552 
Proceedings of the Royal Irish Academy. 
above recited facts, I waited to report further on the structure and 
life history of Hyalonema, until I would have the benefit of Professor 
"Wyville Thomson's then expected memoir on the subject. Engaged now 
in exploring the deeply seated beds of the oceans of the globe, he is 
not likely for years to come to have time or leisure to return to this 
subject. When he does, doubtless, the results of his great experience 
will totally eclipse all that has hitherto been done in reference to the 
vitreous sponges. In the meanwhile the publication of this brief 
Eeport is called for by the Academy, and it may help to make good 
a series of facts now indeed but little disputed, and some of which 
have since been so well established that one is apt to forget how very 
long they were held in the category of very doubtful statements. 
LII. — ScEEW Coordinates and their Applications to Problems on 
THE Dynamics or a Higid Body. Ey Kobert Stawell Ball, 
LL. D., E. B. S. (Abstract). 
[Read, January 12, 1874], 
Screw coordinates are an adaptation to physical purposes of Dr. Felix 
Klein's"^' coordinates of a linear complex referred to six fundamental 
complexes of which each pair are in involution. 
The present paper is an application of screw coordinates to the de- 
velopment of the theory of screws, f 
The word Dyname is employed (Pluecker, IS'eue Geometric des 
Raumes, p. 24) as a generic term to include what in the language 
of the present theory are severally known as wrenches, twists, or twist 
velocities. 
If a dyname of one unit about a screw a be decomposed into com- 
ponents &c. ag, about six coreciprocal screws, then the six quantities 
&c., oe are the coordinates of a. 
If Si, &c., 56 he the pitches of the six coreciprocal screws of reference, 
then the pitch of a is 
For kinetic purposes the group of coreciprocals which are most natural, 
are the six principal screws of inertia. 
If a free and quiescent rigid body receive an impulsive wrench 
about a principal screw of inertia, then the body commences to twist 
about the same screw. 
* Mathematische Annalen, Band ii., p. 204. 
t Transactions of the Royal Irish Academy, vol. xxv., pp. (157-217), Philosophi- 
cal Transactions, 1874. 
