BIBLIOGRAPHICAL NOTES. 529 



MINCHIN (G. M.) Treatise on Statics. 3rd edition, Vol. ii. (1886). 



In pp. 1743 of this standard work the Theory of Screws is discussed. An 

 instructive construction for the cylindroid is given on p. 20. We may also note 

 the following theorem proved on p. 25, &quot; If the wrench on any screw of the 

 cylindroid is replaced by a force and a couple at the centre of the pitch-conic 

 (centre of the cylindroid) the axis of this couple will lie along the perpendicular 

 to the diameter of the pitch-conic which is conjugate to the direction of the force 

 or in other words, the plane of the couple will be that of the axis of the cylindroid 

 and this conjugate diameter.&quot; 



SCHONFLIES (Arthur) Geometrie der Bewegung in synthetischer Darstellung, pp. 

 1-194, 8vo. Leipzig, 1886. 



The third chapter of this work, pp. 79-192, is devoted to the geometrical study 

 of the movement of a rigid system. The author uses the word parameter to express 

 what we have designated as the pitch. As an illustration of the theorems given I 

 cite the following from p. 92, &quot; Bewegt sich ein unverdnderliches System beliebiy im 

 Bourne, und ist in iryend einem Augenblick eine Gerade desselben senkreclit zur 

 Tangente der Bahn eines ihrer Punkte, so ist sie es zu den Bahntangenten oiler 

 Punkte.&quot; 



In the language of the present volume in which the dynamical and kinetical 

 conceptions are so closely interwoven, this theorem appears as follows. Let two 

 screws a and ft be reciprocal and let the pitch of a be zero. A twist of a rigid 

 body about (3 can do no work against a force on a. But a may be considered to 

 act on the rigid body at any point in its line of application. Hence the displace 

 ments of every such point must be perpendicular to a. 



The following suggestive theorems may be quoted from pp. 116, 117 : 



&quot; Die sammtlichen Punkte des Systems deren Bahnen nach einem festen 

 Punkte D des Raumes gerichtet sind, liegen in jedem Augenblick auf einer Raum- 

 curve dritter Ordnung C.&quot; 



&quot;Die Raumcurve C enthalt die unendlich fernen imaginaren Kreispunkte 

 der zur Axe der Schraubenbewegung senkrechten Ebenen.&quot; 



This work contains indeed much that it would be interesting to quote. I must 

 however content myself with one more remark from p. 153, which I shall give in 

 our own terminology. When a rigid body has freedom of the second order it can 

 of course be twisted about any screw on a cylindroid. Such a twist can always 

 be decomposed into two rotations around the two screws of zero pitch P and Q. 

 The rotation around P does not alter P. Hence whatever be the small displace 

 ment of the system the movement of P can never be other than a rotation 

 around Q, and the movement of Q can never be other than a rotation around P. 



BALL (R. S.) Dynamics and Modern Geometry : a new chapter in the Theory of 

 Screws. Sixth Memoir. Cunningham Memoirs of the Royal Irish Academy, 

 No. iv., pp. 1-44 (1886). 



We represent the several screws on the cylindroid by points on the circum 

 ference of a circle. The angle between two screws is the angle which their 

 corresponding points subtend at the circumference. The shortest distance of any 

 two screws is the projection of the corresponding chord on a fixed ray in the plane 

 of the circle. Any chord passing through the pole of this ray intersects the circle 

 in points corresponding to reciprocal screws. The pitch of any screw is the 

 distance of its corresponding point from this ray. A system of points representing 

 instantaneous screws and the corresponding system representing the impulsive 

 screws are homographic. The double points of the homography correspond to the 

 B. 34 



