572 EEPOET — 1887. 



A single step remained to complete the examiuation of the freedom of the body. 

 Mr. Helix continued his experiments and presently detected a third screw, about 

 which the body can also twist in addition to those on the cylindroid. A flood of 

 geometrical light then burst forth and illuminated the whole theory. It appeared 

 that the body was free to twist about ranks upon ranks of screws all beautifully 

 arranged by their pitches on a system of hyperboloids. After a brief conference 

 with Anharmonic and One-to-One, Helix announced that sufficient experiments of 

 this kind had now been made. By the single screw, the cylindroid, and the family 

 of hyperboloids, every conceivable information about the mobility of the rigid 

 body can be adequately conveyed. Let the body have any constraints, how- 

 soever elaborate, yet the definite geometrical conceptions just stated will be 

 sufficient. 



With perfect lucidity Mr. Helix expounded the matter to the committee. He 

 exhibited to them an elegant fabric of screws, each with its appropriate pitch, and 

 then he summarised his labours by saying, ' About every one of these screws you 

 can displace the body by twisting, and, what is of no less importance, it will not 

 admit of any movement which is not such a twist.' The committee expressed their 

 satisfaction with this information. It was both clear and complete. Indeed, the 

 chairman remarked with considerable force that a mure thorouyh method of specify- 

 ing the freedom of the body xvas inconceivable. 



The discovery of the mobility of the hofLj completed the first stage of the 

 labours of the committee, and they were ready to commence the serious 

 dynamical work. Force was no>v to be used, with the view of experimenting on 

 the behaviour of the body under its influence. Elated by their previous success the 

 committee declared that they would not rest satisfied until they had again obtained 

 the most perfect solution of the most general problem. 



' But what is force ? ' said one of the committee. ' Send for Mr. Cartesian,' said 

 the chairman, 'we will give him another trial.' Mx-. Cartesian was accordingly 

 requested to devise an engine of the most ferocious description wherewith to attack 

 the rigid body. He was promptly ready with a scheme, the weapons being drawn 

 from his trusty but old-fashioned armoury. He would erect three rectangular axes, 

 he would administer a tremendous blow parallel to each of these axes, and then he 

 would simultaneously apply to the body a forcible coupb around each of them ; 

 this was the utmost he could do. 



' No doubt,' said the chairman, ' what you propose would be highly effective, 

 but, Mr. Cartesian, do you not think that while you still retained the perfect gene- 

 rality of your attack, you might simplify your specification of it? I confess that 

 these three blows all given at once at right angles to each other, and these 

 three couples which you propose to impart at the same time, rather confuse me. 

 There seems a want of unity somehow. In short, Mr. Cartesian, your scheme 

 does not create a distinct geometrical image in my mind. We gladly acknowledge 

 its suitability for numerical calculation, and we remember its famous achievements, 

 but it is utterly inadequate to the aspirations of this committee. We must look 

 elsewhere.' 



Again Mr. Helix stepped forward. He reminded the committee of the labours 

 of Mathematician Poinsot, and then lie approached the rigid body. Helix com- 

 menced by clearing away f.'artesian's arbitrary scaffolding of rectangular axes. 

 He showed how an attack of the most perfect generality could be delivered in a 

 form that admitted of concise and elegant description. ' I shall,' he said, ' administer 

 a blow upon the rigid body from some unexpected direction, and at the same 

 instant I shall apply a vigorous couple in a plane perpendicular to the line of the 

 blow. 



A happy inspiration here seized upon Mr. Anharmonic. He knew, of course, 

 that the efficiency of a couple is measured by its moment. — that is, by the pro- 

 duct of a force and a linear magnitude. He proposed, therefore, to weld Poinsot's 

 force and couple into the single conception of a xorench on a screw. The force 

 would be directed along the screw while the moment of the couple would equal 

 the product of the force and the pitch of the screw. ' A screw,' he said, ' is to be 

 regarded merely as a directed straight line with an associated linear magnitude 



