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 empyrean, he showed that all the instantaneous 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 &quot; Theory of systems 

 of rays&quot; 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 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 



will 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. 



