, B,/r, B,/7 are

0 {AN +(B —C)a"} + 005(A-+ BC) —» (0%, +P) = 0 |

0’. {BN + (A — C) 0%} — ho (A+ B—C) — 4 (0°, 4+) =0
f(a? +y°) 2 — 407a?} — 2wihy’? — (Me 4w*)(a? —y*) #',= 0
3 9 9 ) * 13}. 9 / 9 9 9 7

SUB by?) BM 40°B?} + 2widy? + d2(N — 40”) (B= y?) 6 = 0

(a). We have seen that in every case )? = w is one root of the period equation ;
when \ = o the equations (46) reduce to

Ba 6
Otery 2

GEN BPO} Eh (NBC) =p

TO
,{A+B-C—p}—i6, (A+ B-OC)+p-2=0,
B

2
9
TO"

B, 9 2 07.9 Be 2 }/
2 (Y? — 3B") + Qi? — 3 (8? — 7’) 0 = 0,

TO
382

B, 5 ON 70
5 1 38 (e — y) F,—= 0,

(9? — S22) — Bin?

TO

500 MR. S. S. HOUGH ON THE OSCILLATIONS OF A

which are satisfied by

(= mm 105 = —

_ Suppose 6, = ¢e‘°'*? where ¢ is a real quantity ; we have as one solution
Gh = Gh. Hy SS hg 9)
Changing the sign of 7 wherever it occurs, another solution is given by
0, = hemi ett9, 6, = — ie ~itetto

and this corresponds to the value — o of Xd. .
Combining these two solutions we get as the real motion corresponding to the root
Ne == 1075

0, = 2¢ cos (at + «), 6, = — 2¢ sin (at + e).

Now @,, @, serve to determine the position of that principal axis which in the
steady motion coincides with the axis of rotation, relatively to axes which are
themselves revolving with angular velocity o.

Let us consider the angular displacements relatively to fixed axes O€, On, O€
coincident with the position occupied by the moving axes at the time ¢=0; they
are

@, cos wt — 6, sin wt = 2¢ cos «,

#, sin wf + 8, cos ot = — 2¢ sin ge,

and these are constant quantities. Thus, the apparent oscillation which corresponds
to the root \* = w*, consists of a small permanent displacement of the axis of rotation,
and the system rotates as if rigid about an axis which does not accurately coincide
with our axis Oz. It is obvious that if » be the angular velocity of rotation about
this axis, the system and the moving axes Ox, Oy, Oz will return to their original
positions after an interval 27/o, and, therefore, the system will appear to oscillate in
a period 27/w relatively to these moving axes.

It is easy to see that the fluid motion, indicated by the analysis, also consists of a
motion of pure rotation.

For when 6, = de**!*®

Br 0 B,/7a” = — 2B,/Tw* = ide“.

Therefore, from (34),

ww, = wide faz + yz},
and from (6),

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 501

{ — daze — 26w*ze*} = — daze“

@

1 “tO. te Vente * ie
= ipw*ze* — 2ipw*ze*} = — haxric
WwW, = ho (x + wy)e*,

whence

u = — gaze*, v= — dare '*9, w= dpo(x + ty) &*9,
and, in the corresponding real solution, -

u = — 2fwz cos (wt + €), v = 2da2 sin (wt 4 €),
w = 2ha[x cos (ot + e) — y sin (wt + e)]}.

These are the component velocities relatively to the moving axes. ‘The velocities
parallel to the instantaneous positions of the moving axes are

u— Yo, v+ xo, Ww.

The velocities parallel to the fixed O€, On, OZ, are therefore

(u — yo) cos ot — (v+ wo) sinot = — 2fwz cose — wn,
(v + zo) cos wt + (wu — yo) sin wot = 2do2 sin € + o€,
w = 2bw {Ecose — yn sine}.

Thus the fluid motion is a motion of pure rotation, the component angular velocities
about the axes being
— 2¢w sin e, — 2a cos «, o.

The resultant of these angular velocities is an angular velocity » about the line
whose direction cosines are

— 2sin e, — 2¢ Cos €, il:

The similar case for the spheroid with a free surface has been already discussed by
Bryan (‘ Phil. Trans.,’ 1889).

(6). Next take
A= o[1 + (q+) (1 + gf = (1 + E) say
where

E=4(q+«) (1 +9).

Substituting this value of \ in (46) and putting a = y (1 + 4), &c., we obtain

502 MR. S. S. HOUGH ON THE OSCILLATIONS OF A

{A +B—C+2AE— qe} + i67,{(A+B—O)(1+E)}—gl,= = 0, |

i E

'.{(A + B—C) + 2BE — 904} —i0',{(A-++B—C) (1+ B)} + qq ™ = 0, a
a {1+q—E} +i-$ (eI) les (aeotn) = 0)

ae {l-e_—E} —i= (1+E)+6¢,(83+2E) = 0. j

These equations are correct as far as first powers of €, €, EK only. Solving for the
ratios of @';, 6’,, B,/Tw*, B,/rw*, we have

6", mp
DAO =Osy) Os 0 Pees qCé,, 0
| 3, Iie i suid) | 0 ea) (i215)
| 0, {Dy heise, 10 € (8+2E), —i(1+E), 144—E|
i B,/To"
7 SOSA Cae AARC a ae, (0
0, = 8a, i(1+E)
3€5, 0, 1+e,—E
aa —B, |r?
~ |=1@+B=0) (+E), A+B=C+2BE=9Ce, gCe,
0, Ss, ete =
Be, 0, —i(1+E)
or
a, —i6', —1B,/To* —B,/To?

GEB=Cye te =4m) GEEB= Ce na= 4m a 3(es) OB =0) moe Ge=oE

where the denominators are correct as far as first powers of ¢,, &c., only.
Replacing E by its value $(e, + €,) (1 + g) we obtain

Pie es Ws cet ele oe
Oyo anb) we yee 3 3
Taking
6, = de"
we have
OY, = 19e"

and, in the corresponding real motion,

6, = 2¢ cos (At + 6),
6, = — 2¢ sin (dt + e).

The angular displacements, relatively to the fixed axes O€, On, OG at time ¢ are

on
S
ve

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID.

0, cos wt — 8, sin wt = 2¢ cos [(X — @) t 4 «|,
6, sin wt + 6, cos wot = — 2¢ sin [(A — @) t + e€].

Thus the motion of the principal axis consists approximately of a simple harmonic
motion in period 27/(\ — w) = 27/Ka, in virtue of which it describes a small cone
about its mean position in a direction opposite to that in which the system is rotating.

The position of the instantaneous axis of rotation of the shell is defined by the
direction cosines

b,/0, A,/, iL,
or

S aA
— 26 * sin (Ai+e), — 20 > 008 Qt+e«), 1;

and since X is approximately equal to w, this axis will be very nearly coincident with
the principal axis.
From (48) we have also

and therefore from (34)

Ste ead Pe ienbisen «
w=, “39 ida” (az + wz) e ;
to the same order of approximation we have
t — eae a ry ee Oc Oe)

Whence, in the corresponding real solution

Le — doz cos(At+ €), v= egy wz sin (At + €),

cee

Dap dw | — x cos (At + €) + y sin (At + €)].

The velocity components relative to the fixed axes are therefore

. 6 soo
(wu — yw) cos wt — (v + ow) sin of = Tay poz cos (A — wt + €) — on,

: 6 ==
(v + za) cos ot + (uv — yo) sin of = Teor poz sin (A — ot + €) + o€,

6 : meee !
i ~ 1 + 24% {Ecos (A — wf + €) — nsin(A — wt + €)}.

504 MR. 8S. S. HOUGH ON THE OSCILLATIONS OF A

Hence, the motion of the fluid will consist very approximately of a rotation, as if
rigid, with angular velocity # about the line whose direction-cosines are

Tee ¢ sin (\ — ot + €), 7 p cos (X — wt +), 1.

This axis will itself describe a cone in period 27/Ko, and it will be so situated that
the axis Oz lies in the plane containing the axes of revolution of the fluid and of the
shell, and is between these two axes. The semi-vertical angles of the cones described
by the axes of rotation of fluid and the shell will be in the ratio 3 : 2g + 1.

The motion under discussion is that which would ensue if the shell were set
rotating about its principal axis, while the fluid possessed a rotatory motion in the
same period about some other axis. It is clear, that as €,, 6, and consequently E,
diminish, the period of this oscillation will be prolonged ; that is to say, the motion of
the axes of rotation will become slower. This motion will be reduced to zero when
€,, €, vanish. In this case the internal surface of the shell is spherical, and the
shell and fluid, of course, move independently. So far as this (apparent) oscillation
is concerned, they will each be rotating with angular velocity w, but about
different axes.

From the expression for the ratio of the amplitudes, we see that when q is large,
that is when the effective inertia of the fluid is large, compared with that of the shell,
the disturbance of the shell will be considerable, compared with that of the fluid ;
whereas if g be small, the disturbance of the shell bears to that of the fluid, a ratio
which approximates to, but is always in excess of, 1 : 3.

This oscillation has been previously examined by Hopkins (‘ Phil. Trans.,’ 1839)
under certain special assumptions, as to the initial circumstances, and to the law of
distribution of density in the shell.

(c). Lastly, suppose \ = w(K, + Ge) (kK. + Ge)

The approximate form of equations (46) is now

yy. sgt EA sis B,
8, {xy + geo} B— 16',B V/(«, + G61) (Ka + Ge) + Ce, * = 0,

T

y “ar / B,
O's {mq + qq 5 A + OA V (1, + 961) (Ke + Gee) — Qa, a 0,

eS

B, Baty ase = :
Bee (1 + 2e) + UV (1, + Ger) (HF Ye) = 0,
>) Bs ¢ ea, Bs
Lies (1 + 2) — iV (Kk, + Ge) (Kz ++ Ge) Sr 0.
Hence approximately B,/7 = B,/7 = 0, and
a; 16’, = ge", say ;

J (ky, + Ge) == VJ (kz + Ge)

ROTATING ELLIPSOIDAL SHELL CONTAINING FLUID. 505

therefore .
0, = $/(m + 9a)e*,
Oy = — Ip r/ (ity + Jen).

The corresponding real solution is

0, = 2b4/(m, + 941) cos (M + €),
0, = 26 \/ (ky + Gey) sin (Aé + €).

The angular displacements about O€, Oy are therefore

9; cos wt — 8, sin wt = $ {o/ (mq, + Ge) + (Ka + Geo) cos[(w + d)t + €]

+b {V(r + 96) — A (Ke, + Je2)} cos [(o — A) t—e],
§, cos wt + 6, sin wot = o{4/(K, + Ge) + V(Ko + Ge)} sin [(w + A)t + e€]

+ ob {J (e + 9a) — (ke + Ge)} sin [(w — A)t — €]

The motion of the principal axis in space consists, therefore, of a combination of
two simple harmonic motions, the period of each being approximately equal to
the period of rotation of the system, and the amplitudes being in the ratio
J (Ky + 96) = VA (Ka + 9) 2 A (KH, + Ge) + A (ka + Gea); in virtue of each of these
oscillations, the principal axis will describe a cone of revolution in the direction in
which the system is rotating. In the event of the system being symmetrical about
the axis of rotation x, = «, and ¢ =, in this case the amplitude of one of the
oscillations reduces to zero.

We have likewise

— ~ 26 * /(m, + ge:) sin (At + €),
6, r
*= + 2¢ is / (Kz + qéq) cos (At + €),

@

#1 08 wt 7 3, ol ot = — > * J («, + 96) + S(k2 + Geo)} sin (w + At + e€)
—¢ ~ iV (er + 941) — V/ (ke + Ge2)} Sin (v/@ — Mt — €),

Cae 6, : :
(> Snot + ~-cos wt = > VAC + ge) + / (ky + Geq)} cos f(a + A)t + ef
+b 6 (1, + Ge) — V/ (He + Ge)} cos (=A) eh.

The motion of the instantaneous axis of rotation of the shell is therefore in all
respects similar to that of the principal axis, but the semi-vertical angles of the cones
described are smaller in the ratio \: @.

MDCCCXCV.—A. 3 °T

506 ON THE OSCILLATIONS OF A ROTATING ELLIPSOIDAL SHELL.
The direction-cosines of the instantaneous axis referred to the principal axes of the

shell Ox), Oy,, Oz, are
0, — 06, 6, + of,
SS Sa Ns
@ @ 5
or

— 26] * in, +96) + ve +44) |sin Oe +)

26| Hat 4a) + Vat ge) eos (Mt +6), 1:

therefore, relatively to the shell, the instantaneous axis describes a cone in period 27/h.

This motion would ensue if the shell were started rotating about an axis not
coincident with its principal axis, and it is analogous to the motion of a rigid body
under no forces when slightly disturbed from a motion of pure rotation about a

principal axis.

[ 507 ]

XII. On the Velocities of the Ions.
By W. ©. Dampier Wuetuam, W.A., Fellow of Trinity College, Cambridge.
Communicated by Professor J. J. Tomson, F.R.S.

Received May 2,—Read May 30, 1895.

IN a previous communication to the Royal Society (‘ Phil. Trans.,’ 184 (1893), A,
p- 337), I have described a method of experimentally determining the velocities of the
ions during electrolysis, by observations on the phenomena at the junction of two
salt solutions, one at least of which is coloured, when a current of electricity is
passed from one to the other.

For the success of the method it is necessary to choose two solutions which (1)
are different in density, (2) different in colour, and (3) have nearly equal conduc-
tivities at equivalent concentrations, 7.c., when the number of gram-molecules dis-
solved in 1 litre of solution is the same for both. These conditions seriously restrict
the number of cases to which the method is applicable, but the results obtained for
copper and for the bichromate group (Cr,0,) agree well with the values theoretically
deduced by Koutrauscu from measurements of the conductivity. Alcoholic solutions
of cobalt nitrate and chloride were also used, and the sum of the velocities of the
opposite ions, in each case, observed in my experiments, was as nearly as could be
expected, the same as their sum calculated from the conductivities by KoHLRAUSCH’S
method.

In order to extend the method to cases in which there was no colour to be
observed, I have returned to the use of solid solutions in agar-agar jelly, by means of
which the first direct experimental measurement of the velocity of an ion was made
by Dr. Otiver Lopes (‘ B.A. Report,’ 1886), who traced the course of the hydrogen
ion as it travelled along a tube filled with a jelly solution of sodium chloride, forming
hydrochloric acid, and decolorizing phenol-phthallein as it went. Dr, LopGE tried to
determine the velocity of other ions, such as barium, by tracing the precipitates
which they formed with suitable reagents, but the results were not satisfactory.

The chief objections to the use of precipitates in jelly solutions are (1) the jelly
exudes from the tube under the action of the current; (2) the formation of the
precipitate withdraws some of the electrolyte from the solution, and hence changes in
conductivity result, which alter the potential gradient, or form surfaces separating
liquids of ditferent conductivity, over which distributions of electrification will occur.

a) 2 22.8.95

508 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

The motion of the jelly as a whole is very slow compared with the speed of the
ions, and, if we can measure the velocity while the ions are only moving over a small
distance in a short time, it need not affect the result by disturbing the experiment in
any other way.

In order to test whether trustworthy observations could be made with jelly
solutions, | determined the velocity of the bichromate group when travelling through
them. Decinormal solutions of potassium bichromate and potassium chloride were
used in the manner presently to be described, and the velocity of the Cr,O, ion under
unit potential-gradient (one volt per centimetre) came out 0°00044 centim. per
second. In the earlier investigation the same group travelled through an aqueous
solution of the same strength with a velocity of 0°00047 centim. per second. The
effect of the jelly thus appears to be only slightly to retard the motions. Moreover,
ARRHENIUS has shown (‘ B.A. Report,’ 1886, p. 344) that the viscosity of jelly
solutions has but a small influence on the conductivity.

The alteration in concentration, due to the formation of a precipitate, appears to
have been very considerable in Dr. LopGr’s experiments, and may explain his
uncertain results. It can, however, be made very small in the following way. Instead
of setting up, in contact with each other, two solutions, like barium chloride and
sodium sulphate, which completely precipitate each other, the solutions used were
barium chloride and sodium chloride, just enough sodium sulphate being added to
the latter to enable the motion of the barium ions to be traced by watching the
formation of a slight precipitate of barium sulphate. That this did not seriously
affect the result was shown by repeating the experiment with less sodium sulphate.
The specific ionic velocity then came out 0°000386 centim. per second, a number
agreeing with that first obtained, 0°000390, quite as well as the unavoidable errors
of experiment would lead us to expect.

The use of jelly solutions, and of precipitates as indicators, being thus justified,
many ions could be examined which could not have had their velocity determined by
means of a colour boundary. Kontrausca has lately given corrected values for a
number of ionic velocities (‘ Wied. Ann.,’ 1893, vol. 50, p. 385), and, in some cases,
tabulated them for solutions of various concentrations. It was, therefore, convenient
to determine some of these, and barium, calcium, silver and the SO, group, present in
sulphates, were chosen as convenient examples.

The apparatus used and the method of measurement were the same as those of the
former investigation.

Two vertical glass tubes, about 2 centims. in diameter, were joined by a third,
considerably narrower, which was bent parallel to the others for the greater part of
its length. One jelly solution was melted and poured into the longer limb till it
about half filled it, and was allowed to cool and solidify. The other solution was
then poured into the shorter limb, and, when it was solid, the whole was placed in a

glass water-bath in front of a window, with a transparent glass scale fixed behind

MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS. 509

the junction tube. A precipitate formed at the surface of contact between the
two solutions, and, when a current was passed from one platinum electrode to the
other, the precipitate gradually spread upward or downwards with a velocity which
could be measured on the scale by means of a telescope.

Fig. 1.

TOTTI

If the potential gradient at the junction is dV/dz, we have
AV /da = yr'/A,

where y represents the total current, 7 the specific resistance of the solution, and A
the area of cross-section of the tube.
If v be the observed velocity, the specific velocity for unit potential gradient is
given by
v vA.
(ae dVjde yr”

A is determined by filling a known length of the tube with water or mercury, y is
read off on a galvanometer previously graduated, and is determined by KoHLRAUSCH’S
method of a Wheatstone’s bridge with alternating currents. In order that the
method should be a success, it is necessary that the solutions should be of nearly
equal specific resistance, so that a mean value of r may be taken. The shght
disturbing effect of any small difference is shown in the former paper to be eliminated
if measurements be made when the current is passing in both directions, and the
mean taken. But, unlike the colour boundary method, the formation of a precipitate
is an irreversible process, so that measurements of the velocity can only be made when
the current passes in one direction. All that can be done is to choose solutions of

510 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

nearly equal specific 1esistance, so that the uncertainty, which must appear in the
result, shall be, at all events, as small as possible.

Bariuwm.—Decinormal* solutions of sodium chloride and barium chloride, the former
containing a little sodium sulphate, were made up with agar jelly just strong enough
to set. The resistance of each was determined in a cell of the form shown in fig. 2,

Fig. 2.

the constant of which was known, and gave the conductivity of any solution in
reciprocals of legal ohms, by dividing 1°5596 by the observed resistance measured in
legal ohms.
Resistance of sodium chloride solution at 15°°8 =: 161°8 ohms.
is barium a 45 a 163°0__,,
* = Ei , 13°4= 1730 ,,

I

The temperature coefticient of resistance is, therefore, about 2°5 per cent. per degree,
and the mean conductivity of the two solutions at 15°°8, 9°60 X 107%.

A small tangent galvanometer was adjusted and graduated by passing the current
from a freshly prepared Daniell’s cell through it and a box of resistance coils arranged
in series. The following readings were obtained—

Resistance. Reading. | Resistance. Reading.

vbms. a , onms. @
250 216 170 28:7
240 22°1 | 160 29°8
230 22°9 | 150 313
220 23:8 140 32:7
210 24-5 130 34:5
200 25-4 120 361

| 190 2674: 110 384

| 180 27°5 100 40:6

The resistance of the galvanometer and its leads was 10 ohms.

* A decinormal solution contains one-tenth of the equivalent weight of the substance in grams in one
litre of solution, e.g., 1 x $ BaCi, =°1 x 4 (137 + 70°8) = 10°39 grams per litre.

MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS. 511

The solutions were then placed in the velocity apparatus, and measurements taken,
the temperature of the water bath being 15°°8.

Time. Galvanometer. | Scale reading, | Displacement in
° 10 minutes.
11.14 35°8 24°39
16 i. 24-98
18 é 24:20
11.24 35:9 23°93 0:46
26 3 23°83 0°45
98 x 23°75 0-45
11.34 36°0 23°50 0.43
36 a 23°40 0-43
38 ‘ 23-30 0-45
11.44 | 36:0 23-05 0-45
46 ie 29-95 0-45
48 2 29-86 0-44
11.54 36:0 22-60 0°45
56 | i 22°51 0:44
58 | a 22°41 0°45
12. 4 36°2 22°16 0:44
6 < 29-05 0-46
8 | 50 21:98 0:43
12.14 | 36:3 21:71 0°45
18 a 21°52 0:46

The velocity of the junction thus kept constant throughout. Its mean value is
0°446 centim. in 10’, The mean galvanometer reading is 36:0, which indicates a
current equal to that produced by the electromotive force of one Daniell (= 1:08
volt) working through a resistance of 121 + 10 = 131 ohms. The area of cross
section of the tube is 0°430 square centim., and 7 is the reciprocal of 9°60 X 107%.

We thus get
_ vA _ 0-446 x 0-430 x 131 x 9-60 x 1078
poe gp om 10 x 60 x 1-08

0°000372 centim. per second.

Experiments presently to be described gave for the temperature coefficient of the
velocity the values 2°78 per cent. at 15°°7, and 2°05 per cent. at 12°°8. The mean of
these 274 is very near the value, 2°5, found for the temperature coefficient of the
conductivity, and justifies us in using the latter value for the small correction
necessary to reduce the observations to 18°, the temperature for which KoHLRAUSCH’s
numbers are calculated.

512 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

We thus find for the specific ionic velocity of the barium ion, travelling through
a decinormal solution of barium chloride in solid agar jelly at a temperature of 18°,

Vp, = 0000393 centim. per sec.

For an aqueous solution of corresponding strength, KoHLRAUSCH calculates, that,
in order to give the observed values to the conductivity and the migration constant,
the barium ion must have a specific velocity of

Vp, = 0'000366 centim. per sec.

New solutions were then set up, the amount of sodium sulphate being only just
enough to give a visible precipitate. The voltage used was less—about 24 instead of
40, but otherwise the experiments were similar.

The following mean results were obtained :—

v = 0°244 centim. in 10 mins.

Galvanometer = 22'7. Therefore y = 1:08/243. Mean conductivity of solutions
9°57 X 1072 at 16°°9, ‘Temperature of water-bath 16°°9.

Therefore
v, = 0°000376 centim. per sec.,

which gives for the velocity of the barium ion at 18° the value
Vga = 0°000386 centim. per sec.

Calciwm.—The determination of the velocity of the calcium ion was not quite so
satisfactory. The solutions used were decinormal ones of calcium chloride and sodium
chloride, sodium carbonate being added to the latter as indicator. The precipitate of
calcium carbonate was only visible when a considerable amount of sodium carbonate
was present. This would make the change in concentration, due to the precipitation,
considerable, and tend to increase the potential gradient at the boundary, and make
the observed velocity greater.

The galvanometer had been moved, so that it was re-graduated.

za |
| ||
1]

ee
| Resistance. | Galyanometer. | — Resistance. Galvanometer. |
| Bide pose a
| ohms. | | | ohms.

180 | 27°5 150 31:5

| 170 29°3 | 140 33°5

| 160 30:1 i 130 35'1

|

To these resistances 10 ohms must be added for the galvanometer and leads.

MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS. 513

Resistance of calcium chloride solution in cell at 18° = 180 ohms.

” sodium Dy 2? oy) = 170 7)

Mean conductivity = 8°91 x 107%.
The junction moved the following distances in 10 mins. :

Oo, 3G, SO. Se, SS, BG, Be 88 AO SG) BR, se

Mean = 0°376 centim. Mean galvanometer reading 32°9. Therefore y = 1:08/153.
Temperature of water bath = 18°1. Area of tube = 0°442.
Therefore
v, = 0'000350 centim. per sec.,

which gives for the specific velocity of the calcium ion, moving through a decinormal
solution of calcium chloride in agar jelly at 18°C., the value

Voa = 0°000349 centim. per sec.
For the corresponding aqueous solution KoHLRAUSCH gives
Vcq = 0°000290 centim. per sec.

The temperature coeflicient of the velocity was determined for these solutions by
cooling the water-bath to 13°°2.

Mean conductivity at 13°2 = 7°90 x 107%.

Velocity = «34, -30, °34, -32, 34, °32) -32, :32, 32. Mean = 0324 centim. in
10 mins.

Mean galvanometer reading = 29°7. Therefore y = 1:08/175.

Therefore

v, = 0:000305 centim. per sec.,

which gives a temperature coefficient, at a mean temperature of 15°'7, of 2°78 per cent.
per degree.

Silver.—Decinormal jelly solutions of silver nitrate and sodium nitrate, the latter
containing a little sodium chloride, gave in the resistance cell

Silver nitrate at 17°4 = 171 ohms,
Sodium _,, blige Aetna a

Therefore mean conductivity at 17°°4 = 8°96 X 107%.
MDCCCXCV.—A, 33 0

514 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

Velocity = -46, “48, °48, -48, -46, 49, 50, -49, 48. Mean = 0°480 centim. in
10 mins.

Mean galvanometer reading = 31:0. Therefore y = 1°08/164.

Temperature of water-bath, 17°°4. Area of cross-section of tube = 0°442 square
centim.

Therefore
v, = 0°000481 centim. per sec.

Thus the specitic velocity of the silver ion, moving through a decinormal solution
of silver nitrate in agar jelly at 18°, is

Vag = 0°000488 centim. per sec.

For the corresponding solution in water, KOHLRAUSCH gives

Vag = 0:000462 centim. per sec.

The temperature coefficient was determined by cooling the water-bath to 8°-2.

Mean conductivity at 8°°2 = 7°12 x 107%

Velocity = °37, °37, °39, -40, 40, -40, -41, 43, -40. Mean = 0°397 centim. in
10 mins.

The electromotive force applied being the same as before, we can compare this with
0:480 centim. in 10 mins., the velocity at 17°°4. The temperature coefficient at the
mean temperature of 12°°8 is thus 2°05 per cent. per degree.

The Sulphate Growp.—As an example of an anion the velocity of the SO, group
was determined by the use of decinormal jelly solutions of sodium sulphate and
sodium chloride, barium chloride being added to the latter as indicator.

The galvanometer was re-graduated, the following readings being enough for our
purpose. To the resistances 10 ohms must be added for the galvanometer.

70 ohms 50°8, 230 ohms 23°'8,
LO ea, 2 DIE

Resistance of sodium chloride solution in cell at 14°°6 = 151°5.
53 5 sulphate __,, i 14 65— lion.
Therefore mean conductivity at 15°°2 = 9°69 x 107%.
Velocity = -24, -24, -26, -26, 26, -27, 27, 27, 25, ‘24, °25, -27, -27, -26, -24,
"25, ‘27, °26. Mean = 0°257 centim. in 10 mins.
Mean galvanometer reading = 23°3. Therefore y = 1°08/246.
Temperature 15°-2. Area of cross-section of tube = 0°430 square centim.

Therefore
Vv, = 0:000406 centim. per sec.

oO

MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS. 51

This gives for the specific ionic velocity of the SO, ion, when travelling through a
decinormal solution of sodium sulphate in agar jelly at 18°,

Vso, = 0°0004384 centim. per sec.

Kou rauscu finds for decinormal potassium sulphate solution in water

Vgo, = 0°000492 centim. per sec.

Another determination was then made in another tube having a larger area of
cross-section = 0°746 sq. centim.
Temperature 11°°3. Mean conductivity = 8°79 x 107%.
Welocity = 38, -40, -41, “44, -47, -44) -48, “44, -42; 44, 44, -50. Mean = 0-438
centim. in 10 mins.
Mean galvanometer reading = 48°-4. Therefore y = =p :
Therefore :
V, = 0000388 centim. per sec.,
which at 18° gives us
Vso, = 0:000458 centim. per sec.

The numbers thus obtained all agree with those deduced from theory, to an
accuracy which must be considered to be as great as the unavoidable experimental
errors would lead us to expect.*

Certain substances, such as ammonia and acetic acid, are known to have
abnormally low conductivities, as long, at all events, as the aqueous solutions con-
taining them are not exceedingly dilute. It seemed of great interest to examine
whether the velocities were, in these cases, proportionately reduced. The result of an
investigation on acetic acid, in which phenol-phthallein was used as indicator, has
already been published (‘ Philosophical Magazine, October, 1894), and gave the
velocity of the hydrogen ion travelling through an agar jelly solution containing
0°07 gram.-equivalent of sodium acetate per litre, as

Vi, = 0:000065 centim. per sec.

Now the value given by Kontrauscu for the specific velocity of the hydrogen ion
in a solution of hydrochloric acid of this concentration is

Vu = 00030 centim. per sec.,

so that, when travelling through acetates, its speed is reduced in the ratio of 1 to 46.

* It is worthy of remark that the velocities of all the kations measured come out larger than theory
requires, while that of the one anion (SO,) comes out less. It is possible that this may be due to
tke presence of the jelly.

3) OE

516 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

The ratio of the conductivity of a solution of acetic acid, containing 0°07 gram.-
equivalent per litre, to that of an equivalent solution of hydrochloric acid is 1 to 62.
Thus the velocity of the hydrogen ion is reduced in about the same proportion as the
conductivity.

In order to examine the velocity of the acetate ion (C,H,O,) of acetic acid, some
substance was needed to serve as indicator. With ferric salts, acetates give a deep
red colour, which is also produced if the solid ferric acetate is dissolved in water.

It is weil known that solutions of ferric chloride undergo decomposition into soluble
ferric hydroxide and hydrochloric acid, to an amount which increases as the dilution
gets greater, and as the temperature rises. The hydrochloric acid can, in fact, be
separated from the hydroxide of iron by dialysis through a membrane of parch-
ment paper.

The electrical conductivity of an aqueous solution of ferric acetate shows that, in this
case also, a similar reaction goes on, for it has an abnormally low conductivity, com-
parable with that of equivalent solutions of acetic acid, just as a solution of ferric
chloride has an abnormally great conductivity owing to the presence of hydro-
chloric acid.

The molecular conductivity of an aqueous solution of ferric acetate, containing
one-tenth of a gram.-equivalent of iron in one litre, was determined by measuring its
resistance in another cell, whose constant was found by filling it with standard solutions
of silver nitrate and barium chloride. The conductivity of any solution could be
found by dividing the constant, 1604 x 107%, by its observed resistance in legal
ohms. <A volume of 10 cub. centims. of this solution was then taken, and made up to
100 cub, centims. in a graduated flask.

This process was repeated three times, with the following results :—The first
column, headed 1, gives the concentration of the solution in gram.-equivalents of
iron per litre; the second, R, gives the observed resistance in the cell; the third, T,
shows the temperature; in the fourth are put the values of ho, the conductivity in
C.G.S. units, that of the water being subtracted, reduced to a temperature of 18°,
and the fifth gives k,/n, the molecular conduetivity.

| at mal R. Tad AO) He oreacmL Se: | © jaf at 18°:

| Cees | ras |

El 2455 | 16:3 703 x 10-8 | 70°3 x 10-13
‘J 2is0. | 2-2
‘01 T2600. 9 79be= |) Seo 10 am ee

| 001 49700: | +177 9:99 x 10-1 =)| 9 299)

| -Q001 177000 | 166 6-74 x 10735 67

For equivalent solutions of acetic acid, Kouitrauscu (‘ Wied. Ann.,’ 26, p. 197)
gives the following results :—

MR. W. C.D. WHETHAM ON THE VELOCITIES OF THE IONS. oly

nu. Tig/n.

“Th AGE allies
“O01 ALO
001 404 ,,
‘0001 1058 —C«,,

It is, therefore, probable that, just as ferric chloride decomposes into ferric
hydroxide and hydrochloric acid, thus :

FeCl, + 3H,0 = Fe (OH); + 3HCl,
so ferric acetate gives ferric hydroxide and acetic acid, thus :
Ble (©. Ee Os) iris Or etie| (OI) -13) (ECs EO):

In each case most of the work of carrying the current is done by the acid.

An attempt was made to use the red colour of the ferric acetate as an indicator to
show the presence of the acetate group. A decinormal solution of ferric chloride was
placed in one limb of the apparatus, and a similar solution, coloured red by a little
ferric acetate, in the other. It was thought that, by the motion of the colour
boundary, the acetate group could be traced, and, since the current is almost
exclusively carried by the free acid, that the velocity thus measured would be that of
the anion of acetic acid in dilute solution.

When the current was applied, however, it was at once seen that the colour
boundary moved in the same direction as the current—not against it as an anion
should. The following measurements were obtained :—

Resistance of ferric chloride solution in a third cell at 18°°8 = 363 ohms.
ie =: 34 + acetate solution in Cell No. 2 at 18°°9 = 384°5 ohms.

Cell constant = 2'356.

Therefore mean conductivity at 19°°2 = 6°35 x 107°.

Velocity.—Half-hour intervals. Current upwards. Displacement upwards :

Current downwards. Displacement downwards :
ey, iS Reni ele

Mean velocity = 0°833 centim. in 30 minutes.
Mean galvanometer veading = 46°2. Resistance of galvanometer = 218 ohms.
Graduation with a Daniell cell :

518 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

200nohmseie se cues Oz) SO rohms ane
bes ook eee aL Oras ota Hess
therefore
y = 1°08/243,
therefore
v, = — 0°:000284 centim. per second,

which, reduced to 18°, gives
— 0000276 centim. per second.

If this really represents the velocity of the acetate group in an acid solution, it is
evident that, if a measurement be made of the migration constant of acetic acid, the

concentration round the kathode must increase, since the acetate group travels in the

same direction as the hydrogen.

The current from twenty storage cells was passed for some hours through a deci-
normal solution of acetic acid. The liquid was contained in an apparatus consisting
of two upright glass tubes, in which the platinum electrodes were placed. These
tubes were connected below the level of the top of the solution by a horizontal tube,
made of india-rubber for part of its length, in order that it might be closed by a
screw pinch-cock. After the passage of the current, the two vessels could thus be
isolated from each other, and the contents of each examined.

A current of 0°0014 ampére was passed for 5 hours, at the end of which time the
solution round each electrode was titrated with decinormal soda solution with the
following results :—

Original solution . . . 10 cub. centims. require 10-0 cub. centims soda.
Anode 55) 0 5 5 09 ” 10°4 ” oT)
Kathode __,, rite ie $3 9°9 9 56

This preliminary observation, therefore, gives no evidence of accumulation of acid
at the kathode.

The experiment was repeated. A current, whose average strength was 000178
ampere, was passed through decinormal acetic acid solution for 383 hours.

Original solution . . . 10 cub. centims. require 9°8 cub. centims. soda.
Anode * eae: a 7% 9°85 9» ”
Kathode a9 oa 9 ” 9°4 ” 2”?

Now it is possible that an accumulation round the kathode might be masked by
the reduction of the acetic acid by the hydrogen there liberated, but, if such an
accumulation occurred, it would mean that all the acid decomposed must be taken
from the anode vessel, as well as some which migrates unchanged through the liquid.
The numbers given above seem to show conclusively that the amount of acid round
the anode does not decrease, but that, if anything, a slight increase occurs.

INDEX.

Scauster (A.) and Gannon (W.). A Determination of the Specific Heat of Water in Terms of the
International Electric Units, 415.

Shell containing fluid, the oscillations of a rotating ellipsoidal, 469 (see HoucH).

Silver, on a method of determining the thermal conductivity of metals, with applications to, 165 (see
Gray).

Specific heat of water, a determination of the, in terms of the international electric units, 415 see
ScHusTER and Gannoy).

Specific heats of some compound gases, on the ratio of the, 567 (see Capstick).

Spectra of argon, on the, 243 (see CROOKES).

Spectrum of the great nebula in Orion, on the photographic, 73 (see LockyEr).

Steel and iron at welding temperatures, 593 (see WRIGHTSON).

W.

Water, a determination of the specific heat of, in terms of the international electric units, 415 (see
Scuuster and Gannon).

Water, note on the ratio of the latent heat of steam to the specific heat of, 322 (see Joy).

Water, the latent heat of evaporation of, 261 (see GRirFiTHs).

WuerHam (W.C.D.). On the Velocities of the Ions, 507.

Witson (H.) (see Hopkinson and Witson).

Wericutson (T.). Iron and Steel at Welding Temperatures, 593.

Youne (S.) (see Ramsay and Youne).

HARRISON AND SONS, PRINTERS IN ORDINARY TO HER MAJESTY, ST. MARTIN’S LANE, LONDON, W.C.

INDEX.

J.

JoLy (J.). Note on the Ratio of the Latent Heat of Steam to the Specific Heat of Water, 322.

L.

Lockxyrer (J. N.). On the Photographic Spectrum of the Great Nebula in Orion, 73.

M.

Magnetization of iron as affected by the electric currents in the iron, propagation of, 93 (see HopKinson
and Witsoy).

Mathematical theory of evolution, contributions to the—II. Skew variation in homogeneous material, 343
(see PEARSON).

Metals, on a method of determining the thermal conductivity of, with applications to copper, silver, gold,
and platinum, 165 (see GRay).

N.

Newtonian constant of gravitation, on the, 1 (see Boys).

O.

Otszewski (K.). The Liquefaction and Solidification of Argon, 253.
Orion, on the photographic spectrum of the great nebula in, 73 (see Lockyer).
Oscillations of a rotating ellipsoidal shell containing fluid, the, 469 (see HoucH).

Pp

Prarson (K.). Contributions to the Mathematical Theory of Evolution.—II. Skew Variation in
Homogeneous Material, 34:3.
Platinum, on a method of determining the thermal conductivity of metals, with applications to, 165 (see

Gray).

R.

Ramsay (W.) (see RaynercH and Ramsay).

Ramsay (W.) and Youne (S.). Note on a Comparison of the Vapour-Pressures of Argon with those of
other Substances, 257.

RayxeigH (Lord) and Ramsay (W.). Argon, a New Constituent of the Atmosphere, 187.

Reynotps (O.). On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of
the Criterion, 123.

INDEX.

D.

Dijferential equations and the theory of congruencies, on the singular solutions of simultaneous ordinary,
523 (see Dixon).

Drxon (A. C.). On the Singular Solutions of Simultaneous Ordinary Differential Equations and the
Theory of Congruencies, 523. :

Dynamical theory of incompressible viscous fluids and the determination of the criterion, on the, 123 (see
REYNOLDs).

E.

Evolution, contributions to the mathematical theory of—II. Skew variation in homogeneous material,
343 (see PEARSON).

F.

Fluids, on the dynamical theory of incompressible viscous, and the determination of the criterion, 123
(see REYNOLDS).

Gannon (W.) (see ScoustER and Gannon).

Gases, on the ratio of the specific heats of some compound, 567 (see CapstTIcK).

Gold, on a method of determining the thermal conductivity of metals, with applications to, 165 (see
Gray).

Gravitation, on the Newtonian constant of, 1 (see Boys).

Gray (J. H.). Ona Method of Determining the Thermal Conductivity of Metals, with Applications to
Copper, Silver, Gold, and Platinum, 165.

Grirritus (HE. H.). The Latent Heat of Evaporation of Water, 261.

lel.

Hopkinson (J.) and Witson (E.). Propagation of Magnetization of Iron as affected by the Electric
~ Currents in the Iron, 93.
HovcH (8.8.). The Oscillations of a Rotating Ellipsoidal Shell containing Fluid, 469.

Tons, on the velocities of the, 507 (see WHuTHAM).

Tron, propagation of magnetisation of, as affected by the electric currents in the, 93 (see Hopkinson and
Witson).

Tron and steel at welding temperatures, 593 (see WRIGHTSON).

INDEX TO PART I.

OF THE

PHILOSOPHICAL TRANSACTIONS (A)

FOR THE YEAR 1895.

A.

Argon, a new constituent of the atmosphere, 187 (see RAYLEIGH and Ramsay).

Argon, note on a comparison of the vapour-pressures of, with those of other substances, 257 (see
Ramsay and Young).

Argon, on the spectra of, 243 (see CROOKES).

Argon, the liquefaction and solidification of, 253 (see OLszEwsk!).

B.

Boys (C. V.). On the Newtonian Constant of Gravitation, 1.

C.

Carstick (J. W.). On the Ratio of the Specific Heats of Some Compound Gases, 567.

Congruencies, on the singular solutions of simultaneous ordinary differential equations and the theory
of, 523 (see Dixon).

Copper, on a method of determining the thermal conductivity of metals, with applications to, 165 (see
Gray).

Crookes (W.). On the Spectra of Argon, 243.
4 u 2

Wrightson. Phil. Trans., 1895, A, Plate 17.

\

Temperatures »—>

eta

s0 Seconds.

Temperatures »—>

T.RColtinon se

MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS. 519

We must, therefore, look for some other explanation of the velocity phenomena.
If ferric hydrate be dissolved in ferric chloride solution, a red liquid is obtained.
When it is remembered that the ferric acetate solution contains ferric hydrate, it is
evident that a motion of the colour boundary would be obtained if this ferric hydrate
were carried through the solution, either by its being attached to the kation, or by
a motion similar to that observed in the case of light non-electrolytic particles
suspended in water.

Ferric hydrate can be obtained in a soluble form by dialysing a solution of ferric
ehloride. The ferric chloride solution is placed in a glass cylinder, the lower end of
which is covered by a sheet of parchment paper. The cylinder is then suspended in
such a manner that the lower end is just below the surface of a large volume of
distilled water. At the end of several days, nearly all the hydrochloric acid is found
to have passed into the water, leaving the iron behind as a brown solution of ferric
hydrate. A solution prepared in this manner was found to have a concentration of
00044 gram.-equivalent per litre of chlorine, and 0°0652 gram.-equivalent of total
iron. Its conductivity was, in C.G.S. units, 7°83 x 107%, which gives for the iron a
molecular conductivity of 120 X 107}, a value much below the normal. If, however,
we suppose that it is only the ferric chloride remaining in the solution which is
active, and calculate the molecular conductivity from the amount of chlorine, we get
1780 X 10~%—a number nearly equal to that for the ordinary ferric chloride solution
of equivalent strength.

A series of conductivity measurements of this solution was made at different
dilutions, and then two similar sets for ferric chloride. In the following Table the
results are compared,

|

| Dialysed iron. Ferric chloride.
os poe ts of | Molecular conductivity | Concentration in gram.- | Molecular conductivity
a rs aa ag at 18°. equivalents per litre. at 18°.
chlorine per litre.
0:00968 1445 x 10718
| 0:0044 1780x1078
0:00088 2255 ss,
0:000353 2575,
0:000176 2580 __,, | 0:000131 2690 __,,
| 0:0000968 2747,
| ¢ 0:0000506 2250 ,,
0-0000352 WAY eg
00000176 LONG 4;
|

0:00000968 Omnis

The molecular conductivities are corrected for the conductivity of the re-distilled
water used (2°97 X 10~), and reduced to 18°,

520 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

The two series of numbers correspond with each other within the limits of
experimental error, and this indicates that the conductivity of the solution of dialysed
iron is due, in great part, at any rate, to the presence of residual chloride. Whether
the conductivities of these two solutions are accurately equal or not, it would need a
thorough investigation to decide, and this was unnecessary for the immediate purposes
of this paper. One would imagine that, if the conduction is entirely done by the
chloride, the conductivity of the dialysed iron solution would be a iittle reduced, for
the residual chloride, finding itself in presence of a large excess of ferric hydroxide,
one of the products of its decomposition, would be less completely resolved into
hydroxide and acid than in its ordinary solutions, and would, therefore, have a
molecular conductivity more nearly equal to that of common salts than in the usual
case.

It is interesting to observe that the molecular conductivity, in both these cases,
reaches a maximum as the concentration decreases, and then, as the dilution is pushed
still further, again falls. This is a characteristic property of the solutions of free
acids and alkalis, and confirms the hypothesis that decomposition into ferric hydroxide
and hydrochloric acid occurs. We may take it, then, that the ferric hydroxide, into
which solutions of iron salts are partially decomposed, is electrolytically nearly
inactive, the conductivity being almost entirely due to the acid formed. It is the large
quantity of this hydroxide present that gives the dark red colour to ferric acetate
solutions, and it is the motion of the ferric hydroxide which is measured by observa-
tions on the movement of the colour boundary in the velocity experiment.

In order to examine this conclusion, 10 cub. centims. of a solution of ferric chloride
were run into some dialysed iron solution, and made up to 100 cub. centims. Another
volume of 10 cub. centims. of the same ferric chloride was made up to 100 cub.
centims. with water. These two solutions were placed in the velocity apparatus, and
a measurement of the velocity of the red colour boundary made. It travelled in the
same direction as the current.

Resistance of ferric chloride in cell, 818 ohms at 18°74.

ie s zi + hydroxide, 607 ohms at 16°°8.

Mean conductivity in reciprocals of legal ohms at 16°°2 = 2:12 X 107°,

Velocity—Temperature 16°2. Mean galvanometer reading = 27°5. Current
upwards. Upward displacement during successive intervals of 10 minutes each.
Boundary kept quite sharp.

(yds HH, (OH, SS) «WE

Current downwards. Downward displacement during successive intervals of
10 minutes. |
HL) ete erire tte Vhs to, Th SO, Wo

The first three measurements of the latter series are much larger than the rest,

MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS. o21

and after them the velocity kept constant. It is probable that the extra value was
due to some disturbance at the boundary introduced by the first current, which
gradually got reversed and eliminated when the current was reversed. These three
observations were therefore neglected. The others give a mean velocity of 0°68 centim.
in 10 minutes. We thus get for the velocity with which ferric hydroxide is trans-
ported in the direction of the current through a dilute solution of ferric chloride, by a
potential gradient of 1 volt per centim., at a temperature of 16°°2, the value
0000315 centim. per second, and at 18°

000033 centim. per second.

This is the same, within the limits of experimental error (which with these badly
conducting solutions are considerable) as the value deduced by experiments with
ferric acetate solutions of rather greater concentration, which was

000028 centim. per second.

It seems clear, then, that what we were measuring in that case, was not the
velocity of the acetate group, but the velocity with which the soluble ferric hydroxide
was transported through the solution without undergoing any decomposition.

In order further to examine this explanation, a migration experiment was made with
the dialysed iron solution. A current of 0°003 ampére was passed through the liquid
for five hours, at the end of which time the red colour had become much paler round
the anode, while a precipitate of ferric hydroxide appeared at the bottom of the vessel
containing the kathode.

The volume of liquid in each vessel was 30 cub. centims., and in 30 cub. centims. uf
the original solution the weight of ferric oxide was 0:0780 gram.

In the anode vessel the weight of oxide in solution was 0°0438 gram.

The kathode vessel contained 0°0720 gram. in solution, and 0°0158 gram. precipi-
tated ; total, 00878 gram.

Thus the anode vessel contains less iron, and the kathode vessel more, than an
equal volume of the original solution. This, also, is consistent with the hypothesis
that unaltered ferric hydroxide is carried through the liquid in the direction of the
current.

A similar experiment, made with ferric acetate solution, also showed an accumulation
of iron in solution near the kathode, both as estimated by the colour of the liquid,
and as determined by analysis.

Our attempt to measure directly the velocity of the acetate group (C,H,0,) in acetic
acid solutions has therefore failed, but the migration experiment, described on p. 518,
at any rate showed that no great change of concentration occurred in the neighbour-
hood of the anode, towards which the acetate group travelled. Its velocity is, there-

MDCCCXCV.— A. 3X

922 MR. W. C. D. WHETHAM ON THE VELOCITIES OF THE IONS.

fore, very small, and, as in the case of common mineral acids, the conductivity is
chiefly due to the motion of the hydrogen.
The following table gives the velocities of all ions which have been experimentally

determined.
Specific ionic velocity in |
centims. per second. |
Name of ion. Gtslloninvail Observer.
from Kout-| Directly

RAUSCI’S observed.

theory.
Elydrogenk(Gmichlorides)) js. eae eee le nO,0028 0-0026 O. J. Lover

5 (in serene) Her Meghna pl ne ita a ee O000048 0000065 W. C. D. WuertHam
Copper . Tecan rere Propane Tee 56 0 00031 -
Be ears ate group (Cry 0. ) ME eee at ma ane eee hat On OOO 0:00047 | i
Barium. eae trey otra 0; 00034 9000389 |
(Celkerinyans Iecreead tas in tate renee emai mere lt (OROLO O19) 000035 | ‘
Silver . . SL Oe eke e a eae el ORO OOLG 000049 |
Sulphate group (SO, Ne ible is oh send paca ese || 300049. 0:00045 9
Cobalt (in alcoholic CoC, Es) igh acti acaauibistn ieele iantenlis<| He 0:000022 | A
( bp COUNOD See Boies ater ere a5 0-000044 | 3
Chlorine (in alcoholic CoCl,) . alas 56 | 0000026 | 5
Nitrate group (NO) (in alcoholic Co(NO; 3 ). ae ie 0000035 | 58
|

The values in the second column are calculated from Kontrauscn’s theory for
solutions of the same concentration as those used for the direct observations. LopGE
does not give the strength of his solution, but, as the molecular conductivity of dilute
hydrcchloric acid does not alter much with change of concentration, the number
given, which is calculated for a decinormal solution, is, probably, fairly comparable
with that observed. The velocity of copper was measured in chlorides, and the data for
the calculation from theory are not known for this salt. The specific ionic velocity of
copper, at infinite dilution, is given by KouLRauscH as 0°00031 centim. per second.
The sum of the ionic velocities of cobalt chloride in alcohol, as calculated from the
conductivity of the solution, is 0°000060 centim. per second, and that of cobalt nitrate
is 0°000079. These numbers are to be compared with the sums of the observed
velocities given in the table, namely, 0°000048 and 0-000079 respectively.

[ ae]

XIV. On the Singular Solutions of Simultaneous Ordinary Differential Equations
and the Theory of Congruencies. :

By A. C. Dixon, M.A., Fellow of Trinity College, Cambridge, Professor of
Mathematics in Queen’s College, Galway.

Communicated by J. W. L. GuatsHer, Sc.D., F.RS.
Received June 7,--Read June 21, 1894.

INTRODUCTION.

§ 1. Tuts paper is an attempt to show how the singular solutions of simultaneous
ordinary differential equations are to be found either from a complete primitive or
from the differential equations.

The /atter question has been treated by Maver (‘ Math. Ann.,’ vol. 22, p. 368)
in a somewhat different way, but with the same result. He also gives a reference to
a paper in Polish by ZasaczKowskK1 (summarized in vol. 9 of the ‘ Jahrbuch der Fort-
schritte der Mathematik), and to one by SreRReET in vol. 18 of ‘ Liouvitue’s Journal.’

The general result is that there may be as many forms of solution as there are
variables (the differential equations being of the first order, to which they may
always be reduced). Each form is derived from the one before by the ‘process of
finding the envelope, and each contains fewer arbitrary constants by one than the
form from which it is directly derived.

The general theory is given in {§ 2, 3, and in § 4 it is shown how the singular
solutions are to be formed from the differential equations themselves. In {§ 5-9
the theory is connected with that of consecutive solutions belonging to the complete
primitive. § 10-13 are taken up with geometrical interpretations relating to plane
curves aud also to curves in space of n + 1 dimensions, n + 1 being the number of
variables. In §§ 14-16 the case is discussed in which a system of singular solutions
is included in a former system or in the complete primitive.

The rest of the paper contains the application of the theory to certain examples.
The first example (§§ 17-21) is the case of the lines in two osculating planes of a
twisted curve, and in particular of a twisted cubic. The particular example is given
by Maver and Serrer. The second (§§ 22-26) is that of the congruency of common
tangents to two quadric surfaces, and generally (§§ 27--38) of the bitangents to any
surface. The third (§§ 39-50) is that of the essentially different kind of congruency

BB 25.8.95

524 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

which consists of the inflexional tangents to a surface. It seems natural to call
these two kinds of congruency bitangential and inflexional respectively. The fourth
example (§§51, 52) is that of a system of conics touching six planes. The fifth
(S§ 53-56) is that of a doubly infinite system of parabolas in one plane, the differential
equation being a case of an extension of CLairaAuT’s form y = px + f(p), which is
explained in §§ 53-55.

General Theory. (S§ 2, 3.)

§ 2. Suppose that we have n ordinary simultaneous differential equations, involving
one independent variable x, and n dependent variables y,, y2,... Y,, with their first
differential coetlicients p,, Po, .. - Du

The “complete ” solution of such a system will consist of 7 equations involving
LY ey, ANG 7 aL bibratys COUStANtS, Cine cen Cn:

Suppose that such a solution is known. The question then arises, “ Are there any

”

other solutions which it does not include?” This is the question that we now seek

to answer.
If we take the differential equations in the form

Si (Yas Yoo + + Yous Py +- Pr) =O (TH 1,2...n) . . . . (CL)

and the integrals as
Ey (ae apinne ig Cine Cn) =O (7k 2s 70) eee a GIRL)

we have by differentiating

oF oF, oF,
= font r bs a eeal 5 5) re
A, + p, on +... 4+ pu a (ORRIN Catto etree Pete Grenier (TULL, ))
Let the system
a OH Oe en el eee) meee ot oe So (INS)

be an integral of (I.).
From (LV.) we derive

On, A,
Set Pigg ts. + Peg = 0 (== 1p?) 327) Sow eee Ae
a 1

By eliminating p,,...p, from (III.) and (V.) we find such values of ¢, ¢g,... Cy, as

will make (111.) and (V.) equivalent* ; but if the values of p,,...p, given by (III.)

* This argument must be somewhat modified if the equations (IJI.) are not enough to give the
values of ¢, ¢,... Ca. Suppose that m independent equations, and no more, can be formed from (IIL.)
not containing the quantities ¢,...¢x. These equations must be included in the system (1.), and are
therefore equally satisfied (possibly in virtue of (IV.)) by the values of p,,... pn given by (V.).

The other n — m equations of the system (III.) may then be transformed by substitution of the values

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 525

and (V.) respectively are substituted in (I.), the results are respectively equivalent to

(II.) and (IV.). Hence (II.) and (IV.) are also made equivalent, and therefore (IV.)

may be derived from (II.) by substituting appropriate functions of « for c,,... C.
Hence, by subtracting (III.) from the derivative of (II.), we have

» OF, de

Se eae see /

2s = 0 (EY 298 0) anf ere (AVAL)
Thus, unless ¢,, c,... ¢, are all constants,

SCE een)
Bi SN Regeigt fae al ce tesla came nas GN GLELG)g

§ 3. The equations (II.) and (VII.) may be considered as defining @, y,,...y, in
terms of ¢),¢)... ¢,, and the equations (VI.) will then give the ratios de, :de,:...:de,
in terms of ¢, ¢,...¢, We thus have x — 1 differential equations connecting the
nm quantities c,,...¢,. Their complete primitive will involve 1 — 1 arbitrary constants,
and by eliminating c,...c, from (II.) and (VII.) and this complete primitive we
have a solution of (1.) involving n — 1 arbitrary constants, which we may call the
Jirst singular solution of (1.)

The differential equations given by (VI.) may havea first singular solution involving
7. — 2 arbitrary constants, and from this we should derive the second singular solution
of (I.) by eliminating c,... ¢, as before.

This process may go on till we have n singular solutions, with » — 1,n — 2... 2, 1,0
arbitrary constants respectively, or it may stop at any stage. If, for instance, the
left-hand side of the equation (VII.) were an absolute constant, there would be no
singular solution at all.

Formation of Singular Solutions from the Differential Equations.

§ 4. The equation (VII.) is the condition that two solutions of (II.) when solved for
€), Cy... Shall coincide. But, generally, when this happens, the equations (III.)
give coincident sets of values for p;, DP... + Pu

of p, ... pn from (Y.), and become relations (A) connecting ¢), cz, ... ¢, with x, and yj, y,... yn which
are given as functions of = by (IV.).

Now by substituting the values of p,...p, from (III.) in (1.), we have integral equations which must
be included in (I1.).

The number of these equations will be » — m, because m ave already satisfied identically.

These equations are also satisfied if (A) and (IV.) are; for the values of p,...p, given by (III.) and
(Y.) are then the same and those given by (V.) satisfy (1.).

The system (II.) will supply exactly m further equations which in combination with (A) and (IV.)
give the values of c, c),...c, in terms of a.

526 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

If not, that is if the two sets of values of p,,... are different, all the determinants
of the matrix

Ox; SE Ou eas tan Oy ii
one om |
Ox Oy) |
OF, oF, |
Be 5.0.0 On |

must vanish (compare § 11, below.)

The equations (III.) are then not enough to determine p,, p,...p,, and the
conditions (VI.) do not ensure that the system of equations found by the above
process will satisfy (I.) and be a solution at all.

In general, then, for a singular solution, the two sets of values of p,, py... p, are
coincident. But these are given by the equations (1.).

Hence generally the equation

2 Op ot ee (Valles
O (Py; Pos - + » Pn)

is satisfied by a singular solution.

We have, therefore, the following process for finding the singular solution from the
differential equations (I.) :—

Form the equation (VIII.) and let E = 0 be the result of eliminating p,, po, ... Da
from (I.) and (VIII.). Suppose that ¢ is a factor of E such that the equation
d¢/dx = 0 can be deduced, by substitution without differentiating, from ¢@ = 0 and
(1.). Then, by treating ¢ = 0 as if it were a particular first integralt of (I.), which is
now allowable, reduce (I.) to a system of 7 — 1 differential equations in 1 variables.
The complete integral of this system belongs to the first singular solution of (I). If
is the only factor of E that satisfies the condition of being an integral, then it yields
the whole of the first singular solution.

The first singular solution of the new system of 7 — 1 equations gives the second
singular solution of the original system of m equations and so on (see also § 15,

below).

* Mayer finds this equation as the condition that the second and following differential coefficients, as
given by the equations (I.), should be indeterminate, and thus shows that (VIII.) must always be
satisfied by a singular solution.

+ If the phrase “first integral” is restricted to such as involve only one arbitrary constant, we may
use “singular first integral” for such an equation as ¢ = 0 is here supposed to be.

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 527

Analytical Connection of Differeni Solutions. (S$ 5-9.)

Seoumletusiweite J tore (ftyjars e/a) Cl(PisPos- = Pn) and Ny. Ny ea eeetor tine
minors of Of,/0p,, Ofn/Ops, . . . Ofn/Opn in J.

The equations /, = 0, jf. =0,...f,=0, J =0 give p,, po, - - - Pa Yn aS functions
of @, Yj, -- » Yn», and, for the second singular solution, we have to suppose that two

solutions coincide, that is, we put
O( fir Se --- Sn I)/0 (Dy Pa - ~~ Pus Yu) = 0.

Since J = 0, this equation may be reduced, by multiplication by X,, to

od CHL Clinton os ah
sat... $A err = 0.
* Ops a gi 5p) O (Py, + + + Puy Yu)

(od
Or >, +
Now, y, may equally well be replaced by y,, y,..., oY Y,-1, So that the condition
sought is given by the first factor, which we shall call J,.
we Grpeinows 75 =O; oseje— 0; J = 0, di— 0 GNG fp fon b oc Dy Uhim Uh OS
functions of x, y), .. . Yn», and, if the values of p,_;, P,, given by differentiating those
Of Yn1, Yn, agree with the values given by the solution of the equations, we are to find
the second singular solution by integrating the equations that give p,, ... Py».
To find the third singular solution, we have to make the system f, = 0,...f, = 0,
J = 0, J, = 0 have equal roots. The condition for this is found in the same way*
to be

and so we may pass on to the other singular solutions, if any.

3 ; Ofna : :
S16. .As Ji= i& +h, He +...+,, s we may write for the integrals that
Pi Pz Pn
have to be taken to give the 7™ singular solution
BECHER ert city eset
Tha) fu = 0. (Si le eee 2)

* The condition is ie
O( fp fa--+ tu J, J) _ 0.

O( Py, Po: - + Pas Yur Yur)

Multiplied by X, this becomes
oJ O(f = + Susi Jj) — 9,

SNe xX
Op: @ (pi 2.00 Pr» Yno an)

The second factor, being unsymmetrical, is irrelevant.

528 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

We have also identically

2
Gre) i=0 C2 Woop 1,

\

and therefore

Thus a
(= ap } (AyA + Aah =P 50557 UN) = 0,

where A,, A,... A, are arbitrary functions.

These may be so chosen that SAf is the eliminant of f,, f2...f, with respect to
P2,-++P» We will call this eliminant P,; it does not involve p,... p,.

The equations then become

y

(ng) 2 =° (Sie ee)

\ /
that is to say

ie) pes 0 (Gai b. . Ph
Thus the equation P,; = 0 gives 7+ 1 coincident values of p,. The same holds
OIE (Bey, Vx 3 oo JD

If we take a system of values of a, y;,...y, such that s consecutive members *
of the 7" singular system of solutions are satisfied, then s — 1 consecutive members
of the (7 + 1)™ will be satistied, s — 2 of the (7 + 2)" and so on to the (7 + s — 1)",
after which none are satisfied. Also s+ 1 of the (7 — 1)" system will be satisfied,
s+ 2 of the (7 — 2)" and so on, and lastly s + 7 of the complete primitive system.

§ 7. The second singular solution of (I.) is the first of (VI.) and (VII.) Now
by (VI.) the ratios de,:dce,:...:dc, are given rationally in terms of ¢,, cy... Cy,
and certain other variables x, y,...y, which are connected with c,...c¢, by the
equations (II.) and (VII.) The condition that (II.) and (VII) shall have two
consecutive solutions is

© being written for the left-hand side of (VII).
This equation we may write
) é ho Wai an
(a, + Pig, +225, + ne | Oj —0ROG eNO =—s05

oY

* Different members of the system are got by giving different sets of values to the arbitrary
constants.

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 529

where 7), Pz... +. P, have the values given by the equations (III.), ana ¢,, ¢... are
treated as constants in the differentiation.
Since Q = 0, we may use instead of the operator A, another, V, such that

de, 0 dé, 0

V = Alp Oe, + ae Oey + Ondo

for AO + VO = 02 _
By comparing VO = 0 with (VI.), we see that all the determinants of the matrix

02 OF, oF, OF,
Oa) sandeue aoc rea ince
0 OF,

i aoe

02 ak,

OC, 4 Oe, peas

vanish.

§ 8. For the third singular solution we take the further integral equation A°Q = 0
or V*Q = 0, which forms are equivalent, since already Q=0,AQ=0. The argu-
ment is the same as in §6, and may be carried on till the last singular solution is
reached.

The equations O=0=VO=V70=...=V'!0, which yield the 7 singular
solution, show that the equations F, =0= F,=F,=...=F,, when solved for
Cj, Co, .- + €,, have » + 1 coincident solutions.

§9. The equations in the other form, viz, Q=0,AQ=0... A”’02 =0, show
that the system

1D ei) Se) De iy, Mies aK)
is satisfied by r + 1 consecutive sets of values of , y),... Yn
For suppose E to be the eliminant of F,, F,... with respect to ¢, .... ¢,, we

have then an identity
E = A,F,+4,F,+...+A,F, + Bo.

Differentiate partially as to c,, c,... ¢, in turn, and we have
19) y oF. oB Y oA
pees en gee east > ye — 9
B 26, - =A, 0, o5, ZF 2c, (Gis 1)

Eliminating A,,... A, on the left-hand side, we find

ay Broa al) e CEN and) ee © aan Yep Spa Dy)
2 Gil ren St) ay Be a) OCae cs) ze E, Gi(@p calc Gn)

MDCCCXCV.—A. 3 We =

530 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

Now, in general, the coefficient of B on the left does not vanish when
O=0=F,=...=F,, and therefore B must vanish for such values, and must be
of the form

C.F, + C.F, +...+ Ca.
Thus with a shght change in the meaning of A,, A... ..,
E=Co?+ A\F, +...+A,F,.

Now, AB — 0:— AK, = 1.) identically, “and! 0/— 0) AQ) —10; i Am 0) —s0mor
systems of values that satisfy one of the 7" system of singular solutions. Hence in
such a case

B= 0, N= O0,.5 Vs = ©,
and the number of consecutive solutions of the equations

=O, Si... , 674 1.

Geometrical Interpretations. (S§ 10--13.)

§ 10. The geometrical application of the above theory to curves in space of n + 1
dimensions is easy.

The equations (II.) may be taken to represent a series of curves (that is, singly
infinite continuous series of points) in such space. Through any point a certain
number, z, of such curves may be drawn, 7 being the number of solutions of (II.)
when solved for ¢), Cy, ... Cy

At every point such a curve is met by 2 — 1 other curves of the system, and at
certain points one of these 7 — 1 curves coincides with it.

The direction of the tangent to such a curve is given by the equation (I.) or (III).

The first smgular solution is the envelope of a series of curves of the system, each
of which meets the consecutive one, and the locus of all such envelopes is the surface
(7 infinite series of points) whose equation is E = 0 (see § 4).

In general, the 7" singular solution is the envelope of a series of curves belonging
to the (7 — 1)" singular system, and such that each meets the consecutive one; the
locus of such envelopes is an (7 — + -+ 1)?” infinite continuous series of points at
each of which 7 + 1 consecutive curves of the original system meet, as also do
r—s-+1 of the s™ singular system. All the successive singular curves touch the
original curve.

§ 11. If every curve of the first system (II.) has a node, the equation (VII.) will be
satisfied at every point of the node locus, but (VIII) will not (compare § 4). If

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 531

every curve has a cusp (VII) and (VIII.) will be satishied by the equation to the
cusp locus, but it will not fulfil the condition of being a first integral. If different
curves of the system touch, the tac-locus will satisfy the equation (VIII) but not
(VIL). All this is exactly parallel to the known theory of single differential equations
of the first order.

§ 12. There is also an application to plane curves.

Suppose that the differential equations (I.) include the following :—

1D) = Up joy = Gey 3 ona Ui

Then the system (I.) simply reduces to an equation of the 1 order and its n first
integrals make up the system (II.) from which the singular solutions are derived.
If we write the differential equation

F(%; Ys Pr Pz +++ Pn) = 0,
putting y for y,, then the equation (VIIT.) becomes
of / Op, = 0,

and this is the first integral (if it is one) from which the singular solutions are
derived.

The final integral, found by eliminating p,, py... Pa—, from the system (II.), is the
equation to a system of curves, of which there are 7 passing through any point and
having at that point contact of the (n — 1)
it ; all these have contact with one another of the (7 — 1)" order.

" order with any assigned curve through

If two of them coincide, then a curve of the first singular system passes through
the point and has contact of the (7 — 1)" order with each of the 7 curves, and of the
n™ order with either of the two coincident ones.

A curve of the first singular system can be made to have contact of the (7 — 2)™
order with any given curve at any point of it.

At any point of a curve of the second singular system three coincident curves of
the original system and two of the first singular system will satisfy the conditions
for contact with it of the orders n — 1, n — 2, respectively, and in each case the
contact will be actually of the 7™ order, and so in general. The single curve of the
n™ singular system is the envelope of those of the (mn — 1)", but it is more than
an ordinary envelope since its contact with each of the enveloped curves is of the
nu order.

§ 13. It should be noticed that ifm — 1 of the dependent variables are eliminated
by differentiation from 1 simultaneous equations, the new equation, of order n, will be
satisfied by the same complete primitive, but that its singular solutions will generally

3Y 2

532 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

be different, since the singular solutions of the system do not furnish the same
values as the complete primitive for any but the first differential coefficients
(compare § 17 below).

Singular Solutions Included in the Complete Primitive. (SS 14-16.)

§ 14. In certain cases it appears to be possible for the second singular solution to
exist without the first.

The ratios de, : de.... are given by the equations (VI.) and involve a, y;, Y. . - Yn
which are given in terms of ¢,, c,... by the equations (II.) and (VIL). If these are
not enough, that is to say, if © can be expressed in terms of ¢), c,... ¢,, there is no
first singular solution.

For, from © = 0, may be deduced

n ALO)
> ee dco —10)
7=1 OC,
a further linear equation to be satisfied by de,, dce,,... Thus either ¢), c,... are all

constants, or the further integral equation

whose left-hand side we shall call 9), is satistied.

In virtue of this equation © = 0 is an integral of the equations (VI.). The values
of x, y,... Y, are given in terms of ¢,,...¢, by (II.) and 0, = 0, and by substituting
these values in (VI.) and finding 7 — 2 more integrals of the equations so derived,
we get the second singular solution, containing 7 — 2 arbitrary constants.

It would, perhaps, be better to say that in such a case the first singular solution is
included in the complete primitive, the values of the arbitrary constants being so
chosen as to satisfy the equation 2 = 0.

If Q, can be expressed as a function of c,,...¢, only by means of the equations (II.),
we must use the equation

ONE BO)

to find the third singular solution, the second being included in the first.
Because 2, = 0, 2, = 0 is an integral of (VI.), and because 0, = 0, 9 = 0 is an

integral. Therefore 7 — 3 integrals are still to be found.
This process may be carried on as far as is needed. It is also to be used if 0 has
any factor that does not involve a, y, ... Yn.”

* It sometimes happens that the equations (I.) and (VIL) are enough to define x, y;,... y, in terms

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 533

§ 15. The case of § 14 presents itself quite naturally if we start from the differen-
tial equations (I.) instead of from the integrals (II.). Let ¢, as before, be a factor
of E.

There is no apparent reason why the equation

should follow algebraically from the system (I.) and the equation ¢ = 0.

Let E, = 0 be the result of eliminating p,, p,... p, from the system (I.) and the
equation d¢/dax = 0.

Let ¢, be a factor of EK, and let E, = 0 be the result of eliminating p,,... p, from
the system (I.) and d¢,/dx = 0, and so on for ¢3, ¢,...

There is no apparent reason why any function in the series ¢, ¢, ¢,... should
vanish because all those before it are supposed to vanish. If one of them, say ¢,, does
satisfy this condition, then the equations

are integrals of (I.), and by using them and finding — r other integrals, each con-
taining an arbitrary constant, we have a singular solution of the r” system.

§ 16. Thus, as in the simpler case when there is a single equation of the first order,
the existence of singular solutions appears to be the rule if we consider the integrals,
the exception if we consider the differential equations, and in fact the number of
conditions for the absence of the first r singular solutions rises with r from the first
point of view, while the generality of the conditions for the existence of the (7 + 1)™
from the second point of view decreases as 7 increases.

of 4, C2... C,, but that when 2, y,...y, are eliminated from (VI.) by this means, an integral equation
presents itself as an alternative to a differential equation. In such a case the integral equation will, of
course, relate to the second singular solution, for it contains no arbitrary constant.

Considered geometrically, the second singular solution thus arising will be enveloped by the complete
primitive, and, therefore, also by the first singular solution (for both he on the locus of singular solutions
E = 0), although it may not be a singular solution of the differential equations (VI.).

A proper change in the forms of the arbitrary constants would reduce this case to the ordinary one.
If the integral factor is 61 ¢*!..., 0,6... being functions of ¢,c,... thenif in the system of
arbitrary constants we take 6” ¢’.. . instead of c,, the factor will disappear.

In fact the ordinary equation

y = pz — p*,
or any other, may be transformed so that its singular solution appears as an integral factor. Put

ey 7a 2
y = 1 (@ — 2)
and we find

5384 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

Examples. 1. Congruency of Bitangents to a Torse. (§§ 17-19.)

§ 17. The simplest examples are equations of CLAIRAUT’S form, such as

Y) = Pye + pe + Pips + Po: @
Yo = P2t + PP. + Po

The complete primitive is

yy = Oe + Oy" + yey + Co, (B)
Yq = Cyt + C,CQ + C4"

The singular solutions are given by the equations

0 = (a + 2c, + €,) de, + (c¢, + 1) dea, | s
0=c,de,+ (x +e+ 20) de, J mma yeti e y).

Hence, by eliminating «,

(G.de, —.c, de.) (de, -- de.) des eee eee)
This is also of CLAIRAUT’S form, and its integral is

(l—p)Q—pe =e. PONE A Ci Die tceriiels gol, (e),
so that
de, dG, =: yu: ln.
Thus
(2 + 2c; + &) (1 =p) +e (4 +1)=0,
24 = —w—p-et+ pa,

We eS yw oa
26, = B — PX,

4y, = (uw — &) (uw? + 3p + & — ap), ee ae (O
dy) = — pw (p — a

The equations (¢) furnish the first singular solution. For the second we must
make (e), as a quadratic in p, have equal roots, that is, we must put

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 535

From these and the former equations we find

—l, —17?2 — 2 — 1,2

[Pa eH oy == oes av; Cy a ee
ae SS GD oO
Th = tae ae
Ch, ores

The equations (7) are the second singular solution.

We have here an example of what was pointed out in § 13. If we differentiate the
equations () and eliminate y, and py, the resulting differential equation of the second
order is

d*y,/dx? = 0.

This is satisfied by the complete primitive (8), but not by either of the singular
solutions.

§ 18. To find the singular solutions from the original equations, we have first to try
if the equation

x+2 Do, L
ay a 22 ame 8G)
Pe a 2, - Py
can be used as a first integral.
The elimination of p, and p, gives
4(y, + Yo)? + 2? (yy + Yo)? + 4aey, + 18ay, (yi + Y2) — 27y°=0. . (y).

It is easily verified that the derivative of this equation is an algebraical consequence
of it in virtue of the original differential equations.

§ 19. If we take «, y,, y, as Cartesian co-ordinates, the equations (8) represent a
line common to two osculating planes of the twisted cubic (7), (¢) represent the conic
enveloped by this line when one of the osculating planes is fixed and the other
variable, and (u) is the equation to the torse enveloped by the oscuilating planes.

The General Case. (§§ 20, 21.)
§ 20. For any other twisted curve there is a similar theory.
Let
z+ Ay,+ By,.4 C=0

be the equation to an osculating plane, A, B, C being functions of a parameter yp.
Let A,, B,, C, denote the same functions of y,, and let A’, be written for dA,/du,.

536 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

Then by eliminating p, and p, from the four equations

1+ Ap, + B, p, = 9, a+ Ay, + By + C; = 0,
1+ A,p, + By p, = 0, a+ Ay, + By, + Cs = 0,

we have two relations which may be put in the Clairaut form

Y, = Pye + $y (Pu Po);
Ya, = Pot + hy (Pr; P2)-

§ 21. The complete primitive of these equations will represent the trace of any one
osculating plane on any other. The singular solutions are given by

A py
dz UO:

/ , d / 7 /
(Ay, + Biy. + Ch) =e = 0, (A’oy, + Bioys + C's)

For the first singular solution, either , or py is to be equated to a constant, while
the other satisfies the equation

A'y, + By, + C = 0.

The first singular solution is, therefore, the trace on any osculating plane of the
torse which they all envelope.
For the second we must suppose both p, and p, to satisfy the equation

A’'y, + By, + C= 0.

This gives the original curve, which is the cuspidal edge of the torse, together with
the nodal curve of the torse. The latter is not a solution of the differential equations.
Example II. A Bitangential Congruency. (S§ 22-26.)

§ 22. Take for another example the equations

(A+Bp/+Cp,*) {B(y—pir) +C (v.—pox)?—1} = {Bp, (y,— p12) + Cys (yo— por) }*,
(a+bp,+ep.*) {0 (y:— pix) +e (y2—poe)?—1} = {bp, (y,—p,#) + eps (Yy— pox) }?.

These define y, — pv, and y, — px as functions of p, and pg, and are, therefore, of
the Clairaut form, and may be integrated by substituting ¢, for p, and ¢, for p,.

The integral in this form will represent four lines of a congruency, which consists
in fact of all the common tangents to the two quadric surfaces

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 537

Aa + By? + Cy,” = 1,
ce yee eye = 1.

The first of the differential equations may be written
(A + Bp,? + Cp,*) (Az? + By,? + Cy? — 1) = (Aw + By,p, + Cynp,)’.
One of the integrals is, therefore,
(A + Be? + Ce,*) (Av? + By,? + Cy? — 1) = (Aw + Bye, + Cy.¢2)°.
Thus, one of the equations that give the singular solutions is
(Be, de, + Ce, de.) (Ax? + By,?+ Cy,? — 1) = (By, de, + Cy, dey) (Ax+ Bye, + Cyc).

Unless
Aa? + By? + Cy”,—1=0 and Ax + By,c, + Cy,c, = 0,

this may be reduced to

(Be, de, + Ce, de,) (Ax + By,e, + Cyy¢.) = (By, de, -+ Cyz de) (A + Be,? + Ce,?).

This last equation only contains @, y;, y2, in the combinations y, — cx, yy — Cx,
and the same will be trve for the other equation of the same form that may be
derived from the second -quation of the complete primitive.

From these two equations and those of the complete primitive we can eliminate
the ratio dc, : dc,, and the expressions y, — ¢,” and y, — ¢,x#, so as to have an equation
in ¢, and ¢, only. In accordance with § 14 the first singular solution thus given will
be included in the complete primitive, and the only proper first singular solutions are
given by taking

ax? + by, + cy? —1=0 and ax + bye, + cyoc, = 0,
or
Aa? + By,? + Cy, —1=0 and Aw + Bye, + Cy,c, = 0.

§ 23. In order to integrate for the first singular solution, it will be useful to
transform the equations to others in terms of ¢, uv, v, the values of «4 which satisfy the
equation

Aax? Bby,? Coy,” 1
a+ pA Dee (ds SoA eae
MDCCCXCV.—A. SZ

538 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

The differential equations are then reduced* to

3 (dt)? =
(u—v)t(_+f#) (a+ tA) (6+ tB) +10)” *

and
(dt)? x

> om
“(uw — »v) (1 + #) (@ + tA) (© + EB) (ce + 10)

If Aw’ + By,*? + Cy? — 1 = 0, then ¢, uv, or v vanishes, say ¢; the first equation
is satisfied, and the second is reduced to

u (du)? a v (dv)?
(1 + w) (a + wA) (6 + wB) (¢ + wl) ~ (1 + v) (a + vA) (0 + WB) (¢ + 00) *

The variables are here separated, so that we have one first singular solution.
The other is given by taking

ax + by? + cy. —1= 0, that ist = o,
and
(du)? (dv)?
u(1 + u) (a + wA) (b+ uB) (ce + uC) v(1 + v) (a + vA)(b + WB) (ce + vO)

Either of these two solutions gives as the second singular solution

ax* + by, + cy? —1=0,
Aa? + By,’ + Cy.” — 1 = 0.

* Tn carrying out the reduction we may use the formula

_Aax? Bby,? Coys? Mite ts (a — A) (b — B) (e —C) (un — 4) (uw — wu) (uh — v)
Gp wA b+ eB et paC lta @+ nA) Ob ABC aC) iG) icra Cer

and differentiate it, considering « as constant and ¢, w, v, 7), y2 as functions of a.
The expression

Aa - Bb ie Ce
nk (be)? + 5g En? + ae Cw)

may then be expressed in terms of dt, du, dv by means of the formule for 2, y;, y2, in terms of f, u, v.
Tt will thus be found that the equation

Bas MPs As) Mw Ser) Op AG. DoE Bay Chen O meer

( Aa Bbp,? Cep,” )
FenN We Teas = Ose 70

( Aaz Bboy, p, Ceyss\’ — ( Aax* Bby,? Coys? 1 )

reduces to
d?

=(u—») ((—p) 1 +8 (a + Ad) (© + BE) (CC + CH) — ¢

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 539

§ 24. In order to find the other second singular solution let us write T, U, V for
(wu — v) (1 + 2) (@-+ tA) (6 + ¢B) (c + tC), and the two symmetrical expressions.
The differential equations, cleared of fractions, may then be written

du

UVuv + VTvt ey 4 TUt (Fp = 0,

dt

UV + vase hs mul) = 0.

The Jacobian of these expressions with respect to du/dt and dv/dt is
4 du/dt dv/dt T?UVt (vw — w),
the square of which reduces to a constant multiple of
T?UPVeuv (¢ — u) (t — v).

The factors of this expression are to be considered in turn.

Now the vanishing of such a factor as 1 + ¢ or a + At only causes two solutions of
the equations giving a, ¥;, yz in terms of t, u, v to coincide and only yields a solution
of the transformed, not of the original, equations.

The solutions given by supposing ¢, u or v to vanish or be infinite have been con-
sidered. The case when two of the three are equal is left.

If ¢ = u, then V = 0, so that the equations give

TU (dvjdt)? = 0.

Suppose first that v is constant.
It is easily found, as in the theory of confocal conicoids, that

Paces (6 — B)(«—C) (a + At) (a + Au) (a + Av)
~ Aa(aB— Ab) (aC — Ac) (1 +4144) (142)

x

with like values for y,” and y,”.
Thus if ¢ = ~ and v is constant, x, y,, yz are constant multiples of

m@ sc Me oe BE @ St Ce
jeer en We eg

Hence y, and y, are linear functions of « and p,, py are constants connected by a
single relation since they involve the arbitrary constant v. This solution is therefore
included in the complete primitive and must be the same as was rejected in § 22.

3 Z 2

540 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

§ 25. If ¢ = uw and v is not constant, then TU = 0 and v =#, or else (1 + ¢)
(a + At) (b+ Bt) (e+ Ct) = 0.

The latter condition leads to no solution.

For the second singular solution we must take ¢ = «=v, whence we find that
each determinant of the matrix

ax’, Byi', yy’, 1
|
Cb, b, C, i |=,

if a, B, y are the cube roots of

Aa(aB — Ab) (aC — Ac)
(6 — B) ¢—C)

, &e,

§ 26. In the geometrical interpretation it will fix the ideas if we suppose the two
conicoids projected into confocals.

The complete primitive represents their common tangents. The first singular
solution gives the geodesics on each that touch the other, and the second includes the
curve of intersection, which is the envelope of these geodesics.

The common tangent planes envelope a torse, whose generators will be common
tangent lines. Of the four common tangents to the surfaces from any point of the
torse, two will coincide with the generator of the torse. The equation to this torse is
¢ = u, and every generator of it is a generator of one confocal of the system. Thus
the equations ¢ = uv, v = const. represent the different generators of this torse, and
their occurrence as an apparent singular solution is accounted for.

The cuspidal edge of this torse is a second singular solution, and is represented by
the equations

ax’, By’, ye, L |
a, b, @ i) 0;

The General Case. (§§ 27-38.)

§ 27. The straight lines
= G01 5, 2d 2 ee ee

x= Coe by OS Teal

where the quantities b,, b, c,, cy are connected by two relations, but are otherwise
arbitrary, form a congruency, and, if the relations are properly chosen, may be made
to represent any congruency.

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 541

Thus the lines of any congruency satisfy differential equations of CrLATRAuT’s
form.
§ 28. If two consecutive lines meet, the equations (1) and (2), with

O) aioe Cle le ekg eh 5. 2) 5 8) (8),
DS ava fas eae ein Ve Oe, is oo pe a (A)
must form a consistent system.
Hence
HO Okey —= Wheaten sO) oe ded 5 ge gS)

This equation gives two values for the ratio dc, :dc,, and shows, therefore, that
each line of the system meets two consecutive lines (SALMon, “ Geometry of Three
Dimensions,” § 456).

We are supposing that b,, b, are regarded as functions of ¢,, cg.

§ 29. The elimination of ¢, ¢, de,, de, from the equations (1), (2), (3), (4) will give
the equation to a surface, and the tangent plane to this surface will contain the line
(1), (2). For the equation to the tangent plane is found by eliminating dc, dc,, dr
from the differentials of (1) and (2) and of

gare Ue
DN lrromant aa Ons ey DORM ee Tes sree WO)
ab, ab\

and substituting X — a, Y, — y,, Y,— y, for dx, dy,, dy, (6) and (7) are found
from (3) and (4) by the use of the undetermined multiplier X.
From (1) and (2) we have, considering c, and c, and therefore also b, and bd, as
functions of x, ¥;, Yo;
dy, = c,dx + «dc, + db,,
dy, = Cy da + «de, + dbsg,

and therefore in virtue of (6) and (7)
dy, + \ dy. = (ce, + Ac.) da.
The equation to the tangent plane is therefore

Y¥, — |X +A(Y, — @X) = y, — oy" +A (Ya — C0)
= b, + Aby,

and the tangent plane contains the line (1), (2).

542 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

§ 30. Hence if the equation (5) gives unequal values for de, : dc, the lines of the
congruency are bitangents to the surface whose equation is found by eliminating
C1, Cg, X from (1), (2), (6), (7).

The singular solutions of the differential equations are the solutions of (5), that
is, of

ab,

‘de? +
2

ab, ob,
pce

ob,
ped ee A Ae eu tete Qe
ae a de, dey a dc—s0.

an ordinary differential equation connecting ¢, and c,, from the solution of which two
equations are to be found free from ¢, and ¢, by help of (1), (2), (6), and (7).
§ 31. The equation connecting X, ¢,, ¢ is

52s, (8 By) Bh
oe ae
Now
du, = c, du + adc, + db,

| ab. a
Gr dx — Me dc, | as de., by (6),

abe ay
dy, = c, dx + aE de, — ot de,, by (7).
1 2,

But if the differential equation is to be satisfied we must have

Qi — CN OY — CO a
and therefore
de, + pde, = 0,
where

so that p is the second root of the quadratic for A. This can only hold at one point
of contact.

§ 32. The integral of the equation (5) thus represents a double system of curves on
the surface, one curve being traced by each point of contact of the double tangent.
One curve is such that every tangent to it touches the surface again. This is the
first singular solution. The other curve is the locus of the other points of contact
of the tangents to the first and is not a solution.* One curve of each system goes

* Tn the case of § 17, this curve is found_to be the straight line
yy = x (we — Qn) + Bn? — 25,
Yo = — wp? + Ww,
and it is included in the complete primitive.
This will always happen if the surface is developable, for the first singular solution is then the section of

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 543

through each point of the surface for every double tangent that can be drawn to touch
the surface there.

§ 33. As to the second singular solution, it is apparently given by the equation
\ = p (these are the two values given for — de,/de,), or

Gens ee,
Ge WE Gla, Geamccy

If there is such a solution, which is not generally to be expected, it will represent
a curve on the surface every tangent to which meets the surface in four consecutive
points. Such tangents to the surface do not, however, generally envelope a curve
on it.

Case of a Nodal Curve. (§ 34.)

§ 34. The case of a surface having a nodal curve deserves consideration.

The tangent to such a curve meets the surface in four consecutive points, and is
therefore to be counted as a bitangent. The curve satisfies the same differential
equations as the bitangents, and the two values of x given by the elimination of the
differentials from (3) and (4) are equal, so that the curve is to be reckoned as derived
from the singular solution of (5), or as a second singular solution of (1) and (2).

But here a paradox presents itself. There are two tangent planes, and therefore
two values of \, whereas the equations (6) and (7) only yield one unless they are
identities.

We have then

ae 0c, 0c,
Cli Oi
a an =O

Generally, these equations are not consistent, and therefore, generally, there will
be no nodal curve.

But on the other hand it will generally be possible to find a singly infinite series of
values of #, ¥;, Y,, such that the equations (1) and (2), solved for b,, bg, ¢, ¢a, shall
haye two pairs of coincident solutions, and the corresponding curve will be a nodal
curve on the surface.

The explanation of the paradox is that the surface will generally have other
bitangents as well as those belonging to the given congruency. These will form

the surface by a variable tangent plane and the tangent to this section touches the surface again at a point
on the generator along which the plane touches the surface. The generator is therefore the locus of the
second point of contact, and as it is the intersection of consecutive tangent planes it is included in the
complete primitive.

544 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

another congruency, satisfying another pair of differential equations, which the nodal
curve also satisfies.

For instance, the normals to an ellipsoid are bitangents to the surface of centres,
but there are other bitangents, which form three more congruencies (see SALMON,
‘Geometry of Three Dimensions,’ § 511a). The double curve satisfies the differential
equations to the congruency of “ synnormals.”

If we reciprocate we find the same paradox in relation to the double tangent planes.
The line joining the points of contact will generally belong to the second congruency,
and the cuspidal edge of the torse which it generates will satisfy the differential
equations to this congruency, and belong to its second singular solution, the corre-
sponding first being included in the complete primitive.

Case of a Cuspidal or Parabolic Curve. (§ 35.)

§35. At first sight it would appear as if a cuspidal curve ought to satisfy the
differential equations to the bitangents, since any tangent to it meets the surface in
four consecutive points. But the consideration of the reciprocal surface shows that
the tangent planes drawn through such a tangent include three coincident ones, not
two distinct coincident pairs. The tangents to a cuspidal curve and the inflexional
tangents at parabolic points are therefore not to be counted as bitangents.

When a surface is varied continuously so that a nodal curve changes into a cuspidal,
some of the bitangents become chords of the cuspidal curve, and among them are to
be reckoned the tangents to that curve. In the same way the inflexional tangents at
parabolic points are included in the congruency formed by the intersections of tangent
planes at pairs of parabolic points. Thus in a sense the congruency of chords of the
cuspidal curve, and that of double tangents to the torse enveloped by the tangent
planes at parabolic points, are limiting forms of bitangential congruencies belonging
to the surface, though they cannot be considered as true bitangential congruencies
belonging to it.

Digression on a Certain Singularity of Surfaces. (S$ 36, 37.)

§ 36. If, however, the curve is both cuspidal and inflexional, in a sense which we
shall shortly explain, the tangents to it are true bitangents to the surface.

If we suppose the inflexional tangent at each parabolic point to coincide with the
tangent to the parabolic curve, then that curve must be plane or else a double curve
on the surface. For the tangent plane at each parabolic point coincides with that at
the consecutive point along the inflexional tangent, and hence the tangent plane is the
same all along the parabolic curve. A double curve will, however, satisfy the con-
ditions, if we consider the tangent plane at each point as indeterminate. Buta nodal —

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 545

curve will be an irrelevant solution, unless it has the singularity in question on one or
other of the two sheets. A cuspidal curve may yield us the true solution.

Now it is easily proved that the osculating plane of a curve traced on a surface
will coincide with the tangent plane to the surface when it touches one of the inflexional
tangents, and only then. The osculating planes of the curve we are discussing will,
therefore, be the tangent planes to the surface at the points where they osculate the
curve.

Thus the singularity under discussion consists of a cuspidal curve, such that the
osculating plane at every point of it touches the surface at that point. The corre-
sponding singularity on the reciprocal surface is of the same kind.

§ 37. To prove this write the equation to the surface (multiplied by a factor, it may
be) in the form \¢? = pw’, d, pw, ¢, w being functions of a, y, z, such that 6= y= 0
are the equations to the cuspidal curve.

Put

= py =t,
then
b= Op, b= rp.
Suppose now that

o=2-+rhtoet.
Par Uy ae 5 ar eae

¢, and w, being homogeneous in 2, y, x and of the degree r.
Then we may deduce expansions for y and z in ascending powers of ¢t and was
follows—

y=oa?+PBP+...

+a (y+...)

staves (Olle pres) es
z=aeP+tPBet...

+a(y?+...)

+e (Fe? 4+...) +a7(C4...),

the first power of t being absent throughout.

More generally, we have in the neighbourhood of a cuspidal curve (t= 0) expansions
of the form

“x=e%,+ta,+Pa,+...
Y=Ytimtlyt...
2=%+%+02,4+...

w=wt+tutPwt...
MDCCCXCV.—A. 4A

546 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

where 2%, Yo.-- %, Y,;--. are functions of a second variable uw, such that all the deter-
minants of the matrix

| 2, Yr 2 Wr

| ©, Yor 2 Wo

a R999 opp 0
| Ly, Yor > Wo

vanish, dashes being used to indicate differentiation with respect to uw, and dots

differentiation with respect to ¢.
If € », ¢, w are the determinants of the matrix

a, Oh, By UW |?

/ / f? /
| “x,y, z, W

then the reciprocal surface is the locus of (€, », ¢, @).
We will now find whether the curve ¢ = 0 on the reciprocal surface can be cuspidal.
If € », » are expanded in powers of t we have at once & = 0, yn, = 0, & = 0,
w) = 0, €, denoting the coefficient of ¢” in €, and so on,
We also find

ay & + Yo T % 6 + wo, = 0,
Ly Eo + Yo Nz H 2% & + Wy = 0,7
XE, + Yom +O + wo, = 0,
ty fo + Yo Ns + % & + Wy @, = 2

mY / post / —
Lo» Yor % >» Wy | = 2A, say.

X, Yo, %, Wo
|
©, Yo, 2, Wa |
|

aw, On Bee
| My, Yrs > Wy
and hence, differentiating the first and using the third,

Hoey + Yom’ + 2oby + wow,’ = 0.

Also
‘t ” myth? ; Ww = ee ed? LL v/ piss
®y'E Yo M + 2% G + Wy oy = 2 | “0 » Yo »% » >, | = — 2A, say,

| Zo Yor 20» Wos |

| |

®, Yo, %, We, |

igen tory , , |

| 4 > Yo> % > Wo >»

so that

Go sh Yor =F BiG + Wy Wy, — ON

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 547

If }, p are quantities such that

ty = vy + Mito, Yi = Mo + BYo» ete.,
then it is clear that A, = pA.
Hence, if A = 0, all the determinants of the matrix

| 1 Ny) C Or
| Sy, Uy (Gy Oy. | vanish.
| ane Ma 6 (Gs @ |

This is the condition that the curve ¢=0 should be cuspidal on the reciprocal

surface, for the common factor ¢ has to be taken out of the expressions for & 7, @ @,
and the expressions for the coordinates become

GIT = Siar fot 4+. . . etc.

We find, moreover, that
Lok, + Yons + %lz + Wo; = — WA = O,

so that the reciprocal surface satisfies the condition

Ses 3, Ge Ws
Go tin Gy Or | =O,
| fy; mM» Ge @,' |

| wt

4} 4;
en er p

which is of the same form as A = 0.

Hence this singularity is of the same kind as its reciprocal. The tangents to a
curve of this kind are true bitangents to the surface, since they meet it in four
consecutive points, and their reciprocals meet the reciprocal surface in four consecutive
points.

Lastly the condition A = 0 is that which must be satisfied if the tangent plane to
the surface, namely

Hy, Yo, %, Wy |

coincides with the osculating plane of the cuspidal curve, that is
4a 2

548 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

8
Ss
S
=

a
2
>

I
co)

ad
| ao Yoo 2.9 Cy
This proves the theorem.

It is clear that the cuspidal edges of developable surfaces belong to this category,
and thus the second singular solution in Example I. is accounted for.

Example III. (§ 38.)

§ 38. As an example, we will take the system of lines represented by the differen-
tial equations

Y, = Prt + Fpo’,
eas 1 2
Yo = Pot + gPy’-

It will be more convenient to use y, z, p, q instead of ¥,, Yo, Pi, Po
The complete primitive is clearly

y = pu + 30%,
2 vet op.

The singular solutions are given by the system

cdu+vdv = 0,

vdv+ pd = 0.
We find

ee
pi dp +vdv= 0,

3 + $v? = c, a constant.
Thus, for the first singular solution,

go? == 378 (26 — v7),
y = pau + gr”

= zhv (18¢ — dv’),

By eliminating v from these equations we have the two equations to a curve
belonging to the first singular solution, that is to an envelope of the bitangeuts.

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 549

If now we take the other value of x given by the quadratic x? = pv? we find for
the other point of contact
2 = — 3% (2¢ — e)),

= — yyy (18¢ — 137”),

au 9
Z= Sage i0c <= 110°).

The elimination of v from these equations gives the locus of the other point of con-
tact.

There is no second singular solution.

The equation to the surface which has the lines for bitangents is to be found by

eliminating p, v from

It is
31252 — 9000x7yz? + 8100x>yez + 2592x42° — 19440%y? — 2592x°y2z4 + 648y%23 = 0.

Any point of this surface may be represented by the coordinates

/

(a BoA the)

The direction cosines of the tangent plane are proportional to

Hence if the line
y=ke+l

is a tangent to the surface at this point, we have

Eta she tl,

v

ve+h E = mé Fe N,

ws

pe — : = — ké + mv’,

and therefore

590 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

If the straight line is a bitangent, these equations are also satisfied when other
values &, v,; ave put in the place of €, v respectively.
Hence v and », are either the same root, or different roots of the equation

that is,
ie
or else
VV) 3
yptp,—- 7)
at a p+op ee
and
VV" 3]
——+ = 3],
V+ Vy

Also €/y and €,/v, are either the same or are different roots of the equation

3 (E/v)* — 2k (E/v)? — 2n = 0,
in which case
g/v cae a 1/1,
or else
EB) + Et)n? =H,
BE 2p? = — 3n.
The solution
ae (Ss &

is irrelevant; the solution

gives the original congruency, and

pan, +E = ty

gives

A new series of bitangents is given by taking

Ev = — &/y, v=.
We have
y+ vp, +»? = 2m (v +),

yyy, = — 7l(v+y),

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 551

whence

1 il 1 2) 9

i +5 )=te +m),

Vv Vy

or
— 4py, =v? + v,?.
Hence we deduce that
l= — 3m’.

The elimination of € by help of the equation

3 (E/v)* — 2k (Ev)? — 2n = 0,

gives
8192n (kK? — 2n)? — 384km* (18n — hk?) — 243m8 = 0.

These two equations, connecting k, 1, m, n, define the second congruency of
bitangents to the surface.
A third is given by combining the equations

y+ pv, +r? = 4m(v +n),
vv = — Zl (v +»),

Bt + Bef = Hs

PE t/Pn? = — 4,

EP + p= kEFL

SW ale at ay)" = kg, + 1.

The result of elimination may be expressed by saying that the expression
256u? + 9u? (641m — m*) + 18u (21m? — Im*) — 97? (m3 — 31)?

contains the expression
27u? — 2u(k®? — 18kn) — 2n (k? — 2n)?
as a factor.
The surface has a nodal curve and a cuspidal curve. These are found by expressing
the conditions that the equations
y= 2) +P

z= va + dat)

solved for v, may have a pair of common roots. ’
If the roots are different we have a nodal curve, to wit, the curve traced by the
point
(405, £249, 4948)
for different values of ft.

552 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

If the roots are equal we have the cuspidal curve traced by the point
(Be, Bae, 20%),

It is easily verified that the tangents to either of these curves are included in the
third congruency of bitangents to the surface, and that accordingly the curves will
satisfy the differential equations to that congruency.

The cuspidal curve on this surface has the property discussed above (§ 36), and it
is for this reason that its tangents are included among the bitangents to the surface.

/
Example IV.—Inflexional Congruencies. (S$ 39 to 50.)

§ 39. When the two values of dc, : de, given by the equation db,dc, — de,db, = 0
(§ 28) coincide identically, the lines of the congruency are inflexional tangents to a
surface.

For if the direction-cosines of the normal to a surface at the point (x, y), y2) are
proportional to /, m, n, the directions of the inflexional tangents are given by the
equation

dadl + dy,dm + dy,dn = 0.

Hence, from the last equation of § 29, we find that the directions of the inflexional
tangents in that case are given by

dddy, = dx (de, + dde, + cad).
But the equation

ob 0b, |= 0
| OO; 2
a 0c, ’ Oe, |
ob ob
| ee 2
| agg ae inane
has equal roots, so that
ob Ob,
Be trae Se
Yes? (5, i Zl
Oa ( 0b, 2)
0c, 2 \ de, 0c, |’

= (de, + Adcz).
1

Thus
Ob,
dy, — eda = \ (de, + ddc,),
1

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 553

and the above equation for the inflexional tangents becomes
0b,
(dy, — c.dx) = dy — de) —=10-
1

Hence one of them is parallel to the plane y, = c,w.

But it must lie in the tangent plane and pass through the point of contact. It is,
therefore, the line

Jy = Oe + dy,
Yn = Cyt + ba,
which was to be proved.

It is remarkable that though from this point of view a congruency of inflexional
tangents appears to be a particular kind of bitangential congruency, yet when they
are considered from the point of view of the surface, the one is as general as the
other, and every surface, whose degree is not 2 or 8, has one of each.

Degenerate Inflecional Congruencies. (§ 40.)

§ 40. An interesting question arises as to whether there is a degenerate form of the
inflexional congruency when the surface it envelopes is replaced by a curve. In such
a case the lines of the congruency that meet the curve at any one point will form a
cone, and the cones belonging to consecutive points of the curve must not meet each
other, for if they did they would envelope a surface, and the congruency would be of
_ the bitangential kind. The only kind of conical surface that will meet the case is
easily seen to consist of one or more planes touching the curve, and the congruency is
made up as follows: Planes are drawn through the tangents to a curve according to
some fixed law, and lines are drawn through the points of contact in each plane. The
planes will envelope a torse on which the curve will lie, and thus the congruency may
be said to consist of all the tangents to a surface at the points of a curve on that
surface.

The existence of these two kinds of congruency appears to have been overlooked in
the classification given by Satmon (‘Geometry of Three Dimensions,’ § 453). It
might also be desirable to break up the first category given there into two, the
bitangents to a surface and the bitangents to a torse, that is, the ‘ lines in two planes”
of a curve. The third category would then have to be divided into three, according
as one, each, or neither, of the surfaces was developable, and the fourth into two.

Consideration of the General Surface. (§§ 41-49.)
§ 41. Take the surface

Cl CH Oy OF) =O” phe eae cic gee a bly
MDCCCXCV.—A. 4B

554 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

The line

i On meine ates so 2 ((B),
Yo = Cyt + db, i
will be an inflexional tangent if the equations
WiL== 0, Chile = 0, eMLiGn? =
are satisfied together, where

M= $ (, eye + d,, Cope + 0°).

By eliminating w and putting p, for c,, y, — px for b,, &., we have two
equations of CLAIRAUT’S form satisfied by the lines of the congruency.
§ 42. For the singular solutions we have

wile, dh, = 0. Mee tar (4).

ade dbs = .0' oy, (oh i ss ee re)
= ite des + 55 db, + 5), ds =a ©), (because Fi = 0) nen, (5),

eM ooM o7M OM OM. \
ened de, + ene. dey + ay db db, + anal dos — 0) (because eva a 0) sana)

aye ee, 1 aurea, + ap vas, 2 + 5.35 ate t ae =O rere

But

Oe, a i Ob, ‘ Oc, 7 B Ob,

and (7) gives

cM eM OM oM
eS ak aa 5, des +} ae de, + 5, de, = 0.

Therefore

Of SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 555

and either

eM OM
B= kX OV Anan oo 8 Angi ay, 12 = 0

Also (8) becomes
oM M 2M M OM
(u — 2) {array es + seep, 2 ca} +2 {5 ay Oe + aan Cet + 5a de =O.
§ 43. First, let » =a. Then

M = ¢(, y, Y2) = 0

OM _ 96), oH Ob

au ae Tay, + Gy, =

oM o . oF een ee ee Ob
One — ax? + 2C) Ox Oy, + Cy 0x OY + Cy Oy? ar 2C)€5 Oy), OY» + Cy Oya” rie 0,

OM de, ti oM de, Ue Op de, , 0 de, ne
Ob, dx | 0b, dz ~\ Oy, dz " Oy, dz

The last equation and the equation (8) are satisfied in virtue of the first three and
the equations p, = ¢), Py = Cp.

The integral of these equations represents a series of curves on the surface ¢ = 0,
each tangent to each curve being an inflexional tangent to the surface.

Second Singular Solutions. (SS 44, 45.)

§ 44. If there is a singular solution of these equations, it is given by supposing two
consecutive curves of the series to intersect. At their point of intersection the
inflexional tangents will then be in the same direction, and the singular solution
therefore appears to be the locus of parabolic points on the surface. We shall,
however, find that this curve is not a solution at all in general. The consideration of
the reciprocal surface suggests that a cuspidal curve may supply a solution. We
begin with the parabolic curve.

We take, as a trial solution,

Od , o> Op _ ob
Ox? eG Ox OY, we Ox Oy, Oe?
Op op Op _ op

Ox OY; mi Oy TiS 2 ein | Gyn

Od ae ep os
gues 1 Oy, Oya ate Oy? “Ge
4B2

556 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

In order to test whether this is a solution, we differentiate totally, multiply by
1, ¢,, ¢,, and add, and we have

d F) d\'/0 a ot le Oh
ie + Pig + P25) i. ee toy, — ban) Oe B * Onn ap i Oy, =

where the dashes outside the brackets indicate that in differentiation ¢, and c, are to
be treated as constants,

In this equation the substitution p, =¢,, p, = cy will make the coeflicient of x
disappear, but the other terms will generally not vanish, and therefore the locus of
parabolic points is not generally a solution of the differential equations of the
congruency.

It is, in fact, generally speaking, the cusp-locus of the first singular solution.

§ 45. Suppose, now, that the surface has a cuspidal curve. It may be shown that

this is a solution.
For at any point (#, y,, y2) on the surface, the equations

Op = Gee oD Y, = €,0 4-105:
Mi; oM/op = 0, o°M /op? = 0
are satisfied by putting

[Pe bh =y — oe, by = Yn — Cy

if ¢,, C, ave determined by the equations °

5 ASR 2 Ob Ob As
ay, 1 Oy? ae 2 Oy, Oy, +e e Sy

From the latter may be deduced, by differentiation, on the supposition that
de = dy,/¢, = dy>/¢,, which is consistent with ¢ = 0, that

eee 0 Og Ob Oo
eee % e255) e+ 2(3 alee Bey qe e057) (a, ON + gat oa a)

9 (22 Oey dc, \ / Op Od Op
+2(= 1e Ghar. eG age liGee Fe Gray ° oe )= O.a eee (9).

The equation (9) holds all over the surface.
Now, at a singular point where there are two coincident tangent planes,

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 557
and

19,

0 ra) 0
Ge tag, +%a,) 4

is a perfect square, so that the first equation for c, and c, is nugatory, and the second
may be written in any of the forms

as Od Og
ae oF aP

Ox OY, 2 Oy OY me
Ob Od op
Ox OY), aca oy? T Oy, OY, =
og Ox) Op

Bet, © layer, 2 ae

The equation (9) will therefore not contain the differential coefficients of ¢, and co,
but will be available to determine c, and c¢, themselves.

If there is a cuspidal edge these things hold at every point of it. Let m,, m, be
the values of p,, p, taken along the edge, and let us write D for the operator

6) 0 6
an +m, an + Tivos .
Also we may put

BS Bea db ae) she Coes,
fe? Beg ED Gee OED Gy LP aaey, Ee Bs

The equations giving the inflexional tangents are then

LF py P+ BoP. = 0.
=

mt BPA =o + 3py = gis Big -eariaiate OD e anamians te OL 2. anny

Op 3 Op
ee

og od
ae Die Oy, 33 3p? ay + 3p py"
We shall show that these two equations will, if p,, p, are considered as coordinates,

represent a plane cubic and one of its inflexional tangents.
We have

ee EDN eee
a2

Thus,

Caray Op 5 Op apie
fe Hee a 2D Ee 4+- m,? Des 5+ 2mm, Tae. + m,° D

= 2(A + ym, + sts) (Dd + m7, Dp, + mz Dy)

As

558 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

for the first factor clearly vanishes, since ), p, @, are proportional to the direction
cosines of the tangent plane.
Also
Op C2 Op op
Dae + (m + p,) D ee + (mz + p,) D ay, + mp, D ay

o op
+ (1, Po = Mep;) De. = ar M2P e OY,”

= (A my + pygmy) (DA + p; Diy + P2 Dery)
+ (A + papi + MP2) (DA + mm, Duy + 172 Dury)
= (A+ papi + pops) (DA + m, Dy + my Dpy),

and
ae p?¢ oe on Oe
De® + 2p, Dae + 2p,D a Pa a ee no De

= (A+ mpi + MP2) (DA + p, Dy + py Dyts).

Thus the point (7, m,) lies on the cubic, its polar line is \ + pp; + pap, = 0, and its
polar conic consists of this line and another. Hence the three solutions of the two
equations coincide, and we have p,; = m,, py = Mx.

Thus the cuspidal edge is enveloped by the inflexional tangents, and is a solution
of the differential equation of the congruency.

If the surface has a nodal curve the equations M = 0, 0M/du = 0, 0?M/op? = 0 are
apparently satisfied along it, but these equations, as they stand, are not enough to
determine ¢, and ¢,, and when ¢, and ¢, are evaluated by means of another differen-
tiation they are not generally equal to p, and p, taken along the nodal curve. In
fact there are two inflexional tangents in each sheet at every point, and the tangent
to the nodal curve is not generally the same as any of the four. Hence the nodal
curve, as such, is not a solution.*

Another Second Singular Solution. (§ 46-49.)

§ 46. Let us now take the alternative of § 42 and suppose that

=e, ss 5, es = (0)

* The lines that touch the surface at points on the nodal curve form such a degenerate inflexional
congruency as was discussed above (§ 40), and they will satisfy the differential equations to the inflex-
ional congruency of the surface in the unreduced form in which we have used them. The tangents to the
nodal curve form a first singular solution included in the complete primitive, and the nodal curve belongs
to the second singular solution which also includes the cuspidal edge of the torse enveloped by the
tangent planes.

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 559

Then as c, and c, are not both constant, we have N = 0 where

This is a further condition connecting b,, b3, ¢), ¢:, uw. From it we deduce

oN oN oN oN oN
ano o ae, 02 + my = ay lear an adj = 0.

A
Cc

From this and the former equations we can again eliminate the differentials.
Suppose the resultant equation to be P= 0. Then the equations N = 0, P = 0 afford
an integral of the differential equations. We will verify this.

§ 47. N = 0 may be replaced by

oM oM
0b, Cr T Ob C, = 0,

OM OM

ne LS Gna

where C, and C, do not both vanish.
Also P = 0 may be replaced by
oN ON\ ,, , /ON oN Ne
ae Ay, | Chee ty) Gta K= (10),
oM \ 8M OM
(uo) 1 +(e 2) © + Rew oes (Up

We have also M = 0, 0M/ou = 0, o?M/op? = 0.
The last three equations give

aM fie ONE
Ob, (Hey bY) a ab, (ue's an v’,) =
if we write c’, for de,/dax, &c.
We may then put
poy + by = uC, pe, + bn = uC,
They also give

oM OM , OM. pou
A Ow ee Oe Cle Ce

560 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS
so that we may put
CoC nce — Oe
b', = (u— pr) C,, 0’, = (wu — pr) C,.
Further, they give

OM oM oM oM
OPA © Cr+ serpy WO + 25 = DO reese a5 =

whence, by comparison with (11),
uK = (p— 2) pi.
Again, since N = 0,

el +5. eC +5, (= pe), + ter SS NO. =e.
Multiply this by » — x and (10) by w and subtract.
The equation connecting uv and v is then found to be
fu—v(u—a)} (& Oy + 5 Cs = eee)
Thus in general u—pv= —va, that is, cya@+b',=0=c,4+ b’, and the

ditterential equations are satisfied.
§ 48. In the case when N = 0, P + 0, we still have

les Ok ee Or a Ch eeolby 2Gliny

but the ratio de, : db, is unassigned.
The equation to the tangent plane to the surface at

(mM, ye + b,, Com + bg)

oM oM
(y, — aa — b,) a aL + (Y2 — 9 — bg) Ob

DO)

is, as always,

Hence, when N = 0, the tangent plane at any adjacent point is

me ‘oM, oM, \ lea (OM ie
(y, — qa — b,) ( mm UC Oh } + (yz — cyv — by) (a, +d 2D, ) ai):

Thus the tangent planes at all adjacent points pass through the same straight line

y, = cx +),
Yay = cx + by

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 56]

Hence the point is a parabolic point on the surface, and the line of the congruency
is the intersection of tangent planes at two consecutive parabolic points. All such
lines will generate a torse, and they would belong to the first singular solution were
they not already in the complete primitive.

§ 49. The intersection of two consecutive generators of this torse is given by the
equations

y, = 0,0 + by,
Yo == Cyt ++ dg,
« = — db,/de, or — db,/dey,

where by, ¢, by, c, are connected by the equations
M0 0M op O02 Mion —) Oe N10)

These equations are satisfied if P = 0, and therefore the cuspidal edge of this
torse is the second singular solution given by taking N = 0 = P.

A Particular Kxample. (§ 50.)

§ 50. As an example of an inflexional congruency, we may take the system
of. lines
y = 30°*b'x + 40° (1 — 6a’),
z= b? (1 + 2a3) w — 3 a'd°.

These are half the system of inflexional tangents of the surface of § 38.
It is easily veritied that the cuspidal curve is a second singular solution, and the
nodal curve not.
The first singular solution is given by
a=ab>, b= constant.
lt is

a“
— 1 j9
y= tah,

2=4 5B + ba.
The system
y= (4 ey 2 — 90,

z= 2b°x + 3 atb® — ab ,

MDCCCXCV.—A, 4 ©

562 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

which includes the other inflexional tangents to the same surface, would serve
equally well.

This example shows that it is possible for the inflexional tangents to a surface to
form two distinct congruencies. The parabolic and cuspidal curves, moreover,
coincide.

Example V.—System of Curves ii Space. (S§ 51, 52.)

§ 51, As another example, take the equations

da? CRP 8 GkP

e—1” f-17> #—1°

The complete primitive is the result of eliminating ¢ trom

1 1 1
ZAP a 2y =at+—, 22 = bt +- —

a and b being the constants of integration.
The curves represented are conics touching the six planes

e=+1, = se ils 2—-4-1.

The first singular solution includes six forms—
F 1 1
ple 2y = u + —, Vif, == Oh, > === 3
Uu u
: 1 1
YW = se ll DTA UTD aaa PH = (60) aS
1 L
; 1 it
ole MEM 2) —" CW ae

in each w is a variable parameter, and ¢ an arbitrary constant. The curves repre-
sented are conics inscribed in the six faces of the cube contained by the planes

Cs stale z2z=+1.

The second singular solution consists of the twelve edges of this cube.
§ 52. If we seek the singular solutions by means of the differential equations, we
take
pe — 1) SF 1) 0
g(a —1) —(# — 1) = 0,

and form the Jacobian with respect to p and gq.

OF SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS. 563

We thus find
pq (x —1P=0,

*=+1, ory=+1, orz=+1.

whence

Any one of these is found to be a singular first integral, and tc reduce the equations
to one of the form
p (a? —1)=y?—1,

which we have seen how to integrate.
The singular solution of this is again

(x* —1)(¥° — 1) =0.

System of Plane Curves. Another extension of Cuairaut’s Form. (§§ 53-55.)

§ 53. There is an extension of CLA1RAvT’s form to higher orders, with one dependent
variable.

Write p, for d’y/dx’, so that p, will mean y.

Then integration by parts gives (7 being Kin),

(Pes a“ dx =x; Wires TP OI Des ar r (7 a 1) BB Orr o 0 + ( Fe Vy ue ! Pr
Call this expression q,, and take the equation,

d (Yo > Oh) Riches! Qu) ='(0)

This may be solved at once by differentiating ; since
dq,/dx = 2" r+

) 0 .6 A
Pasi {ge + oge tas De + unt | = 0,

Odo Gn

we have

The first factor gives the complete primitive, which consists of the equations,

Oy Ch Ui Chin oo o Op = Cy

where Mp, @,... G, are constants, connected by the relation

Ol (Ch Chip 6 0 o Wp) = O;
but otherwise arbitrary.

The value of y may be found as follows—in the equation
Uy 0” = py — Tp" > + 1 (7 — 1) pp_2X"”
take differences with respect to 7; thus

[eG PE es (oN pects (A FE Sh ann (Ge eae ern en st olo 6
AN Cre?

564 PROFESSOR A. C. DIXON ON THE SINGULAR SOLUTIONS

Put now s =n, 7 = 0, and we have finally

n(n — 1 :
(= Pal 7S Maya SS Gy = © Gand? oP ae Un2 B... + ( — 1)"a, a,

the constants being connected by the relation

O((Ghy Chy oo» Ge) = O,
§ 54. The factor ' : :
Di Te a Oe yee)
ee ee ste Gn ”
equated to zero, leads to the singular solutions, the first integral being found by
elimination of p, from ¢@ = 0 by means of it.
Thus the solution of $(q, q.--) =O is exactly on the lines of that of
Ws (ap; — ¥, P,) = 0, which is CLatravutT’s form.
§ 55. The equations to be integrated in finding the singular solutions are

a

da, diy __ dts Ut,
ity tht Ohi tng

(hy Chis a 6» Gn) = 0,
For example, when 7 = 2, we have
9
da,” = day das,
@ (Ao, %, A) = 0.
If (a, @, @) ave taken as Cartesian coordinates, the solution represents curves on
the surface ¢ = 0, the tangents to which are parallel to generators of the cone
@,° = Mt, that is to say, meet a certain curve at infinity. The second singular

solution is given by forming the envelope of such curves, which does not generally
exist, but may in particular cases.

Example VI. (§ 56.)
§ 56. As an example take the equation
(2yp, — py’)? = 4p2 (Pi — xp2)*, Or (Yo2 — GV)’ + 4qom? = 0, 7 beg 2.

The ccmplete primitive is

dacky = 1+ 2c + daca + Adateea®.
The equations giving singular solutions are

(1 + 6e?ex). da + 6ax.de = 0,
344

; 2¢ C
(a = Sa | da = mee de a)

OF SIMULTANHOUS ORDINARY DIFFERENTIAL EQUATIONS. 565

The result of eliminating « is
ce da® + 3(cda + ade) { (1 + 2c)eda + (3 + 4c) adc} =
The complete primitive of this is
a — bacra — bac? = 0,
and for the singular solution of it we must take
a= 3ac? = — 2ac,

The solutions a = 0, c= 0 arise by giving « the particular value zero, and the
true singular solution is
2+ 8¢ = 0.

Hence for the first singular solution

a? — 6acta — 6a7%c? = 0,

acy — 307% + 80y — 1 = 0.

For the second
ye
This is the equation to a parabola.

The curves of the first singular system are hyperbolas, having their asymptotes
parallel to the axes of coordinates and having contact of the second order with this
parabola.

The complete primitive represents a series of parabolas with axes parallel to
the axis of y, and each having contact of the second order with some one of the
hyperbolas, and, in fact, with two of them, since « is given in terms of a and ¢ by a
quadratic equation.

§ 57. In order to make up further examples we only need to take :—

(1.) A curve A.

(2.) A series of curves A,, depending on one parameter, each having contact
of order 7 with the curve A.

(3.) A series of curves A,, involving two parameters, each having contact of
order 7 with some one of the curves A,, and so on, till we have a series of curves A,,
involving 1 parameters, each having contact of order n with some one of the
curves A,_).

Then A, is the complete primitive of a differential equation of order n, A,,_, will
be a first singular solution, A,_, an 7" singular solution.

XV. On the Ratio of the Specific Heats of Some Compound Cases.
By J. W. Carstick, M.A., D.Sc., Fellow of Trinity College, Cambridge.

Communicated by Professor J. J. THomson, F.R.S.
Received January 25,—Read February 14, 1895.

§ 1. Introduction.

THE experiments to be described in the present paper are a continuation of those of
which I gave an account in the ‘ Phil. Trans.,’ vol. 185, p. 1.

It is shown there, from experiments on methane, ethane, and propane, and their
derivatives, that the monohalogen derivatives of any one paraffin have in the gaseous
state the same ratio of the specitic heats, and that this ratio is the same as that of the
hydrocarbon itself in two of the three series. Methane proved to be an exception,
having a higher ratio than its derivatives.

It seemed to be a matter of some interest to find whether the same was true of
unsaturated hydrocarbons and their monohalogen derivatives, and also to find the
effect of introducing more than one halogen atom into the molecule. The aim of most
of the experiments described below was to get information on these two points.

It is not necessary to give a detailed account of the apparatus and method of
procedure, since they were the same as those described in the paper mentioned above.
Kunpr’s dust-figure apparatus was used for finding the ratie of the wave-lengths of
sound of a given pitch in air and in the gas under investigation, and the ratio of the
specific heats was calculated by means of the formula

y = 1408 X p X (a) (1 + = PO)
where p is the specific gravity of the gas referred to air, / and /’ the lengths of the
dust-figures in the gas and in air respectively, and the last factor is the correction for
the deviation of the gas from Boyur’s Law.

The vapour density of the gas was found experimentally at several different
pressures, and from the curve plotted from the results p and the correction factor were
determined in the way previously described.

Some of the substances used in this investigation are very difficult to purify, hence

it is a matter of importance that when v is determined in the way described. the
24,.9,95

568 DR. J. W. CAPSTICK ON THE RATIO OF THE

result is only very slightly affected by the presence of a little impurity. Impurities
make themselves felt mainly by their modifying the density of the gas, and error
from this source is avoided by the vapour density determination having been made in
nearly every case on the same samples of the material as were used in the velocity of
sound experiments. Hence impurity only has an effect in so far as the y of the foreign
substance is not the same as that of the gas under investigation. An estimate of the
amount of this error can be got by an application of equation (5) of my former paper.
If, for instance, the methylene chloride contained 1 per cent. of chloroform, the error
in y would be less than one part in a thousand.

Except where the contrary is stated, the materials were obtained from KAHLBAUM
and were dried and fractionated before being used. The following table of the
observed range of boiling-points of definite quantities of the liquids as actually
employed in the experiments will give some indication of the degree of purity
obtained.

TABLE I.
Name. | Quantity. B. P. (uncorrected).

Methylene chloride .. =: ... . 50 ¢.c. 43°5 to 443
Ojnilorgowornin 5 go Sn 300 60°8 ,, 61:2
Carbon tetrachloride. . . . . . 50 76°8 ,, 76°9
Hithylene chloride. . .... . 60 83°9 ,, 84-1
Kithylidene chloride. . . . «.-. 40 59 ,, 6071
Nill Oilevals 55 a Ss a 110 45 ,, 46°5
NIGAM org 5 5 6 a 0 2 oe 70 69 ,, 71
[relat imo 6 A) gb So | 200 56
Methyliacetate.. =. «9. «2. . 400 56 to 57-5
Carbonvbisulphides 9s) - a ome 250) 46°8 ,, 47

As regards the degree of accuracy attainable in the measurements Tinust again
refer to my former paper. On p. 11 is given a typical set of measurements of the
dust figures, and on p. 27 a series of experiments on ethyl chloride that afford a test
of the accuracy of the vapour density determinations.

The experiments on carbon dioxide (Table XXII., below) show further, that whilst the
work was in progress no change took place in the apparatus that affected the results.
The first three experiments on carbon dioxide were made when the apparatus was
first set up; the last three were made two years later, after it had been repeatedly
dismantled for cleaning, and repairs and most of the original tubes had been replaced
by others. The two sets of three give almost identical results.

Many cf the gases used in the experiments have low saturation pressures at the
atmospheric temperature—a fact which tends to increase the experimental error, for
small errors in reading the height of the mercury column in the vapour density
apparatus have a more serious effect when the total pressure to be measured is small,
and in addition to this, the small range of pressure available makes it difficult to

SPECIFIC HEATS OF SOME COMPOUND GASES. 569

draw the isothermal curve accurately. Hence the vapour-density determinations in
some cases give a rather irregular curve, but when the divergences are so great as to
leave much doubt how the curve should be drawn, I have made a separate determi-
nation of the relative densities in the way described under ethyl chloride in my
former paper.

The column headed 8 in the tables below, gives the ratio of the rates of increase
with rise of temperature of the internal energy of the molecule and its kinetic energy
of translation. .

The usual equation connecting 8 and y, viz.,

7 S@=m>

is deduced on the assumption that the gas is perfect, for it neglects the change of
potential energy due to separation of the molecules on expansion, and assumes that
pv is proportional to ¢.

For air and a few other gases this is a matter of no consequence, but when we come
to vapours not far removed from saturation, it is necessary to use a better formula, or
at least to find whether the error made by using the old one is serious compared with
the experimental error.

Since, to a first approximation, pv is equal to Rt, we may write the characteristic
equation in the form

(DO == I SG, DO) ns 2 es 6 eb 2 2 (N),
where f is so small that its square and the squares of its differential coefficients can

be neglected.
Now we know from thermodynamics that

GC, = ©, = t(dpldt)y (didi) is. kyu oh Le)

and from equation (1) we get by differentiating at constant volume and pressure
respectively

a _ R+ dfldt

dt}, v—df|dp
du\ _R+df{dt
Gi » p— afidv
Hence
Ce ¢ (Rh + df/dty
y "(p= adfidv) (v = af dp)
eRe il ay i ay 2 df
~ po G+75¢+ v apt R ak

MDCCCXCV.—A. 4D

570 DR. J. W. CAPSTICK ON THE RATIO OF THE

neglecting squares of the differential coefficients, or, since

z Rt = pv —f,
therefore
es 1 df
C,-G=R(i— oo) ese
ex df df 2 oy ah
SR ba gach each anaes - + (8).

If 67 is the increase of the kinetic energy of translation of the molecules in unit
mass of the gas for a rise of temperature dt, we have

C, dt = 67 + B dr
=2(1+ 6) R&,
since
ae SS Ree
Hence
g Ce
ke as:

and dividing out C,, equation (3) becomes

- 2 1 df Ik Gh 2 df if
91S gel + ARSE Ch ie. ae =a) Bee YA

p dv

If the form of f(p, v, t) were known we could readily put equation (4) into a form
fitted for calculation. Unfortunately we cannot use the characteristic equations
proposed by CLausius, VAN DER Wats, Tart, and others, for the constants of these
equations are not known except for a few gases.

There is however not much lost by taking an approximate value of the term in
brackets, for from the nature of the equation the experimental error in y is consider-
ably increased in £.

By differentiating the approximate equation

Bib Ns aon
we get
68 / 8 2y
B/ 4 (y — 1) (5 — 3y)
Hence, if
68 / dy
== 1/c3} = — 8
y B/ ¥
wile, =

SPECIFIC HEATS OF SOME COMPOUND GASES. 571

Thus, since any error in y is increased tenfold in £, it is useless to do much more
than find roughly the magnitude of the correction, until our experimental methods
for determining y are much improved.

If we take CLAustus’ equation

RT C
v—@ Tw + 6?

p=

as the characteristic equation of a ae we can, by making certain eppromimalions,
express the correction for 8 in terms of | ror = ( pv).

At ordinary temperatures and Ce a ia b are negligible compared with v, so
. that f may be taken to be — C/Tv.

Hence
gp CMC
p dv Tp?” RIy
1 df
v dp ae
an Bs
R dt” RT»
Hepaue C
790) TRAD)
therefore
2 4C
te ream ace
and
git. Gq gC aay ©
p dv (G0) = Tp RI
Hence

2 4
ae le < (pl. ore (5).

Equation (5) has been used in calculating in all the tables that follow.

In my former paper I pointed out (p. 34) that the y of ethyl chloride and a few
other gases appeared to be greater at the higher pressures, and mentioned that the
effect might be due merely to the divergence of the gas from Boyur’s law, and not to
any change in the value of 8. This appears to be the case, for if 8 is calculated from
the results by means of formula (5), the progressive change disappears. The table
below shows this for ethyl chloride, where the change in y is most marked.

572 DR. J. W. CAPSTICK ON THE RATIO OF THE

TABLE IT.
Dp. Y- Bp.
millims.

200 1:180 2°878

205 1:180 2°878

285 1:189 2-751

295 1:180 2:939

400 1191 2°754

400 | 1:188 2-814

410 | 1:184 2896

560 1:193 2°797
| 610 1-190 8 3858
630 | 1:192 2-818

The values of 6 naturally diverge more widely from the mean than do those of y,
but there is no longer any progressive change to be seen, and we may conclude that
the ratio of internal to translational energy of a molecule does not depend on the
average distance between the molecules.

§ 2. Methylene Chloride. (CH,Cl,.)

Table III. gives the results of five determinations of the vapour-density of
methylene chloride. The first column gives the pressure to the nearest millimetre at
which the experiment was made, the second column gives the temperature, and the
third gives the specific gravity of the gas referred to air at the same temperature and
pressure.

Fig. 1 shows the curve plotted from the results.

TABLE IIT.
]

| p: t p-
|
| 135 19-2 | 3-081

155 18°6 3-087
| 160 18:9 | 3-086
| 199 18-6 | 3-094

211 16-7 3:096

SPECIFIC HEATS OF SOME COMPOUND GASES. 573

Table IV. gives the final results calculated from three determinations of the
velocity of sound in the vapour.
The letters at the heads of the columns have the following meanings :—

p. The pressure of the vapour in the Kunpr apparatus when the dust figures
were made.

t. The temperature of the vapour.

i. The length of the dust figures in methylene chloride.

fe be De . 3 alr.

p. The specific gravity of the vapour at the pressure at which the experiment
was made. ‘This specific gravity was taken from the curve in fig 1.

il @/ == : Ons ,
1+ Aen The correction for deviation from Boyur’s Law, calculated as des-

ceribed in my former paper.
y. The ratio of the specific heats, calculated by means of the formula on p. 567.
8. The ratio of the rates of increase of internal and translational energy of
the molecule with rise of temperature,'calculated by formula (5) on p. 571.

TABLE LV.
: a
p | t l L Pp sp p IpP”- 7 B
| s
152 | 16:7 557 48°66 3:085 1011 |) 1-213 2:263
160 19-2 25°76 48-90 3086 1-011 1-219 2174
174 | 19:3 25°81 48°90 3:089 1-011 1225 2:089
Mean 1:219 2175

§3. Chloroform, CHCl,

The tables and figures have in this and most of the succeeding cases the same
meaning as in the case of methylene chloride.

TABLE V.

| |
| Pp: | t P
| |
| 97 | 19:4. 4-112
| 106 21-2 4114
| 121 | 20:6 4118

138 | 20:3 4128

574 DR. J. W. CAPSTICK ON THE RATIO OF THE

FIZ

Fle

Fl
90 100 “0 20 159 140

TABLE VI.
P t l v p jue Sig 1- B.
p dv P

109 | 20 21°73 48-96 4-114 | 1-008 1150 3581
114 | 21 21°81 49°05 4116 1010 1157 3-414
117 H 20°2 21:78 48:99 4-117 1-011 1157 3:427
121 | 19°8 21°69 48°95 | 4118 1-012 | 1152 3°593

Means 1154 3°506

§ 4. Carbon Tetrachloride (CC),).

TABLE VII.

Pp. t p

53 21:7 5-330
64 21°6 5°352
69 19°05 57350
69 188 5°339
77 19:2 57358
86 2071 5°368

SPECIFIC HEATS OF SOME COMPOUND GASES.

Tapue VILL.

| ; lye
p. z. | 1 l p- ae dp PB” of B.
|
|
54 20°6 | 18°86 49:02 5:332 1:012 1:125 4-585
72 20:2 18°55 49-00 5351 1014 1131 4367
73 20°2 18°87 49:00 5354 1:014 11°33 4285
7d 20°5 18°83 49-01 5°356 1-014 1:130 | 44.09
Mean 1:130 4-4) 1
§5. Ethylidene Chloride (CH,.CH Cl,).
TaBuLeE [X.
Pp. te p-
121 23°6 3439
138 25 3°4.46
146 23°8 3447
153 24, 3:451
TABLE X.
io
p- | t. ib lie p- oar Tp BP? Y: B.
125 21 23°50 49-03 3°440 1-013 1:127 4-518
132 24, 23°74. 49°36 3°443 1:014 1137 4133
138 23°9 23°73 49°34, 3-445 1015 1189 4-079
Mean 1:134 4243

576 DR. J. W. CAPSTICK ON THE RATIO OF THE

§ 6. Ethylene Chloride (CH,Cl.CH,C)).

Ethylene Chloride boils at 85°, and its vapour-pressure at ordinary temperature is
so low, that small errors in reading the height of the mercury columns, or, in weighing
the liquid, have too great an effect to allow a reliable curve to be drawn frorn
the vapour-density determinations. Consequently these determinations were all
made near the same pressure, and the mean of the results was used in the final

calculations.
The values found were as follows :—
TABLE XI.
P t. p
42-9 23 3°460
46°71 24 3°442
4671 23°8 3437
45:7 24-4, 3°448
43°8 22°8 3:443

To find the value of the correction factor a determination of the relative densities at
three pressures was made with the apparatus described under Ethyl Chloride in
my former paper. The experiment was made at 24°, with the result shown in

Table XII.

TABLE XII.
| as
| v. p- pv.
|
122-00 37°40 4566
| 91:17 49°83 4543
66°57 67:88 4519

This gives 1'017 as the value of the correction factor at 45 millims.
Finally, Table XIII. gives the details of the velocity of sound determinations.

TABLE XII.

|
ld
p | t 1 | l p TF ame 1
| |
4d 19-4. | 2356 | 48-92 3-446 | 1-017 1-144.
42 | iss | 9846 | 48:90 = 1-135
48 194 | 23:44 | 48:92 | 1133

Mean .| 1:137

SPECIFIC HEATS OF SOME COMPOUND GASES. 577

§7. Ethylene (C,H,).

For the material I was indebted to the kindness of Professor DEwaAR, who gave me
a cylinder of compressed ethylene. As the critical temperature of ethylene is near
the ordinary atmospheric temperature, the bottle was placed in a freezing mixture to
ensure the contents being liquefied, and so to keep back by fractional distillation any
ether and water that had escaped the preliminary washing and drying of the gas.

AMAGAT’S experiments on the compressibility of ethylene enable us to calculate
the correction due to deviation from Bovis Law. Since, however, the lowest
pressure used by AMAGAT was 30 atmospheres, the correction term must be put in a
slightly different form. Using VAN DER WAALS’ equation

(p + a/v’) (v — b) = Rt

to express the relation between jp, v, and ¢, it is easily shown that the correction term
takes the form 1 + a/pv? — b/v.

Baynes has calculated VAN DER WAALS’ constants from AMAGAT’s observations,
and finds (‘ Nature, vol. 22, p. 186) a =-00786, b = ‘0024. Hence since in my
experiments p = 1 and v = 288/273, we get the correction 1:007.

Two determinations of the velocity of sound at atmospheric pressure gave the
following results, the theoretical value of the density of the gas being used in the
calculation of y.

TABLE XIV.

| ld
t. 1. } eZ Dp. 1 ——— . vee .
| as f ar Aan pe 1 B
| |
| 15°4 | 46°32 48:51 9675 1-007 ° 1-251
15 46°32 48°54. | i: ae 1-249
Mean 1 1:250 1:740
| | |

§ 8. Vinyl Bromide (C,H,Br).

The material was made by gently warming ethylene dibromide with alcoholic
potash. The issuing gas was condensed, fractionated, allowed to stand over calcium
chloride, and again fractionated.

Four weighed tubes to contain the liquid for vapour-density determinations were
filled in a freezing mixture, but on coming to the temperature of the room two burst,
so that only two were left for use. These gave the following results :—

MDCCCXCV.—A. 4 E

578 DR. J. W. CAPSTICK ON THE RATIO OF THE

TABLE XV.
|
| P- t p
311 15:2 3°677

Since two observations are not sufficient to give the curve, a set of relative density
determinations was made in the usual way. The results are shown in Table XIV.

TABLE XVI.
p- v. pr.
|
155°35 12°415 1928 |
220°6 8°68 1915
250°3 7627 1914
305°35 6:224. 1901
503 3°721 1872

The reciprocals of the numbers in the third column are proportional to the specific
gravity of the vapour. These reciprocals with the scale suitably altered so as to
coincide as nearly as possible with the values in Table XV. are marked by circles on
the curve of fig. 5. The two values of the absolute density are marked by crosses.

The curve was employed in the usual way for finding the numbers in the fifth and
sixth columns of Table XVII.

SPECIFIC HEATS OF SOME COMPOUND GASKS.

579

560

Taste XVIL.
! 1
t. 1. U. p. 1+ -— pv Ye B.

P
15 22°98 48°53 3°690 1:026 1:195 2°770
15°6 22°97 48°63 3°705 1-026 1193" | 2:808
15:2 22°91 48°54 3°749 1:027 1:207 2-566
Mean 1:198 2-715

§ 9. Allyl Chloride (C,H,Cl).

TasLe XVIII.

p- t,
96 14-2
116 13:2
128 12°8
152 126
184 15:0

48°42
48°40
48°43,
48°52

4k 2

1134 4-090
1137 4-016
1154 4-128
1142 3°859
1-137 4-023

580 DR. J. W. CAPSTICK ON THE RATIO OF THE

§ 10. Allyl Bromide (C;H,Br).

TABLE XX.
p. ths p»
52 13°4 4174
74, 14-9 4-187
70 16°4 4184
68 16:2 4188

TABLE XXI.
t 1 d 974
p | t 1 1 | Pp. st p A; Pp Y | B.

| |

| | |
ai || HE 21:29 48:57 | 4195 1-013 1:149 3-704
SO) telibs be eee 21528 48°59 4194 | 1-013 1147 | ~ 3-768
Wa | 15:5 21-25 4858 | 4189 | 1-011 1141 3-929

| | |
Mean: |) ease etsican

|

§ 11. Carbon Dioxide (CO).

The gas was prepared from marble and hydrochloric acid. It was purified by being
washed with water and passed over bicarbonate of potash and calcium chloride.

REGNAULT’s value, 1°529, was taken as the specific gravity of the gas.

: : . 1d —

The experiments of ANDREWS afford material for calculating the term 1 + rr = pu.
Using the results as tabulated by Lanpour and Bornstein (2nd edition, p. 83), the
term has the value 1:007 for atmospheric pressure and temperatures between
0° and 30°.

The following table gives the results of the experiments, the pressure of the gas
being in each case that of the atmosphere.

SPECIFIC HEATS OF SOME COMPOUND GASES.

TABLE XXII.
|
dee
t l. 1 p. 1+ i Tp P: "f Bp.
|
18-2 37-92 48:84 1529 1:007 1:306
181 37-97 48:83 Sy a 1311
Geez) )| 87.02 48:75 1312
| 14-7 37-65 48:53 1:304
11-9 37-48 48-28 1:306
12-6 37°57 48-34. | 1:310
| Mean. . ; 1:308 1-224.

Previous determinations of the ratio of the specific heats of carbon dioxide have

given the following results :—

|
| t. Yy
1-291
| 19° 1:305
20-25 1-292
0 L311
100 1-282
0-34 1:265
1:29

Observer.

Cazin (‘ Ann. de Chim.,’ 56, 206)
Rontcen (‘ Pogg. Ann.,’ 148, 580)
De Luccut (‘ Nuov. Cim.,’ 11, 11)
Winer (‘ Wied. Ann.,’ 4, 321)

Mirer (‘ Wied. Ann.,’ 18, 94) |
Jamty and RicHarp (‘Comptes Rendus,’ 71, 336)

All these observers have used the
would be 1°299 without the correction for deviation from Boyvie’s Law.

equations of a perfect gas.

§ 12. Carbon Bisulphide (CS,).

My own result

The liquid was first distilled from lime over which it had stood several days. It
was then shaken repeatedly with mercury, dried with calcium chloride, and redistilled.
As the determinations of the absolute vapour density give an unsatisfactory curve,
two of the experiments giving values rather more than a tenth per cent. away from
the curve through the other three, a separate experiment was made to find the
relative densities in the usual way. The results of this experiment are shown in

Table XXIIL., and fig. 8.

TABLE XXIII,

1b p v. | pv/T.
|
286°7 1233 118°6 49°56
| 170 §5°8 49-48
197°9 73:6 | 49°38

582 DR. J. W. CAPSTICK ON THE RATIO OF THE

Fig. 8.

Table XXIV. gives the results of the vapour-density determinations. The numbers
in the fourth column are taken from the curve in fig. 8, and when multiplied by the
corresponding numbers in the third column should give a constant, if the two series
of experiments are consistent. The products are shown in the last column.

TABLE XXIV.
p- | t, p: pr/T. prp|T.
}

134 | 11°4 2°647 49°53 1311
147 | 11°6 2°644 49°50 1309
193 | 11:6 2°654. 49°39 | 1310
125 12°4 2°643 49°56 1310
161 | 9-8 2°648 49°47 1310

Meanie iF 5 eke | 1310

The mean of the numbers in the last colunin of this tabie divided by the ordinate
of the curve in fig. 8 for a given pressure, gives the best value of the vapour-density
for that pressure. The fifth column of the table below was calculated in this way.

TaBLE XXV.
| | | ' ld |
| p. | t. | l l p- pee Y | B
| |
mer | if : z | | |
121 14 |) 2 | 8:23 2°643 1006 | 1:236 1:890
130 16 | 27:94 | 48°63 2644 | 1006 | 1:236 | 41-890
| 141 | Wes} || ETT 48°24 2:°645 1:007 1243) || = Ae8r9
| 150 134 | 2er29 48°42 | 2-647 1:008 1:237 1:903
| 156 14 27°86 48-46 | 2-648 1:008 1°242 1:843
| | |
Mie aT iets ass 1239 1:869

SPECIFIC HEATS OF SOME COMPOUND GASES. 583

§ 13. Sulphuretted Hydrogen (HS).

The gas was prepared by warming antimony sulphide with hydrochloric acid. It
was washed with water, and dried by being passed over calcium chloride.
An experiment to determine the deviation of the gas from Boyie’s Law gave the

following result :—
Taste XXVI.

at v. | p. pr|T.
| 291°8 38°67 967'8 1282
| 49°8 75465 | 128°7
64:07 587°85 129-0
| | 85:12 443°05 129°2
| | 102°2 369°5 129°4

These numbers give ‘011 as the value of = ee at 760 millims.

The theoretical density 1°177 is used in the calculation of y.
Three determinations of the velocity of sound at atmospheric pressure give the

following results :—
Taste XXVIII.

| ]
1a

| ’ t 1. 1 | ps 1 + Dp Sep: Oy B
| | | | |
| 17-8 43:31 | 48-78 V7 | 1-011 | 1391 |

18 | 4346 | 48:85 | ne | sil 1322
E18 43-42 48-83 1-321
| WMigem 4 1321 1-165

§ 14. Ethyl Formate (HCOOC,H;).

The ethyl formate used in the experiments was allowed to stand over anhydrous
carbonate of potash and calcium chloride, and was then fractionated. This treatment
made the boiling-point steady, but the substance is so readily decomposed, that the
operation had to be repeated at times, and consequently the material used was not
the same in all the experiments.

Every precaution was taken to keep the apparatus thoroughly dry inside and so
prevent decomposition; but in spite of this the vapour-density results were not
concordant enough to give a trustworthy curve. Hence it was necessary to make a
determination of the relative densities.

584 DR. J. W. CAPSTICK ON THE RATIO OF THE

The tables and figures have exactly the same meaning as the corresponding ones
for carbon bisulphide. Table XXVIII. and fig. 9 exhibit the results of the relative
density determination, Table XXIX. those of the absolute determinations, and
Table XXX. gives the values found for y and 8.

TABLE XXVIII.

| P t $+ 273
$2 179 20°67
| 105 i | 25°62 |
119 | | O555 |
134 | | 25°52
148 | 25°
|

257 >

25-6

25°5

254
&0 90 100 0 120 150 440 190 460

TABLE XXIX.

Ut | eee LU Pies

ie ff Se t+ 273 t+ 273 |
ae: |

105 18 2-487 25°61 6368

109 178 2-489 25°59 6369

110 18-4 2-485 25°59 6359

13 18:2 2-498 25°52 6372

131 183 2-499 25°52 6377

149 18°6 2-498 25-45 6357
|

Mean. Ss 6367

SPECIFIC HEATS OF SOME COMPOUND GASES, 585

TABLE XXX.
leh
t 1 1’ b@e E
P | Pp 1 v5 dp & 1 B
94 | 20:8 27-67 49-03 2482 1-014 1-129 4450
99 18-9 27-49 48:86 2-485 1:015 1-124, 4694
101 19:9 27:49 48-96 2-486 1-015 1:120 4-883
122 | 203 27-57 49-05 2-492 1-018 1:128 4-578
141 20-0 27-43 48-97 2-500 1-021 1:128 4640
142 19-4 27-42 48°92 9-500 1:021 1-129 4597
| Wire 5 oe ell SDS 4-640
i

§ 15. Methyl Acetate (CH,COOCH,).

Methyl acetate proved to be more troublesome than any of the other substances
investigated, and it is with some hesitation that I venture to publish the results of
my experiments on it. Time after time the liquid was shaken with calcium chloride
and fractionated, but the boiling-point was never as steady as could be wished. One
of the decomposition products is methyl alcohol, which has nearly the same boiling-
point as methyl acetate itself, and cannot be removed by fractionation, so that it
is hardly to be hoped that the final product was quite pure.

The experiments with the Kunpt apparatus, given below in Table XXXLI., are not
the only ones that were made. After each purification several experiments were
made, and it was found that the wave-length of sound in the vapour gradually
diminished—presumably in consequence of the gradual removal of methyl alcohol.
The set given below were made on the particular sample that gave the shortest
wave-length.

If the vapour-density determinations gave the true density of the material used in
the velocity of sound experiments, a little impurity would have scarcely any effect
on y, but the vapour-density observations are specially liable to error. The quantity
of methyl acetate used in an experiment is small—not more than a quarter of a
gramme—and a very little moisture on the glass may bring about the decomposition
of quite an appreciable percentage of the vapour. It is probably for this reason that
the experimental error of the vapour-density observations is greater than usual, the
divergence from the mean reaching 1 part in 400.

The tabulation of the results is the same as before. Table XXXI. and fig. 10 give
the relative density determinations. Table XXXII. gives the absolute density
results, and Table XX XIII. gives the values found for y.

MDCCCXCV.—A. 4 F

Se nn

586

DR. J. W. CAPSTICK ON THE RATIO OF THE

TABLE XXXI.

pr
Dp. te Pa 273°
85 189 33°58
105 50 33°38
117 33°35
127 33:28
137 33°20
| 153 33:09

Fig. 10.

forelrr]

go 90 /00 uo 20 /40 160
Skee) DOXOCHE
| pv wy 2gp
| BP: f Ps f+ 273 P+ 973°
—
68 18-6 2-483 3372 8373
“1 18-1 2-488 3368 8379
| 82 18-8 2-486 3362 8360
87 17-4 2-485 3357 8343
92 17-6 9-498 3353 8375
97 18 2-491 3350) 8345
| 100 Wey, 2-506 3347 8385
| 100 16-8 2-503 3347 8375
| 102 16-6 2-500 33-46 8364
114. 18-4 2-509 3337 8360
| Mean 8366

SPECIFIC HEATS OF SOME COMPOUND GASKS.

TABLE XXXIID.

587

| | i —

p- | t. l. | 1 p- y= P de 2: 7. p.
93 | 18:2 27°51 | 48°82 2°4.96 1019 1:137 4234,
102 19°7 27°57 48°96 2501 1:020 1139 4172
108 19°8 ZO 48597) 27502 1-020 1134 4°365
104 18:3 2748 | 4884 2-502 1-021 1139 4-194
86 9°05 20:10) 1} 48:03 2-492 1018 Wei337/ 4-212

| | |

Mean . Wemss7/ 40235

§ 16. Silicon Tetrachloride (SiC\,).

Silicon tetrachloride is much more unstable even than the two substances last

described.

silica are given off if the bottle containing the liquid is left open.

'The Kunpr apparatus was easily dried, so there was probably no appreciable
decomposition in the velocity of sound experiments, but the vapour-density apparatus
was more difficult to keep from contact with moist air, and at the end of the set of
experiments a slight dimming of the glass from the deposit of silica showed that the
attempt to keep out moisture had not been entirely successful.

TABLE XXXIV.

p- t. p- |
| = aa
84 14. S797
88 141 5810
106 14-1 5848
110 13°6 5875
126 16 5879
138 161 5878
Iie, Wl.

130 4o 150

It decomposes so readily in the presence of moisture that white fumes of

588 DR. J. W. CAPSTICK ON THE RATIO OF THE

TABLE XXXV.

L@=
Pp t l l Pp nape q B

105 13°9 1782 48°46 5838 1:024 1:138 4-289
118 14 17-75 48-4 5857 1:026 1135 4-453
128 13°8 17°62 43°45 5871 1:028 1124 4-975
141 13:9 17°60 48°46 5°888 1:031 1127 4-898
144 148 17°54 48°53 5891 1:032 1119 oll

Mieaness ata 1:129 4585

§ 17. Discussion of the Results.

As many of the above gases are closely related to those included in my former
paper, the whole of the results of the two series are included in one table.

TABLE XXXVI.

| |

| Name. Formula. | Oy B. 2 | Gad
| n | n

a cary |
WEiNstinies Jee 4 oe ee CH, | 1°313 1129 "226 | “4.26
| Methylchloride. .... . CH,Cl | IE) 1506 | -301 | “501
eevle thw lioromid ceeas eitntne CH, Br We DA | eG O73 i mens Lee “514
Methylsodiders =). -nee CH,I | 1-286 Ty I) BIE) 519
| Methylene chloride. . . . . CH,Cl, | Iezils) 2175 4.35 635
| Chloroform . . Tie eas CHCl, | 154 3°506 “701 ‘901
| Carbon tetrachloride . . . . CCl, leila y0) 4411 882 1-082
z thane. . cease 20 Gas C,H, |} leisy 2°659 332 457
Kthyl chloride. Sas oa C,H.Cl 1187 2°838 "355 “479
Hithyli bromide.) sean C,H.Br 1188 | 2-809 ‘Bol “4.76
Ethylene chloride C,H,Cl, 1137 =| = 4-184 523 648
Kthylidene chloride . as C,H,Cl, 1134. 42.4.3 “530 655
Propane. SEA C,H, 1-139 44.27 “4.02 “4.93
Normal propyl chloride | C3H,Cl 1-126 4-493, “4.08 “4.99
Isopropyl chloride ee ace C3H,Cl 1-127 4465 “406 497
Isopropyl bromide . . . . .| C,H,Br 1-131 44.15 401 4.92
Ethylene Re hic cent JgH, 1250 1-740 “290 “457
Vinyl bromide 56 6 0) ~GAaGlsye 1:198 2715 “452 619
FAlielbchlomdome euret ele mana C,H,Cl 1137 4-023 “4A7 558
EAU ylUbromude sey). sles et] C,H,Br 1145 3°800 4.22 ys)
Mthyl formatel .). . 6). «| Le COOCIH: 1124 4-640 “4.22 513
Methyl acetate . . 4) CHCOOCH, ie y/ 4°235 385 “4.76
| Sulphuretted hy drogen SL SH, els 27 | 1165 388 (22
| Carbon dioxide . . A ae CO, ls 30S es eel 2a “408 “TAL
| Carbon bisulphide . . . . . CS, 1-239 | 13869 | 623 956
Silicon tetrachloride . . . . SiCl, Heys) i) abate NL? Teil

SPECIFIC HEATS OF SOME COMPOUND GASES. 589

My former conclusion that monohalogen derivatives of the same paraltiin have the
same y can now be stated in more general terms. The two ally} compounds show
that it is not restricted to saturated hydrocarbens, and the equality of y of ethylene
and ethylidene chlorides extends it to isomeric dihalogen derivatives. Hence, so far
as the experiments have gone, we can say that without any exception corresponding
halogen derivatives of the same hydrocarbon have the same ratio of the specific heats.

Similarly it appears that the equality of y for the two propyl chlorides is not an
isolated fact, for two other pairs of isomeric bodies, viz., ethylene and etbylidene
chlorides and methyl acetate and ethyl formate prove to have the same y. As I have
mentioned above, there is some doubt about the results for the two last mentioned,
but at present the balance of evidence is in favour of the statement that zsomeric com-
pounds have the same y.

In the case of the paraffins ethane and propane, it was one in my former paper
that one H can be replaced by a halogen without altering the value of y, but that the
introduction of a halogen into rbthans causes a fall in y. We see now that the
unsaturated gas ethylene behaves in the same way as methane, for the y of vinyl
bromide is markedly lower than that of ethylene. Thus the possibility of inter-
change of hydrogen with a halogen without altering y is not general, a fact that is
brought out still more clearly by a consideration of the higher substitution products.

It was shown by StrecKER* that hydrochloric, hydrobromic and hydriodie acids
all have nearly the same y as hydrogen, namely 1:4, whilst the y's of chlorine, bro-
mine, iodine and iodine chloride all lie near 1°3. Hence in this case one halogen can
be put in the place of hydrogen without affecting y, but the introduction of a second
halogen causes a large fall.

The parafiin derivatives show the same feature. he second Cl introduced into the
molecule invariably causes a large fall in y whether the first has done so or not.
Thus, whilst ethyl chloride has the same y as ethane, ethylene and ethylidene
chlorides are 4 per cent. lower.

The methane substitution products are volatile enough to allow the whole series to
be investigated, and here we find that every successive chlorine atom introduced
causes a fall in y.

The work done on the last four gases in the table is only the beginning of a line of
investigation, the completion of which would require an entire remodelling of my
apparatus, so as to enable it to stand higher temperatures. The object of the experi-
ments was to find whether other chemically analogous atoms are interchangeable in
the same way as the halogens.

Although C and Si replace each other in many compounds, CCl, and 8iCl, are not
strictly analogous, for they violate the usual rule that the compound with the higher
molecular weight has the higher boiling-point. They appear however to have the
same y.

‘Wied, Ann.’ vol. 13, p. 20, and vol. 17, p. 85.

ee

ee

590 DR. J. W. CAPSTICK ON THE RATIO OF THE

The further investigation of the relations of carbon and silicon would be a
matter of some difficulty, from the readiness with which the silicon compounds are
decomposed.

Corresponding oxygen and sulphur compounds are numerous and stable, but most
of the sulphur compounds have too high boiling-points to give a sufficiently dense
vapour at the atmospheric pressure.

The value of y for sulphuretted hydrogen was got for comparison with that found
by other observers of water. Experiments made on water vapour have given
the following results :—

TaBLE XXXVII.

: ) |

t. Y: Observer.
| 78 1274 | Brym (‘Beibl., vol. 9, p. 503) |
| 94 1:33 | J&cer (‘ Wied. Ann.,’ vol. 36, p. 165)
| 100 | 1:321 | Neyrenevur (‘Ann. de Chim.,’ vol. 9, p. 535) |
103 ; 1277 | De Loccur (‘Nuov. Cim.,’ vol. 11, p.11) — |
144-300 | 1287 | Counen (‘ Wied. Ann.,’ vol. 37, p. 628) |

These are very discordant, but some of them seem to be of doubtful validity.
BEYME made only a single experiment, aud measured only three dust figures.
De Luccut used CLiment and Dersormes’ method, with a receiver so small that, in
the light of RontGEN’s experiments, his result is probably too low. NryreNeur and
Coen both assumed that the vapour obeys Boyue’s Law, the latter observer trusting
to superheating of the gas to justify the assumption. JAGER alone carried out his
calculations in a manner that seems allowable, and his result is almost the same as I
have found for sulphuretted hydrogen.

The two gases CO, and CS, have widely different values of the ratio of the specific
heats, so that the possibility of interchange of O and 8 without altering y does not at
least extend to two atoms.

It is worth noticing that according to Recnautt’s results the molecular heat
at constant pressure is nearly the same for the members of any one of the groups—
H.S and H,O ; (C,H;),8 and (C,H;),0 ; SiCl, SnCl, and TiCl, ; so that it seems likely
that the laws I have found to hold for the halogens will prove to hold for other groups
of analogous elements.

Up to this point, only the relations of the y’s of the gases to each other have been
discussed, though it is from their enabling us to calculate 8 that the values of y are
likely to prove ultimately most useful.

If two gases have the same y, they have approximately the same £, that is, for a
small rise of temperature the quantity of energy absorbed by the internal vibrations
of the molecules bears the same ratio to the increase of kinetic energy of translation
of the whole molecule in the two cases.

SPECIFIC HEATS OF SOME COMPOUND GASKS. 591

Thus, for instance, the molecules CH;,Cl, CH,Br and CH,I have the same energy
absorbing power, from which it follows, with a high degree of probability, that the
halogen atoms in these molecules, in spite of their great difference in mass, absorb the
same share of the total energy. It is very improbable that if they did not, the
redistribution of energy in the molecule on interchange of the halogens would result
in the total capacity being unchanged. Similarly, we may infer from the behaviour
of hydrogen, ethane, and propane that the chlorine atom may in some cases have the
same energy absorbing power as the hydrogen it replaces.

An instance of another kind of interchange that can be made without disturbing
the distribution of energy, is seen in the case of the two propyl chlorides and the two
dichlorethanes. Trusting to graphic formule the chemist explains the difference be-
tween the two members of a pair as being due to a hydrogen changing places with a
chlorine within the molecule, the configuration being in other respects unchanged.

The relation of methyl acetate to ethyl formate is explained in a somewhat similar
way, for if we write the formula of ethyl formate in the form CH,—CH,—O—CO—H
—we can convert it into that of methyl acetate by interchanging CH, and CO. Thus
it appears that, if we can trust graphic formule to give information of this kind,
groups may be interchanged without disturbing 8. It would be of interest to earry
out this point farther, and find whether one of the groups could be removed from the
molecule, and the other put in its place without altering 8. Has, for instance,
methyl-ethyl oxide, which would be obtained by replacing CO in either of the above
by CH,, the same y? It is probable that valuable information on the status of the
radicle might be got by the determination of @ for a number of suitably chosen com-
pounds.

It appears then that a single atom of hydrogen, oxygen or carbon can in many cases
be replaced by chlorine, sulphur and silicon respectively, without disturbing the
distribution of energy in the molecule, but in no case investigated can the replacement
be repeated without bringing about a large increase in 8. Hence we conclude that
an atom has not an intrinsic heat capacity which it carries with it unchanged into any
gaseous molecule of which it forms part, but that it is affected by its neighbours. In
other words f is not an additive quantity, for the configuration of the molecule plays
a part in the distribution of energy.

My experiments would not be inconsistent with the supposition that the configura-
tion is the sole feature that fixes the distribution, but until more definite evidence is
obtained—especially with regard to the physical significance of radicles—this must
remain no more than a suggestion.

It was pointed out many years ago by Naumann, when experimental evidence was
seanty, that 6 divided by the number of atoms in the molecule was nearly equal
to 33. If this held generally, it would be an important fact, for it would point to
something of the nature of Borrzmann’s Theorem being true, and as the statement is
sometimes quoted by writers, I have given the quotients in question in the fifth

592 ON THE RATIO OF THE SPECIFIC HEATS OF SOME COMPOUND GASES.

column of Table XXXVI. It will be seen that in many cases B/n shows a rough
approximation to ‘33, but no more. Even allowing for the exaggeration of the
experimental error by the nature of the equation connecting and y, it cannot be
said that the intramolecular energy is proportional to the number of atoms in the
molecule. The paraffins themselves and their monohalogen derivatives show the
closest approximation, but even in their case the quotient appears to increase as 7
increases.

This last fact and the extract below from an article by Professor J. J. THomson
(Warts, ‘ Dictionary of Chemistry,’ vol. 1, p. 89), suggest another relation among the
B's that looks more promising. The extract in question is as follows :—‘ Though
there is strong evidence against the truth of the theorem (7.e., Bourzmann’s Theorem)
in this form, and the mathematical proof of it is unsatisfactory, yet a very special
case of it is probably true, viz., that if we have a molecule consisting of 7 atoms
approximately symmetrically arranged (that is, if the distance between a particular
pair of atoms is not always very much less than the distances between the other
pairs), then the ratio of the mean total kinetic energy of the molecule to the energy
due to the translatory motion of the centre of gravity is proportional to n, the number
of atoms in the molecule.”

Tf then the molecules of the gases I have investigated are symmetrical in the above
sense, we ought to find (8 + 1)/n constant. Looking down the last column of the
table it will be seen that, though this is by no means the case throughout, yet if we
confine ourselves to the paraftins and their derivatives that have not more than one
halogen atom in the molecule, there is a very striking agreement. .

The mean of the eleven quotients so defined is 493. Methane, as we have already
seen, falls out of the series, and here it diverges to the extent of 13 per cent., which
is equivalent to a divergence of about 3 per cent. in y. The y of ethane would have
to be about 1 per cent. lower to give complete agreement. In the case of all the rest
the divergence is well within the probable experimental error.

[ 5938 ]

XVI. Iron and Steel at Welding Temperatures.
By T. Wricutson, M.P., Memb. Inst. CE.

Communicated by Professor Roperts-Austen, C.B., F.R.S.
Received February 2,—Read February 21, 1895.
[Puate 17.]

Ty 1879-80 I drew attention to a method of measuring the changes of volume
taking place in cast iron while passing through the varying temperatures lying
between its cold and its molten state.

If a ball of cast iron at atmospheric temperature be immersed in a vessel of
molten iron of the same quality, it first sinks. In a few seconds it comes to the
surface, owing to the heat penetrating and expanding the ball, which, causing
increased displacement of the fluid metal, produces the increased buoyancy observed.

The increase of buoyancy does not stop here, as the ball continues to rise above
the surface of the fluid metal to a considerable height, until it arrives at the melting
point, when it rapidly melts down and joins the molten iron in the vessel.

An instrument was designed by me* to measure this change in the volume of iron.
The principle of the instrument is based on the law of flotation of bodies in liquids,
by which an increase of buoyancy in a submerged body is equivalent to an increase
in weight of the displaced fluid.

The ball of cast iron to be experimented upon is hung by a chain and rods from a
frame, and lowered over a pulley into a ladle of molten iron. The instrument is
suspended between the chain and lower rods, and contains a spiral spring similar to
that used in a Saurer’s balance; this spring is arranged so that the ball and rods
hang with their full weight upon the spring.

If the ball be kept well below the surface of the fluid metal it will, in expanding,
and displacing the fluid, relieve the tension on the spring to an extent equivalent to
the weight of the displaced metal.

The spring is placed in a brass frame, on which is also mounted a cylinder, which
revolves uniformly by clockwork. A pencil attached to the moving end of the
spring presses against a sheet of paper wound round the cylinder. This vertical

* ‘Journ. Iron and Steel Inst.,’ vol. 2, 1879, p. 418,
MDCCCXCV.—A, 4g 3,10,95

594 MR. T. WRIGHTSON ON IRON AND

motion of the pencil, when combined with the horizontal motion of the paper on
the revolving cylinder, produces the curve of volume.

The first operation is to hang a rod on the spring balance with a piece of wrought
iron at the end, which is an exact facsimile of that part of the shank of wrought
iron fixed in each ball which will eventually protrude above the molten iron when
the ball is submerged. ‘This weight brings down the spring balance to indicate from
1 to 2lbs. The cylinder is then thrown out of gear and moved round, the pencil
making a straight zero line, which represents the position when the cold and molten
iron have the same specific gravity. The smal] piece of iron representing the upper
part of the shank is then removed, and the actual ball put in place. This ball has
been accurately weighed before, and its specific gravity also taken. Hanging it
on the spring balance brings the index below the zero or equilibrium line. The ball
is now lowered into the metal, the clockwork having been previously put in action.

A diagram is thus drawn during the heating and melting of the ball, of which the
vertical ordinates represent change of volume in ounces of increased displacement, and
the horizontal element represents time in minutes.

A number of diagrams were taken with 3-inch and 4-inch diameter balls, the specific
gravities of which had previously been ascertained. The general character of these
is shown on fig. 1, which is one of the numerous diagrams taken, in which B, F
represents the liquid volume, and A, B, C, D, E, F the changing volume in passing
from the solid to the liquid state.

Fig. 1.

o 3

[x (4 8

3

~ is)

~

as)

2

3

vy
SESE ck ae LTS a EM oe NR NN 1 1
6 Min. 6 5 3 7

4-inch ball of No. 4 foundry iron (Cleveland) ; poured from very hot
metal; immersed in No. 4 foundry iron.

Weight of ball and immersed part of stalk . . . . 132 on.
Specific gravity of ball, and immersed part of stalk . 6:95
Maxcimumysiniin pet ec teases. eae een OZ
Maximimyt oabinovetiect amir) ii-tieetna enlist aemnLe HA
Specific gravity of fluid iron = eee = 6°84.
Specific gravity of plastic metal = a = 6°32

Between A and B, fig. 1, the average density of the ball changes, until at B it has

STEEL AT WELDING TEMPERATURES. 595

become the same as that of the molten iron. It is at this point that a freely floating
ball would just appear at the surface. The expansion beyond this corresponds to the
gradual rising of a free ball above the surface, the disturbances in the flotation due
to the cooling of the emergent part of the ball, and to the interference of the floating
scoria in the more crude experiment, are obviated by keeping the ball submerged.

As the ball becomes hotter the curve flattens between C and D, the conduction of
the heat into the ball becoming slower, until no further expansion takes place.
Several balls, removed at this stage, were found complete in form, but so soft that a
steel pin could be pushed right through them. ‘This plastic condition of the mass
remains for a short time, when it quickly passes into the liquid condition, the metal
of the ball joining the molten iron in the ladle. Of course, so soon as the melting of
the ball begins, the pencil no longer registers measurable changes of volume, as a
reduction of mass is taking place, but the maximum volume of the ball can be
measured in the plastic condition, and the volume when it reaches the liquid con-
dition being known, it can be stated with certainty that it passes rapidly from one
condition to the other. The conducting power of iron is so good that little wasting
of the surface takes place, until the whole ball from surface to centre is in a plastic
condition, and then it very rapidly melts and joins the bath ; as shown by the sudden
drop of the curve at E.

The mean average of a number of experiments upon grey Cleveland iron led me
to conclude that the

Specific gravity of the solid iron at atmospheric temperature was 6°95
That the specific gravity of the molten iron was. . . . . . 6°88
That the specific gravity of the plastic iron was . . . . . . 6°50

In other words, while cast iron passes from the solid to the liquid state its volume
is at its minimum when the mass is solid. As the temperature rises the metal
first expands 1°02 per cent., and then has the same specific gravity as the liquid
metal, viz., 6°88. It then continues expanding until it reaches the plastic condition,
when it assumes its maximum volume with a specific gravity of 6°5, the total increase
of volume from the solid to the plastic state amounting to 6°92 per cent.

After this, expausion by heat ceases and a quick centraction takes place, until the
mass becomes liquid, when its specific gravity is, as before, 6°88. If this is expressed in
terms of the volume of liquid iron, taken as 100, the volume of the solid iron at
atmospheric temperature is 98°98. That of plastic iron is 105‘85, in which condition
an increase of heat to the melting point reduces the volume to 100, representing
its liquid condition.

These changes of volume were much greater than was expected, and it was thought
well to verify them by a converse series of experiments which enabled the changes
in a cast iron ball in passing from the liquid to the solid state to be observed. Two

: 4G 2

596 MR. T. WRIGHTSON ON IRON AND

spherical moulds of dried loam were made 15°09 and 15°28 inches diameter
respectively. Into these, molten iron was poured, in the former case, Cleveland white
iron, and in the latter, Cleveland grey iron. A few minutes after the iron was run,
the top of the mould was raised and the diameter of the congealed surface measured
with callipers. This was continued at intervals of time, and the diagram, fig. 2,
shows the gradual increase of diameter of the grey and white iron balls as they cooled.

Fig. 2.
S
a J @ 3
White sron. iS <3
eg ai TE ~ eoQ) $
BRO SS "Ss e}]s
ae oS i S
-- H oe S
as G nS S res
a rey _/ron. ac Sole yo
ey — ise BUSES
86 moe
lel v 3% 3 s
Sines a, 2 we S $ A§
5 SS Rig Sais
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Woke eS Se S8
BSS Sd SIO §
13 Soe "SS Va Ss
ige rss
XL 2 Bx4s
'g Ps ' > 8 cy
wees 2, 8 Sais
U '
S x = N
nN
S ad S
Scale of Time. 7 ads
0 5 0 I 20 2 50 35 % 45 50 55 60 Minutes aes
SSS SS ee ee ee ee ee ee ee ee 2
+
©
o
5 nN
Grey fron
Ls)
2
Diameter g
when cold S
. . N
White iron =

[4 13

Diagram showing progressive increase of diameter and final contraction of grey and white balls,
15 inches diameter.

The large size of the balls made the cooling a slow process, and the horizontal
line representing time could not conveniently be extended in a diagram, but the final
diameter, when the balls, after ten or twelve hours, became cold, is shown. The
general result is a qualitative confirmation of the previous experiments, although not
quantitative, as the early consolidation of the outer layers of metal prevents the
free expansion of the interior.

These experiments were made in 1879-89, and proved that grey iron and white iron
possessed the property of expanding when cooling, and contracting when heating,
within a range of temperature approaching the melting points, and to an extent
near that found in the case of water, which in solidifying expands in volume 9°3 per
cent., while grey iron expands nearly 6 per cent., and white iron even more; the
approximation appearing to indicate that the phenomena were of the same order.

These facts led me to suggest that the phenomena of regelation and welding

STEEL AT WELDING TEMPERATURES. 597

might probably prove to be identical. I afterwards found that the same suggestion
had been made by Love.* As, however, this hypothesis was not based on a know-
ledge of the properties of wrought iron, which can be welded, but upon those of cast
iron, which cannot be welded, it appeared that the suggestion could only be regarded
as speculative, until some method of examining the physical properties of wrought
iron within the range of temperature known as the welding heat could be devised.

This brief statement of my earlier researchest will serve to lead to the work
embodied in the present paper, which shows that wrought iron at the welding
temperature possesses the property of expanding when cooled and contracting when
heated, and that the welding property is intimately connected with the critical
condition in which this abnormal behaviour is exhibited.

Professor JAMES THOMSON was the first to show that although in the case of
normal bodies which expand by heat and contract by cold, the effect of impact or of
pressure is to heat them; theoretical considerations rendered it probable that in
a material which possessed the physical property of expanding during cooling and
contracting during heating, a contrary effect would be produced. ‘The effect of
pressure or impact would cool and not heat it. This was subsequently experimentally
demonstrated, in the case of freezing water, by Lord Krtvin.{

These theoretical deductions of Professor JAMES THOMSON, and the well-known
confirmatory experiments by Lord Ketvin, led to a theory of regelation now
generally accepted, which depends upon the lowering of the solidifying (or freezing)
point by pressure.

The condition known as “ the welding state” of iron or steel is one which exists
only within a very limited range of temperature. If the smith takes his iron bars
out of the fire at too low a temperature welding cannot be effected. If, on the other
hand, the iron is too hot, a failure is also certain.

The range of temperature during which impact or pressure causes the union known
as the welding of two masses of iron or steel, is therefore comprised within narrow
limits, and the familiar operation is really a critical one.

In order that the phenomenon of the welding of iron may be identified with
the regelation of ice, it must be experimentally proved that the surfaces of the iron,
at the moment of welding, are in that peculiar and critical condition in which an
increase of heat will cause contraction and a diminution of heat will be followed by
the expansion of the mass. On the other hand the identification of regelation and
welding will be equally satisfactory if the collateral property of the cooling of the
hot iron by pressure or impact can be demonstrated.

The first method of demonstration is impracticable, as the welding state is transient

* ‘Proceedings of Civil and Mechanical Engineering Society,’ February 19th, 1880.
+ © Proc. Iron and Steel Institute,’ 1879-80.
tf ‘ Proc. Roy. Soc. Edin.,’ January, 1850.

598 MR. T. WRIGHTSON ON IRON AND

and only affects a portion of the mass, so that methods which are available for
measuring changes of volume in cast iron are inapplicable.

The only method of proof left open was to show that pressing the welding masses
is attended by a fall in their temperature.

Unfortunately, fourteen years ago, when I made my earlier experiments, the
investigation could not be continued as there was no suitable pyrometer with which
such a delicate experiment could be carried out.

The recent successful application to metallurgical research, by Professor RoBERTs-
AusTEN, of a recording pyrometer,* led me to resume the investigation of the
question.

This pyrometer, which depends upon the use of a thermo-junction, consisting of a
platinum wire twisted with another wire of platinum alloyed with 10 per cent.
of rhodium, had been of service in the investigation of critical temperatures in various
metals and alloys, and as Professor Roperts-AUsTEN offered to place his laboratory
and appliances at my disposal, and to aid me by advice, the opportunity for
conducting the new experiments was gladly accepted.

The first experiments were made by placing the thermo-couple between the two
welding faces of bars heated in an ordinary smith’s fire. The wires of the thermo-
couple were carried from the smith’s shop to the pyrometer in the laboratory, but
signalling was necessary to ensure the taking of the photographic record of the
temperature at the exact moment the smith applied pressure, and it soon became
evident that the arrangement was awkward. The results were far from being
uniform, although on several occasions a distinct fall of temperature was apparent
when welding was effected, which encouraged the expectation that with a more
perfect system of work the true facts of the case would be revealed.

After full consideration it was decided that the only satisfactory way to proceed
would be to use the electric welding apparatus of THompson Houston with alternat-
ing currents. The Electric Welding Company readily put one of their admirable
apphances and a suitable dynamo at my disposal; the manager, Mr. ARMSTRONG, and
the electrician, Mr. REF, assisted in installing it at the Mint, and helped in every
way to make the arrangement effective. By the kindness of Mr. R. A. Hix, Super-
intendent of the Operative Department, the composite alternating dynamo was driven
from the Mint engines, and the conductors from the dynamo were carried over the
intervening buildings to Professor Roperts-AusTEN’s laboratory, where they were
connected to the electric welder.

The wires of the thermo-junction, which was placed in contact with the surfaces to
be welded, were carried from the welder, round the walls of the laboratory to the
galvanometer placed inside the camera of the recording pyrometer.

It may be well to point out that the deflection of the galvanometer mirror causes a

* ¢Proc. Roy. Soce.,’ vol. 49, 1891, p. 347, and ‘ Proe. Inst. Civil Engineers,’ vol. 10, 1891-2, Part 4,
where a full description of the pyromeier is given.

STEEL AT WELDING TEMPERATURES. 599

spot of light to move horizontally across the plate in the photographic slide, which
slide moves vertically upwards at a uniform speed controlled by clockwork. The
spot of light thus describes a curve, the ordinates of which represent respectively
temperature and time. By this means a photographic record is produced. A base
line (also produced by photography) represents the zero of temperature. When the
indications of the thermo-junction are calibrated the diagram affords a complete record
of the changes of temperature in the material in contact with the thermo-junction.

Plate 1, figs. 1 and 2, were the first taken, and some transient surprise was caused
by finding that on the pressure being applied, by a hand lever acting on a pinion and
rack, there was a rise instead of a fall of temperature. On reflection it appeared that
this would certainly be due to the distortion and crushing up of the soft heated iron
when the bars were pressed together at the welding temperature. Work was thus
done, and the heat evolved masked any true fall of temperature.

To get rid of this heat of distortion it was necessary to confine the bar when pressed
in some rigid envelope, which, from the conditions of the experiment, must, because
of the electric current used for the heating, be a non-conductor of electricity.

After many attempts and failures the plan was adopted of placing the bar inside a
close-fitting cylinder of porcelain, outside of which was closely fitted a strong steel die.

Both porcelain cylinder and steel die were cut through the centre in a plane trans-
verse to the axis. This plan enabled the wires of the thermo-junction to be led to the
centre of the bar, where the maximum heat was evolved. The bar was perforated by
a minute hole, into which the wires forming the thermo-junction passed from each
side.

Fig. 3.

PORCELAIN

Pipe-clay insulators encircled the wires and rested in grooves between the faces of
the transverse cut, through the die, so as to prevent contact between the die and the
wire.

After the temperature of welding had been noted on a series of photographic plates,
there was no object in severing the bar so as to make a welded junction for each
experiment,

600 MR. T. WRIGHTSON ON IRON AND

Ali that was necessary was to heat by electricity in the electric welder a continuous
bar until the position of the spot of light on the scale made it certain that the tempera-
ture was within the welding limits in the neighbourhood of the thermo-junction.
The pressure was then applied.

When the bar was raised to welding heat inside the cylinder of porcelain, the
pressure was applied. The time of its application is marked P on the photographic
eurve in each case. The position of this point was indicated by a signal made by
momentarily obscuring the light which feli on the galvanometer mirror, thereby
producing a brief interruption to the continuity of the curve.

These signals could be varied at will and proved to be of great service (see
Plate 1, figs. 3, 4, 4a, 5, 6 and 7).

The current which heated the bar was not entirely cut off. This was done to avoid
any fall of temperature before the pressure was put on, and in some of the diagrams
it will be seen that it has not always been possible to avoid a slight and uniform rise,
which merely means that the current of the electric welder did something more than
counterbalance the loss of heat by radiation.

The pressure was applied when the temperature of the bar was 1347° C. (see Plate 1,
fig. 3). A sudden rise of 27° C. showed itself, but a rise in temperature might be
expected to take place, until all interstices between the outside of the bar and the
envelope were filled by the plastic iron. The porcelain of course cracked, and the
minute cracks had also to be filled before the effect of pressure in producing a fall in
temperature could be demonstrated.

The second time the bar was heated to 1371° C., and on pressing a rise of tempera-
ture equal to 8° C. was shown (see Plate 1, fig. 4).

This smal] rise appeared to indicate that the interstices were nearly, or quite filled.

The third time the same bar was heated to 1420° C. and pressed, a distinct fall of
27° C. was indicated by the diagram, thus for the first time realizing the anticipation
with which I began the investigation (see Plate 1, fig. 5).

The fourth time the bar was heated to 1400° C., when a pressure of about 1200
pounds per square inch of the area of the bar, or 80 atmospheres, gave the remarkable
fall of 57° C. (see Plate 1 fig. 6).

The fifth time the bar was heated to 1300° C., a much lower temperature than the
last, when, on being pressed, the fall in temperature was recorded as 19° C. (see
Plate 1, fig. 7).

If the bar experimented on be examined, a number of vein-like protuberances will
be seen, showing that the plastic iron had to fill the crevices in the cracked porcelain,
before the pressure could cause a fall of temperature.

It appears from the series of experiments on this bar, that the limits of temperature
within which the thermal expansion is negative, certainly include a range between
1300° C. and 1420°C., and they may extend both above and below these limits,
although, the fall being only 19° C. at the lower temperature as compared with 57° C.
at the higher, it looks as if the lower temperature were approaching the limit,

STEEL AT WELDING TEMPERATURES. 601

No doubt a series of experiments to determine the exact limits of the critical state
would be full of interest.

Between the temperature of 1400° and that of melting wrought iron (stated to be
1600°) there are doubtless increasing degrees of mobility in the material. When
pressure is put on the bar, say at 1400°, it not only lowers the temperature of the
melting point, but increases the mobility at lower temperatures, so that if before
pressure the temperature be 1400°, after pressure there may be a condition of mobility
between the molecules which corresponds to a temperature without pressure of 1500°,
although the temperature has been reduced by pressure to 1848°.

If two pieces of iron, or almost any metal, be raised to the melting point, union can
no doubt be effected, but this is by melting together and not by welding. The pro-
cess of welding appears to be that by which complete union can be effected- by
hammering or pressure, at a temperature considerably below that required to melt
the material. The heat of the fire having raised the bars within the critical range of
temperature above described, the smith in striking with his hammer is assisted by the
special properties of this welding material in producing an increased mobility of the
molecules, which approach though never arrive at liquidity. This condition is favour-
able to the interpenetration of the molecules, and consequent adhesion of the surfaces
on hammering.

Since I made this experiment in Professor RoBERTSs-A usTEN’s laboratory, I have had
the opportunity of experimenting in steel works upon the behaviour of solid masses
of soft weldable rolled steel when lowered into molten steel of the same quality. The
mass at first sinks, and then quickly floats to the surface, where it remains until
melted, showing that weldable low carbon steel follows the same law as cast iron, and
therefore possesses that property which it is contended is essential to bodies which
can be united by the process of regelation or welding. The increase of carbon in
steel appears to prevent welding just as it does in the case of the more highly car-
bonized form of iron known as cast iron.

In conclusion J would observe that if I have been able to demonstrate this remark-
able property in wrought iron of being cooled by pressure when at the welding
temperature, it would not have been possible to attain this result without the aid of
Professor Roperts-AUSTEN’S admirable pyrometer, and without the help which he
and his able assistants, Mr. STANSFIELD and Mr. RreGinaLp Roperts, have contributed.

EXPLANATION OF PLATE.
Effect of Pressure on an Iron Bar.

Fig. 1.—Current cut off before pressure. _
Fig. 2.— ,, 2 at a lower temperature.
In each experiment pressure applied at point marked P.
MDCCOXOV.—A, 4 4

602 ON IRON AND STEEL AT WELDING TEMPERATURHS.

Effect of Pressure in a series of Five Experiments on an Iron Bar 4" in
diameter, enclosed in a Porcelain and Steel Cylinder.

Ist Experiment.—Fig. 3 at a temperature of 1347° C. gave a rise of 27° C.
2nd i —Fig. 4 % ik 1371: 5, . 8° C.
Fig. 44 is a diagram produced at the same time as fig. 2, but from
a more sensitive galvanometer. The same scale of tempera-
ture is not applicable.
In each experiment pressure applied at time marked P.

Fig. 5.—3rd Experiment at 1420° C. pressure gave a fall of 27° C.
Fig. 6.—4th i at 1400° C. i As 5 a Oe
Fig. 7.—5th 3 at 1300°'C. ms se 5 19° C.
In each experiment pressure applied at time marked P between first two signals,
and relieved between last two signals. The current was cut off immediately
aiter the fourth signal. ;

6624

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