A. CAYLEY, Sc.D., F.R.S.,

SADLERIAN PROFESSOR OF PURE MATHEMATICS IN THE UNIVERSITY OF

CAMBRIDGE;

J. W. L. GLAISHER, Sc.D., F.R.S.,

FELLOW OF TRINITY COLLEGE, CAMBRIDGE;

A. R. FORSYTH, M.A., F.R.S.,

FELLOW OF TRINITY COLLEGE, CAMBRIDGE,,

VOL. XXIII.

London:

LONGMANS, GREEN, AND CO.

PATERNOSTER ROW.

1889.

CAMBRIDGE:

PRINTED BY W. METCALFE AND SON, TRINITY STREET AND ROSE CRESCENT.

112842

TIBBYDA

CONTENTS OF VOL. XXIII.

ALGEBRA.

Systems of reduced simultaneous ternary forms equivalent to a given ternary

form, which involves several sets of variables. By A. R. Forsyth

The eliminant of two binary quantics. By Capt. P. A. Mac Mahon •

The investigation by Wallis of his expression for . By Prof. Cayley

Simultaneous reciprocants. By A. Berry

A theorem on trees. By Prof. Cayley -

GEOMETRY.

PAGE

102

139

A symmetrical system of equations of the lines of a cubic surface which has

a conical point. By H. W. Richmond

170

On the circles, which are described about the four circles, escribed and

inscribed in a given plane triangle, taken by triads. By H. M. Jeffery 180

On the circles, which may be described about the eight small circles of a
sphere, taken by triads, which are inscribed in the triangles formed
by three planes intersecting in the centre. By H. M. Jeffery -

On twisted cubics which fulfil certain given conditions. By A. C. Dixon

On the generalised problem of contacts. By H. M. Jeffery

A property of bicircular quartics. By C. M. Jessop

198

343

358

. 369

DIFFERENTIAL AND INTEGRAL CALCULUS, DIFFERENTIAL
EQUATIONS, AND SPECIAL FUNCTIONS.

On synthetical solution and on deformation. By Sir James Cockle -

1

On the theory of forms in the integration of linear differential equations

of the second order. By A. R. Forsyth

45

On some expressions of a function of a single variable in terms of Bessel's
functions. By W. F. Sheppard

223