APPENDIX II. 501 



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

 called the pitch. The screw has for us a dual aspect of much significance. No 

 small movement of the body is conceivable which does not consist of a twist 

 about a screw. No set of forces could be applied to the body which were not 

 equivalent to a wrench upon a screw. Everyone remembers the two celebrated 

 rules that forces are compounded like rotations and that couples are compounded 

 like translations. These may now be replaced by the single but far more com 

 pendious rule which asserts that wrenches and twists are to be compounded by 

 identical laws. Would you unite geometry with generality in your dynamics ? 

 It is by screws that you are enabled to do so. 



These ideas were rather too abstract for Cartesian, who remarked that, as 

 D Alembert s principle provided for everything in dynamics, screws could not be 

 needed. Mr Querulous sought to confirm him by saying that he did not see how 

 screws helped the study either of Foucault s Pendulum or of the Precession of the 

 Equinoxes. 



Such absurd observations kindled the intellectuaPwrath of One-to-One, who 

 rose and said, In the development of the natural philosopher two epochs may be 

 noted. At the first he becomes aware that problems exist. At the second he 

 discovers their solution. Querulous has not yet reached the first epoch ; he cannot 

 even conceive those problems which the &quot; Theory of Screws &quot; proposes to solve. 

 I may, however, inform him that the &quot;Theory of Screws&quot; is not a general dynami 

 cal calculus. It is the discussion of a particular class of dynamical problems 

 which do not admit of any other enunciation except that which the theory itself 

 provides. Let us hope that ere our labours have ended Mr Querulous may obtain 

 some glimmering of the subject. The chairman happily assuaged matters. We 

 must pardon, he said, the vigorous language of our friend Mr One-to-One. His 

 faith in geometry is boundless in fact he is said to believe that the only real 

 existence in the universe is anharmonic ratio. 



It was thus obvious that screws were indispensable alike for the application 

 of the forces and for the observation of the movements. Special measuring 

 instruments were devised by which the positions arid pitches of the various 

 screws could be carefully ascertained. All being ready the first experiment was 

 commenced. 



A screw was chosen quite at random, and a great impulsive wrench was ad 

 ministered thereon. In the infinite majority of cases this would start the body 

 into activity, and it would commence to move in the only manner possible i.e. it 

 would begin to twist about some screw. It happened, however, that this first 

 experiment was unsuccessful ; the impulsive wrench failed to operate, or at all 

 events the body did not stir. I told you it would not do, shouted Querulous, 

 though he instantly subsided when One-to-One glanced at him. 



Much may often be learned from an experiment which fails, and the chairman 

 sagaciously accounted for the failure, and in doing so directed the attention 

 of the committee to an important branch of the subject. The mishap was 

 due, he thought, to some reaction of the constraints which had neutralised the 

 effect of the wrench. He believed it would save time in their future investi- 



