A Treatise on the Theory of Screws

BIBLIOGRAPHICAL NOTES. 525 Clifford (W. K.) Elements of Dynamics. 1878. In this work, designed no doubt to be elementary but perhaps rather illus- trating the breadth of view so characteristic of its gifted author, the fundamental theorem of the composition of twists and wrenches by the cylindroid is assigned an important position at the basis of mechanics. Schell (W.).—Theorie der Bewegung und der Kräfte. 2nd edition. Leipzig, 1879. Vol. ii. This is a comprehensive and valuable treatise on Theoretical Dynamics. It merits particular mention here because it contains an excellent exposition in the German language of many of the most important parts of the Theory of Screws. Part III., Chap, x., pp. 211-235, discusses the Cylindroid and reciprocal Screws, and includes a general account of the properties of the different screw-systems. Part IV., Chap, vm., gives a general account of the Dynamical parts of the Theory, including the principal Screws of Inertia and Harmonic Screws. Ball (R. S.)—Note on the application of Lagrange's Equations of Motion to Pro- blems in the Dynamics of a Rigid Body. Proceedings of the Royal Irish Academy. 2nd Ser., Vol. iii., p. 213 (1879). In this paper it is shown from Lagrange’s well-known equations of motion in generalized co-ordinates that if T be the kinetic energy of a body twisting about a screw whose n screw co-ordinates referred to any co-reciprocal system with pitches Pt, ■■■ Pn, are ^n, then the impulsive wrench which would have been capable of producing from rest the actual motion which the body possesses must have as its coordinates (§ 86) 1 dT 1 dT Pt d0t" ’ pnd0f Ball (R. S.)—Extension of the Theory of Screws to the Dynamics of any Material System. (Fourth Memoir.) Transactions of the Royal Irish Academy, Vol. xxviii., pp. 99—136 (1881). The conception of a screw-chain is here introduced. The screw-chain is a geometrical entity which bears to an entire system, no matter how complex its parts oi' tbeir connexions, the same relation which a screw beai's to a single rigid body. One screw-chain can always be found which is reciprocal to Gy - 1 screw- chains where p. is the number of material parts in the system. One of the chief results obtained shows the extension of the notion of the principal screws of inertia of a single rigid body to a system of rigid bodies. Chap. xxiv. of the present volume contains the essential parts of this memoir. Schell (W.)—Die sechs Grade der Beweglichkeit eines unveränderlichen Systems. Central Zeitung für Optik und Mechanik, 1881. Here is an interesting geometrical study of the degrees of freedom of a rigid body under the several conditions that 1, 2, 3, 4 or 5 of its points shall be con- strained to lie on given surfaces. If a force be applied along a normal to the surface at the point of the body which is constrained to lie on that surface then that force will be counteracted by the constraints. Every motion of the body which is possible must be a twist about a screw reciprocal to a screw of zero pitch on that normal.