

CONTENTS. 



PAGE 



On the term hy term integration of an infinite series over an infi/nite ran^e 

 and the inversion of the order of integration in repeated infinUe 

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

 (Communicated by Professor G. H. Hardt) 1 



Ifote on Mr Eardy's extension of a theorem of Mr Polya. By Edmund 



Landau. (Communicated by Professor 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 determini7ig the viscosity of very 

 viscous liquids. By Kurt Molin, Filosofie Licentiat, Physical 

 Institute, Technical College, Trondhjem. (Communicated by 

 Dr G. F. C. Searle.) (Four Diagrams 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 test) 45 



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



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



Lagrangian Methods for High Speed Motion. By C. G. Darwin . . 66 



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

 Sc.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 values. By Alfred Kienast. 



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



Notes on the Theory of Vibratiom. (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 Shadoio 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 bidrcular quartics . . . 122 



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



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



On a proof of the theorem of a double six of lines by projection from 



four dimensions. (Three Figs, in text) ...... 183 



On transformations with an absolute quadric . . . . . 145i 



Oyi a set of transformations of rectangular ctxes. (One Fig. in text) , 147 



On the generation of sets of four tetrahedra of which any two are \ 



mutually inscribed 155 



On the reduction of homography to movement in three dimensions. (One 



Fig. in text) 158 



On the transformatiooi of the equations of eleot.rodynamics in the Maxwell 

 and in the Einstein forms . . , . . . . .166 



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