532 THE THEORY OF SCREWS. 



Chap. ii. is devoted to groups of screws. He discusses in detail groups con 

 taining three members, investigating some special cases not dwelt on before. He 

 then gives the formulae for what are termed &quot;Oblique Co-ordinates.&quot; 



In Chap. in. the application of the Theory of Screws to mechanics is discussed 

 and the leading parts of the Theory of Screws in relation to dynamical problems 

 with freedom of the th order are set forth, and he adds, &quot;The lack of books on the 

 Theory of Screws both in Russia and abroad makes us hope that our work will be 

 received with indulgence.&quot; 



BALL (R. S.) The Theory of Permanent Screws. Ninth Memoir. Transactions of 

 the Royal Irish Academy, Vol. xxix., pp. 613 652. 1890. 



Using Screw-chain co-ordinates an emanent (see Salmon s Higher Algebra, 

 125, or Elliott s Algebra of Qualities) is here shown to vanish. This involves a 

 general property of the function T which expresses the kinetic energy. 



dT dT 



X l -j -- b ... + X H -j = 0. 

 CtOC-^ CvXft 



It is shown that for the permanent screw-chains, 



The special cases for the different degrees of freedom of a single rigid body are 

 considered in detail. If the rigid body has three degrees of freedom then there 

 are three permanent screws, about any one of which the body will continue to 

 twist if once set twisting. 



In general, if the body be set twisting about a screw 6, a restraining wrench 

 on some other screw rj would be necessary if the motion were to continue as a twist 

 about 0. 



To find 7) we employ the plane representation. We construct first a system 

 of points homographic with the points 0. The double points of the homography 

 are representative of the three permanent screws. If we draw the ray connecting 

 6 with its correspondent, then 77 is the pole of this ray with respect to the conic of 

 zero pitch, while the pole of the same ray with respect to the conic of inertia gives 

 the screw about which the acceleration is imparted to 0. 



For freedom of the first and second orders there is only one permanent screw ; 

 for freedom of the third, fourth, and fifth, there are three permanent screws. 

 When the body is quite free the permanent screws are triply infinite. The Theory 

 of Permanent Screws is given in Chap. xxv. 



HENRICI (Q.)The Theory of Screws. Nature, xlii. 127-132. London, 1890. 



Under the form of a review of the work of Gravelius (see p. 531) we have here 

 an original and suggestive discussion of the entire subject. Professor Henrici has 

 pointed out several promising lines along which new departures might be taken in 

 the further development of the present theory. 



KUPPER (C.) Die Schraubenbewegung, das Nullsystem und der lineare Complex. 

 Monatshefte fur Mathematik und Physik. Vienna, 1890, pp. 95-104. 



In this the theory of the linear complex has been developed from the Theory of 

 Screws. The object appears to have been to introduce the study of the subject 

 into the High Schools in Germany. 



