CAMBRIDGE:

PRINTED BY W. METCALFE & SONS, TRINITY STREET, CORNER OF GREEN STREET.

T

J. J. SYLVESTER, M.A., F.R.S.,

PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY,
WOOLWICH; AND

N. M. FERRERS, M.A.,

FELLOW AND TUTOR OF GONVILLE AND CAIUS COLLEGE, CAMBRIDGE:

LUCASIAN PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF CAMBRIDGE;

A. CAYLEY, M.A., F.R.S.,

SADLERIAN PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF

CAMBRIDGE; AND

M. HERMITE,

CORRESPONDING EDITOR IN PARIS.

VOL. XI.

ὅ τι οὐσία πρὸς γένεσιν, ἐπιστημὴ πρὸς πίστιν καὶ διάνοια πρὸς εικασίαν ἔστι,

LONDON:

LONGMANS AND CO.,

PATERNOSTER ROW.

CONTENTS OF VOLUME XI.

On the Relation between the Angular Velocity about and the Angular Velocity of the Instantaneous Axis of a Body revolving spontaneously about a fixed point, and on the Axes of Greatest and Least Mobility. By William Walton

On the Quartic Surfaces (*XU, V, W)2 = 0—continued from Vol. x., p. 34. By Prof. Cayley

PAGE

15

General Solution and Extension of the Problem of the 15 School
Girls. By Andrew Frost

Mathematical Notes. By W. H. Besant

26

42

Note on a Binary Evectant Form. By Samuel Roberts
Electro-Dynamics. Ampere's Theory of the Solenoid. By Percival
Frost

47

57

On the Algebra of Magic Squares. No. I. By Joseph Horner
Note to the Article on Porisms, Quarterly Journal, No. 30. By
Joseph Wolstenholme

66

On the Stress exerted by a Rigid Body on a Fixed Point rigidly connected with the Body, which is revolving spontaneously about the Point. By William Walton

Note on Euclid, Book VI. Prop. 7. By J. F. Wolff, Jun.
Theorem on the Action of an Electric Current in a Helix wound
on a Cylinder of any Form upon the Pole of a Magnet. By
Percival Frost

On the Evolutes of Cubic Curves. By Henry M. Jeffery

Note on a Relation between Two Circles. By Prof. Cayley

On the Porism of the In-and-Circumscribed Polygon, and the (2, 2)
Correspondence of Points on a Conic. By Prof. Cayley

Note on Rhizic Curves. By William Walton

On a Problem of Elimination. By Prof. Cayley

Equilibrium of One Heavy Rough Body on Another. By E. J. Routh
Moment of Inertia of a Quadrilateral. By E. J. Routh

On the Quartic Surfaces (*XU, V, W)2 = 0—continued. By Prof.
Cayley

On Axes of Lug and Axes of Kick. By William Walton

On the Algebra of Magic Squares. No. II. By Joseph Horner
Note on a System of Algebraical Equations. By Prof. Cayley
Electro-Dynamics. By Percival Frost

83

91

99

102

109

111

114

123

. 132

134

145

On the Evolute of Cubic Curves--continued. By Henry M. Jeffery
On the Motion of Fluids-continued from Vol. x. p. 311. By Sir
James Cockle

A Demonstration of a Property of Elliptic Functions. By William
Walton

A Demonstration that every Equation has a Root. By William Walton 178 On Evolutes and Parallel Curves. By Prof. Cayley

183 On the Spoke Asymptotes of Rhizic Curves. By William Walton 200 The Deduction of Euler's Equations from the Lagrange Equations. By W. H. Besant

244

The Small Oscillations of a Particle and of a Rigid Body. By
Robert Stawell Ball

Note on Osculating Curves. By Joseph Wolstenholme
Example of a Special Discriminant. By Prof. Cayley

On the Algebra of Magic Squares. No. III. By Joseph Horner
On Concyclic Conicoids. By Henry M. Jeffery

On the Envelope of a Certain Quadric Surface. By Prof. Cayley Tables of the Binary Cubic Forms for the Negative Determinants, = 0 (Mod. 4), from – 4 to 400; and = 1 (Mod. 4), from – 3 to -99; and for five Irregular Negative Determinants. By Prof. Cayley

On the Transformation of Two Simultaneous Equations. By William
Wallon

On Riccati's Equation. By J. W. L. Glaisher