190 APPENDIX I. 



then \\U\ + . . . + A n 7 M = o also denotes a linear complex, pro- 

 vided that a certain condition is satisfied. This condition is 

 presented as a homogeneous function of the second degree in 

 A!, . . -. A w equated to zero. The discriminant of the function is 

 the invariant in question. 



BALL (R. S.) The Theory of Screws a geometrical study ofihe 

 kinematics, equilibrium, and small oscillations of a Rigid 

 Body. Transactions of the Royal Irish Academy, Vol. 

 xxv., pp. 137-217 (November 13, 1871). 



This is the original paper on the Theory of Screws. In 

 estimating how far the contents of this paper are novel, it is to 

 be remembered that the cylindroid had been discussed by 

 Pliicker two or three years previously, while the conception of 

 reciprocal screws had been announced by Klein a few months 

 before. Both these authors would, of course, have been re- 

 ferred to in this paper had I been acquainted with their works at 

 the time the paper was written. 



CLIFFORD (W. K.) On Biquaternions. Proceedings of the Lon- 

 don Mathematical Society, Nos. 64, 65, p. 382 (i2th 

 June, 1873). 



A Biquaternion is defined to be the ratio of two " motors." 

 A "motor" may be said to bear the same relation to the dyname 

 of Pliicker which a vector bears to a linear magnitude. The 

 Biquaternions are shown to be intimately associated with the 

 speculations of the geometry of elliptic space. See Klein's 

 wonderful paper, " Ueber die nicht Euclidische Geometric." 

 Math. Ann., Band IV., pp. 573-625. 



BALL (R. S.) Researches in the Dynamics of a Rigid Body by the 

 aid of the Theory of Screws (June 19, 1873). Philosophical 

 Transactions, pp. 15-40 (1874). 



The n principal screws of inertia belonging to a rigid body 

 which has freedom of the n ih order are here discussed. 



