500 THE THEORY OF SCREWS. 



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 more thorough method of specify 

 ing the freedom of the body was inconceivable. 



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

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

 dynamical work. Force was now 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 1 ? said one of the committee. Send for Mr Cartesian, said 

 the chairman, we will give him another trial. Mr 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 couple 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 

 generality 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 he approached the rigid body. Helix com 

 menced by clearing away Cartesian 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, admin 

 ister 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 momentthat is, by the product 

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

 force and couple into the single conception of a wrench 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 



