BIBLIOGRAPHICAL NOTES. 535 



In this paper also the notion of chiastic homography is introduced. The 

 characteristic feature of chiastic homography is, that every three pairs of corre 

 spondents a, &amp;gt;/ ; /3, E, ; y, , fulfil the relation 



The homography of impulsive and instantaneous systems is chiastic, and the 

 relation has other physical applications. The substance of this paper has been 

 reproduced in Chaps, xx. and xxi. of the present volume. 



APPELL (B.) Sur le Cylindro ide. Revue de mathematiques speciales, 5th year, 

 1895, pp. 129, 130. 



It had been shown in the Theory of Screws, 1876, that the projections of any 

 point on the generators of a cylindroid form an ellipse. Appell has here shown 

 conversely that if the projections of a point on the generators of a conoidal surface 

 lie on a plane curve, then the conoid can be no other than a cylindroid. ROUBADI 

 (C.), pp. 181183 of the same volume, gives some further geometrical investigations 

 about the cylindroid. 



We may now enunciate a theorem still more general, that if the projections of 

 every point on the generators of a ruled surface other than a cylinder are to form 

 a plane curve then that curve must be an ellipse and the ruled surface must be 

 the cylindroid (see p. 20). 



BALL (R. S.) Further Development of the Relations between Impulsive, Screws 

 and Instantaneous Screws. Eleventh Memoir. Transactions of the Royal 

 Irish Academy, Vol. xxxi., pp. 99-144 (1896). 



It is shown that when 77 is the impulsive screw and a the instantaneous screw, 

 the kinetic energy of the mass M twisting about a with a twist velocity a is 



J/a 3 



cos (arj) aq 

 The twist velocity acquired by a given impulse is proportional to 



cos 



Pa 



There is a second general relation, besides that proved in the last Memoir, 

 between two pairs of impulsive screws t], , and their corresponding instantaneous 

 screws a, (3 for a free rigid body. 



This relation is as follows 



r cos 



. 



cos (aaj) cos 



The following theorem is also proved. 



If two cylindroids be given there is, in general, one, and only one, possible 

 correlation of the screws on the two surfaces, such that a rigid body could be 

 constructed for which the screws on one cylindroid would be the impulsive screws, 

 and their correspondents on the other cylindroid the instantaneous screws. 



KOTELNIKOF (A. P.) Screws and Complex Numbers. Address delivered 5th May, 

 1896. Printed (in Russian) by order of the Physical Mathematical Society 

 in the University of Kazan. 



After an introduction relating to the place of the Theory of Screws in 



