TEANSACTIONS OF SECTION A. 



579 



lliat double screw, tbe only effect of the wrench will be to make the body twist 

 :about a^. Thus we see that the body will twist to and fi-o on a^ for ever; precisely 

 similar statements could have been made about a.,, a.^, &c., corresponding to the 

 other double screws. Finally, we can show that the most elaborate oscillations the 

 body can possibly have may be produced by compounding the simple vibrations on 

 the screws a,, a„, &c.' 



Great enlightenment was now diffused over the committee, and even Mr. 

 Querulous began to think there must be something in it. Cordial unanimity 

 prevailed among the members, and it was appropriately suggested that the screws 

 of simple vibration should be called harmonic so-ews. This view was adopted by 

 the chairman, who said he thought he had seen a similar expression in 'Thomson 



and Tait.' , . ,, , 



The final meeting showed that real dynamical enthusiasm had been kmdled 

 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-cfiatn, 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. Oue-to-One expounded the ' Ausdehnungslehre ' and showed that the theory 

 of screws was closely related to parts of Grassman's great work; while Mr. 

 Anharmonic told how Pliicker, in his celebrated ' Neue Geometrie des Raumes,' 

 had advanced some distance towards the theory of screws, but still had never 

 touched it. 



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 ' Oayley ' 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, J as it should 

 be, perhaps even as it is. Talk not of your scanty straight line as 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 (Jlifibrd proved. Then will the theory of screws_ shed away 

 some few adhering deformities and fully develop its shapely proportions. Then 



-will ' But here the chairman said' he feared the discussion was beginning 



to enter rather wide ground. 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 labours were now completed, for they 

 had ascertained everything relating to tbe rigid body Avhich had been com- 

 mitted to them. He hoped they would agree with him that the inquiry 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.' 



The following Reports and Papers were read : — 



1. Third Report of the Gommittee fnr promoting Tidal Ohservations in 

 ICanada. — See Reports, p. 31. 



p p 2 



