THESE Memoirs are also issued as Volume XVIII. of the Transactions

of the Cambridge Philosophical Society.

IN HONOREM

GEORGII GABRIELIS STOKES

PHYSICAM ET MATHEMATICAM

APVD CANTABRIGIENSES

IAM QVINQVAGINTA ANNOS PROFITENTIS

CONTENTS.

Order of Proceedings at the formal celebration by the University of Cambridge of

the Jubilee of Sir GEORGE GABRIEL STOKES, Bart., Lucasian Professor 1849-1899

The Rede Lecture: La théorie des ondes lumineuses: son influence sur la physique
moderne. By ALFRED CORnu......

PAGE

vii

xvii

I.

On the analytical representation of a uniform branch of a monogenic function.

By G. MITTAG-LEFFLER

1

II. Application of the Partition Analysis to the study of the properties of any system

of Consecutive Integers. By Major P. A. MACMAHON, R.A., D.Sc., F.R.S., Hon.

Mem. C.P.S.

12

III.

On the Integrals of Systems of Differential Equations. By A. R. FORSYTH, Sc.D.,

F.R.S., Sadlerian Professor of Pure Mathematics

35

IV. Ueber die Bedeutung der Constante b des van der Waals'schen Gesetzes. Von L.

BOLTZMANN und Dr MACHE, in Wien

91

V.

On the Solution of a Pair of Simultaneous Linear Differential Equations, which

occur in the Lunar Theory. By ERNEST W. BROWN, Sc.D., F.R.S., Professor of

Mathematics at Haverford College, Philadelphia

94

VI.. The Periodogram of Magnetic Declination as obtained from the records of the

Greenwich Observatory during the years 1871-1895 (Plates I, II). By ARTHUR

SCHUSTER, F.R.S., Professor of Physics at the Owens College, Manchester

VII. Experiments on the Oscillatory Discharge of an Air Condenser, with a Determina-

tion of "v." By OLIVER J. LODGE, D.Sc., F.R.S., Professor of Experimental

Physics, University College, Liverpool, and R. T. GLAZEBROOK, M.A., F.R.S.,

Director of the National Physical Laboratory

107

136

VIII.

The Geometry of Kepler and Newton. By Dr C. TAYLOR, Master of St John's

College

197

XI.

On a Class of Groups of Finite Order. By W. BURNSIDE, M.A., F.R.S., Professor

of Mathematics, Royal Naval College, Greenwich

269

XII. On Green's Function for a Circular Disc, with applications to Electrostatic Problems.

By E. W. HOBSON, Sc.D., F.R.S., Fellow of Christ's College...

277

VOL. XVIII.

b

XIII. Demonstration of Green's Formula for Electric Density near the Vertex of a

Right Cone. By H. M. MACDONALD, M.A., Fellow of Clare College

PAGE

292

XIV.

On the Effects of Dilution, Temperature, and other circumstances, on the Absorption

Spectra of Solutions of Didymium and Erbium Salts (Plates 3-23). By

G. D. LIVEING, M.A., F.R.S., Professor of Chemistry

298

XV.

The Echelon Spectroscope. By A. A. MICHELSON

316

XVI.

On Minimal Surfaces. By H. W. RICHMOND, M.A., Fellow of King's College,

Cambridge

324

XVII. On Quartic Surfaces which admit of Integrals of the first kind of Total

Differentials. By ARTHUR BERRY, M.A., Fellow of King's College, Cambridge' 333

XVIII. An Electromagnetic Illustration of the Theory of Selective Absorption of Light by

a Gas. By HORACE LAMB, M.A., F.R.S., Professor of Mathematics at the Owens

College, Manchester

348

XIX.

The Propagation of Waves of Elastic Displacement along a Helical Wire. By

A. E. H. LOVE, M.A., F.R.S., Sedleian Professor of Natural Philosophy in

the University of Oxford

364

XX.

...

On the construction of a Model showing the 27 lines on a Cubic Surface (Plates

XXIV, XXV). By H. M. TAYLOR, M.A., F.R.S., Fellow of Trinity College 375

XXI. On the Dynamics of a System of Electrons or Ions: and on the Influence of

a Magnetic Field on Optical Phenomena. By J. LARMOR, M.A., F.R.S., Fellow

of St John's College

380

XXII.

On the Theory of Functions of several Complex Variables. By H. F. BAKER, M.A.,

F.R.S., Fellow of St John's College

408

Index...

445

PLATES.

Frontispiece. Portrait of Sir George Gabriel Stokes, Bart.

I, II, illustrating Professor Schuster's paper, page 107.

3-23 (contained in 14 leaves) illustrating Professor Liveing's paper, page 298.

XXIV, XXV, illustrating Mr H. M. Taylor's paper, page 375.

ERRATA.

Page 210, line 5 from the top, omit the equation AB. CD = kBC . DA.

332. In regard to $$ 7-11, reference ought to have been made to the results of
Lie, Math. Ann. xiv. pp. 373-378, or to Darboux § 325, from which the special type of surfaces
considered might also be derived.