40 
DR. R. S. BALL ON THE DYNAMICS OE A RIGID BODY. 
complexes is A sin q>-\-(7c-\-7c') cos <p. If this invariant vanish, the two complexes are 
in “ involution.” The physical interpretation of this expression is found in what we 
have called the virtual coefficient of a pair of screws of which the pitches are 7c, 7c', the 
perpendicular distance A, and the angle sr— < p. If the virtual coefficient vanish, the 
screws are reciprocal. 
Dr. Klein (Math. Ann. Band ii. p. 204) has introduced the conception of six funda- 
mental complexes, each pair of which are in involution. If the principal axes of the 
six complexes be regarded as screws of which the parameters of the corresponding com- 
plexes are the pitches, then these six screws will form what has been termed a coreci- 
procal group in the present paper. 
In this postscript the writer’s desire has been twofold. First to do justice to those 
authors from whose works he had found, after he had written these papers, what ought 
to have been ascertained before, namely, that in a few points he had merely rediscovered 
(though usually from a different point of view) what was already known. Second, to 
point out the intimate connexion which exists between the physical conceptions of the 
Theory of Screws and the modern geometrical speculations on the linear complex. 
