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 Krdfte. 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, vni., 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 Lagranges 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 

 !, ... p n , are 1 , ... 9 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) 



! dT \dT 



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 or their connexions, the same relation which a screw bears to a single rigid 

 body. One screw-chain can always be found which is reciprocal to 6/u. - 1 screw- 

 chains where yu. 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 iinverdnderlichen Systems. 

 Central Zeitung fur 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 pitcli on that normal. 



