530 THE THEORY OF SCREWS. 



two principal screws of inertia. This paper is the development of an earlier one. 

 See Proceedings of the Eoyal Irish Academy, 2nd Series, Vol. iv. p. 29. The 

 substance of it has been reproduced in Chaps v. and xn. of the present volume. 



BALL (R. S.) On the Plane Sections of the Cylindroid. Seventh Memoir. Trans, 

 of the Royal Irish Academy, Vol. xxix., pp. 1-32 (1887). 



This is a geometrical study of the cylindroid regarded as a conoidal cubic with 

 one nodal line and three right lines in the plane at infinity. Plane sections of the 

 cylindroid are shown in plates drawn to illustrate calculated cases. It is shown 

 that the chord joining the points in which two reciprocal screws intersect a fixed 

 plane envelops a hyperbola which has triple contact with the cubic curve in which 

 the fixed plane cuts the cylindroid. See Chap. xiu. of the present volume. 



I may take this opportunity of mentioning in addition to what has been said 

 on the subject of models of the cylindroid in Chap. xm. that very simple and 

 effective models of this surface can now be obtained from Martin Schilling. Halle a 

 Saale. See his catalogue for Feb. 1900. 



ROBERTS (R. A.) Educational Times, xlvi. 32-33 (1887). 



In this it is shown that under the circumstances described the shadow of the 

 cylindroid z (x* + y 2 } 2mxy = on the plane z = exhibits the hypocycloid with 

 three cusps. 



BALL (R. S.) A Dynamical Parable, being an Address to the Mathematical and 

 Physical Section of the British Association. Manchester, 1887. 



This has been given in Appendix n. p. 496. It may be added here that it has 

 been translated into Hungarian by Dr A. Seydler, and into Italian by G. Vivanti. 



TARLETON (P. A.) On a new method of obtaining the conditions fuljilled when 

 the Harmonic Determinant has equal roots. Proceedings of the Royal Irish 

 Academy, 3rd Series, Vol. i. No. 1, p. 10 (1887). 



This discusses the case of equal roots in the harmonic determinant so important 

 in the Theory of Screws as in other parts of Dynamics. It should be studied in 

 connection with 85 of the present volume ; also Note n. p. 484. See also 

 Zanchevsky, p. 531. 



BALL (R. S.) How Plane Geometry illustrates general problems in the Dynamics oj 

 a Rigid Body with Three degrees of Freedom. Eighth Memoir. Transactions 

 of the Royal Irish Academy, Vol. xxix., pp. 247-284 (1888). 



The system of the third order is of such special interest that it is desirable 

 to have a concise method of representing the screws which constitute it. We here 

 show that the screws of such a system correspond to the points in a plane. This 

 is the development of an earlier paper communicated to the Royal Irish Academy 

 in 1881. Proceedings, 2nd Series, Vol. iii., pp. 428-434. 



In this method of representation the screws on a cylindroid belonging to the 

 system are represented by the points on a straight line. The screws of any given 

 pitch will have as their correspondents the points on a certain conic. A pair of 

 points conjugate to the conic of zero pitch will correspond to a pair of reciprocal 

 screws. The conic which represents the screws of zero pitch, and the conic which 

 represents the screws of infinite pitch, will have a common conjugate triangle. 

 The vertices of that triangle correspond to the principal screws of the system. It 

 is proved that the pitch quadrics of a three-system are all inscribed in a common 

 tetrahedron and have four common points on the plane at infinity. 



