CONTENTS. vii 



NOTICES AND ABSTRACTS 



OP 



MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 



MATHEMATICS AND PHYSICS. 



Page 



Address by Professor Balpoub Stewart, M.A., LL.D., F.U.S,, President of 

 the Section 1 



Mathematics. 



Professor H. S. Ball on a Screw-complex of the Second Order 10 



Professor Cayley on the Analytical Forms called Factions 10 



Professor Clieford on the Theory of Linear Transformations : I. The Gra- 

 phical Representation of Invariants ; II. The Expansion of Unsymnietrical 

 Functions in Symmetrical Functions and Determinants ; III. The Notation 

 of Matrices 11 



Professor J. D. Everett on the Calculus of Motors 11 



Mr. J. W. L. Glaisher on Formulae of Verification in Partitions 11 



on Theorems on the n**" roots of Unity 13 



Mr. W. Hayden on some Geometrical Theorems 14 



Mr. Henry M. Jeffeby's two Memoirs : — I. On the Shadows of Plane Curves 

 on Spheres ; II. On Cubic Spherical Curves with triple Cyclic Arcs and 

 ti-iple Foci 15 



Professor Paul Mansion's Elementary Solution of Huyghens's Problem on 

 the Impact of Elastic Balls 18 



on the singular Solutions of Differential Equations 



of the First Order which represent Lines at Infinity 19 



Professor IIenry' J. Stephen Smith on Singxdar Solutions 21 



on the Effect of Quadric Transformation 



on the Singular Points of a Curve 21 



on Continued Fractions 21 



Mr. H. Martyn Tayt^ob's Contributions to the Mathematics of the Chess- 

 board 21 



Sir W. Thomson on Laplace's Process for determining an Arbitrary Constant 

 in the Integration of his Differential Equation for the Semidiurnal Tide . . 23 



General Integz'ation of Laplace's Differential Equation of 



the Tides 23 



on the Integi-ation of Linear Differential Equations with 



Rational Coefficients 23 



on some Effects of liaplace's Theory of Tides 23 



