Minutes of Proceedings. 115 



Members of tlie Academy. It is not, however, for those more popular 

 results of Dr. Ball's labours that the Council have on this occasion 

 showed their sense of his merits as an original thinker and discoverer 

 in Science, but for work of a more recondite character, the nature of 

 which is much less capable of popular description, but the value and 

 importance of which has been abundantly vouched for by the suffrages 

 of eminent mathematicians throughout Europe. I refer to the series 

 of Memoirs published partly in our Transactions, and partly in those of 

 the Royal Society of London, and finally completed and published in a 

 separate and independent form in his work on the Theory of Screws, 

 a Study of the Dynamics of a Rigid Body. 



In this remarkable work, which is based mainly on the appli- 

 cation of the principles of the new linear geometry, which we owe to 

 the labours of Poinsot, of Pliicker, and of Chasles, Dr. Ball studies 

 the kinematics, equilibrium and small oscillations of a rigid body. 

 The direct problem to be dealt with may be thus stated : — To deter- 

 mine at any instant the position of a rigid body subjected to certain 

 constraints, and acted on by certain forces. Adopting one position of 

 the body as a standard of reference, a complete solution of the pro- 

 blem must provide us with the means of deriving the position at any 

 subsequent epoch from the standard position. Then arises the inquiry 

 into the most natural method of specifying one position of a body with 

 respect to another. It had been established by Poinsot that a force 

 and a couple perpendicular to the force constitute what may be called 

 the canonical form of a system of forces applied to a rigid body, and 

 it was discovered by Chasles that the canonical form of the displace- 

 ment of a rigid body consists of a rotation about an axis combined 

 with a translation parallel to that axis. We can thus, in the method 

 used by Dr. Ball, have a movement prescribed by which the body can 

 be brought from the standard position to the sought position ; a certain 

 axis can be found, such that if the body be rotated around this axis 

 through a certain angle, and translated parallel to the axis for a cer- 

 tain distance, the desired movement will be effected. 



It will simplify the conception of the movement to suppose that 

 at each epoch of the interval of time occupied by the operation for 

 producing the change of position, the angle of rotation bears to the 

 final angle of rotation the same ratio which the corresponding trans- 

 lation bears to the final translation. Under these circumstances the 



