CONTENTS. 



VOL. XX. 



PAGE 



On the term by term integration of an infinite series over an infinite range 

 and the inversion of the order of integration in repeated infinite 

 integrals. By S. Pollard, M.A., Trinity College, Cambridge. 

 (Communicated by Prof. 6. H. Hardy) 1 



Note on Mr Hardy^s extension of a theorem of Mr Polya. By Edmuxd 



Landau. (Communicated by Prof. G. H. Hardy) .... 14 



Studies on Cellulose Acetate. By H. J. H. Fenton and A. J. Berry . 16 



An examination of Searle's method for determining the viscosity of very 

 viscous liquids. By Kurt Molin, Filosofie Licentiat, Physical 

 Institute, Technical College, Trondhjem. (Communicated by Dr 

 G F. C. Searle.) (Four figs in Text) 23 



Preliminary Note on Antennal Variation in an Aphis (Myzus ribis, 

 Linn.). By Maud D. Haviland, Fellow of Newnham College. 

 (Communicated by Mr H. H. Brindley) ..... 35 



The effect of a magnetic field on the Intensity of spectrum lines. By H. P. 

 Waran, M.A., Government Scholar of the University of Madras. 

 (Communicated by Professor Sir Ernest Rutherford.) (Plates I 

 and II and one fig. in Text) ........ 45 



Further Notes on the Food Plants of tite Common Earwig (Forficula 



auricularia). By H. H. Brindley, M.A., St John's College . . 50 



Lagrangian Methods for High Speed Motion. By C. G. Darwin . . 56 



A hifilar method of measuring the rigidity of wires. By G. F. C. Searle, 

 Se.D., F.R.S., University Lecturer in Experimental Physics. (Five 

 figs, in Text) 61 



The Rotation of the Non-Spinning Gyrostat. By G. T. Bennett, M.A., 



F.R.S., Emmanuel College, Cambridge ...... 70 



Proof of the equivalence of different mean vahies. By Alfred Kienast. 



(Communicated by Professor G. H. Hardy) ..... 74 



Notes on the Theory of Vibrations. (1) Vibrations of Finite Amplitude. 

 (2) A Theorem due to Routh. By W. J. Harrison, M.A., Fellow of 

 Clare College ■ 83 



Experiments with a plane diffraction grating. By G. F. C. Searle, 

 Sc.D., F.R.S., University Lecturer in Experimental Physics. (Ten 

 figs, in Text) 88 



The Shadow Electroscope. By R. Whiddington, M.A., St John's College. 



(One fig. in Text) 109 



Mathematical Notes. By Professor H. F. Baker and C. V. Hanumanta : 

 On the Hart circle of a spherical triangle . . . . . .116 



On a property of focal conies and of bi circular quartics . . . 122 

 On the construction of the ninth point of intersection of two plane cubic 

 curves of which eight points are given ...... 131 



