A Treatise on the Theory of Screws

APPENDIX II. 509 mity prevailed among the members, and it was appropriately suggested that the screws of simple vibration should be called harmonic screws. This view was adopted by the chairman, who said he thought he had seen the word harmonic used in ‘ Thomson and Tait.’ The final meeting showed that real dynamical enthusiasm had been kindled in the committee. Vistas of great mathematical theories were opened out in many directions. One member showed how the theory of screws could be applied not merely to a single rigid body but to any mechanical system whatever. He sketched a geometrical conception of what he was pleased to call a screw-chain, by which he said he could so bind even the most elaborate system of rigid bodies that they would be compelled to conform to the theory of screws. Nay, soaring still further into the enipyrejin, he sliowocl that till the iiist<iiit<ineous motions of every molecule in the universe were only a twist about one screw-chain while all the forces of the universe were but a wrench upon another. Mr One-to-One expounded the ‘Ausdehnungslehre’ and showed that the theory of screws was closely related to parts of Grassmann’s great work; while Mr Anharmonic told how Sir W. R. Hamilton, in his celebrated “ Theory of systems of rays” had by his discovery of the cylindroid helped to lay the foundations of the Theory of Screws. The climax of mathematical eloquence was attained in the speech of Mr Querulous, who, with newborn enthusiasm, launched into appalling speculations. He had evidently been reading his 1 Cayley ’ and had become conscious of the poverty of geometrical conception arising from our unfortunate residence in a space of an arbitrary and unsymmetrical description. ‘ Three dimensions,’ he said, ‘may perhaps be enough for an intelligent geometer. He may get on fairly well without a four dimensioned space, but he does most heartily remonstrate against a flat infinity. Think of infinity,’ he cries, ‘as it should be, perhaps even as it is. Talk not of your scanty straight line at infinity and your miserable pair of circular points. Boldly assert that infinity is an ample quadric, and not the mere ghost of one; and then geometry will become what geometry ought to be. Then will every twist resolve into a right vector and a left vector, as the genius of Clifford proved. Then will the theory of screws shed away some few adhering incongruities and fully develop its shapely proportions. Then wjll_____’ But here the chairman said he feared the discussion was beginning to wax somewhat transcendental. For his part he was content with the results of the experiments even though they had been conducted in the vapid old space of Euclid. He reminded them that their functions had now concluded, for they had ascertained everything relating to the rigid body which had been com- mitted to them. He hoped they would agree with him that the enquiry had been an instructive one. They had been engaged in the study of Nature, they had approached the problems in the true philosophical spirit, and the rewards they had obtained proved that ‘ Nature never did betray The heart that truly loved her.’