A Treatise on the Theory of Screws

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 intellectual wrath 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 “ Theory of Screws ” proposes to solve. I may, however, inform him that the “ Theory of Screws” 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 theoi'y 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 and 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-