Sept. I, 1887] 



NA 1 URE 



429 



oth in position and in pitch, the body was displaced by a twist 

 bout this screw and was then released. As the forces were 

 ncompensated, the body of course commenced to move, but the 

 scillations were of unparalleled simplicity. With the regularity 

 f a pendulum the body twisted to and fro on this screw, just as 

 ■ it were actually constrained to this motion alone. The com- 

 littee were delighted to witness a vibration so graceful, and, 

 ;membering the complex nature of the ordinary oscillations, 

 ley appealed to Mr. Anharmonic for an explanation. This he 

 ladly gave, not by means of complex formulae, but by a line of 

 ?asoning that was highly commended by Mr. Commo.isense, 

 nd such that even Mr. Querulous could understand. 



" This pretty movement,'" said Mr. Anharmonic, "is due to 

 [le nature of the screw a^. Had I chosen any screw at random, 

 [le oscillations would, as we have seen, be of a very complex 

 ype ; for the displacement will always evoke an uncompensated 

 trench, in consequence of which the body will commence to move 

 y twisting about the instantaneous screw corresponding to that 

 /rench ; and of course this instantaneous screw will usually be 

 uite different from the screw about which the displacement was 

 lade. But you will observe that a.^ has been chosen as a screw 

 1 the instantaneous system, corresponding to one of the double 

 crews in the and ^ systems. When the body is twisted about 

 1 a wrench is evoked on the double screw, but as Oj is itself the 

 istantaneous screw, corresponding to the double screw, the only 

 ffect of the wrench will be to make the body twist about a,, 

 'hus we see that the body will twist to and fro on aj for ever, 

 "inally, we can show that the most elaborate oscillations the 

 ody can possibly have may be produced by compounding the 

 imple vibrations on these screws aj, a.„ &c." 



Great enlightenment was now diffused over the committee, 

 nd even Mr. Querulous began to think there must be something 

 ii it. Cordial unanimity prevailed among the meaibers, and it 

 I'as appropriately suggested that the screws of simple vibra- 

 'on should be called kannojiic screzus. This view was adopted 

 ly the chairman, who said he thought he had seen a similar 

 Ixpression in " Thomson and Tait.'' 



The final meeting showed that real dynamical enthusiasm had 



lean kindled in the committee. Vistas of great mathematical 



leories were opened out in many directions. One member 



lowed how the theory of screws could be applied not merely to 



ttitvrle rigid body but to any mechanical system whatever. He 



cd a geometrical conception of what he was pleased to call 



■-chain, by which he said he could so bind even the most 



liaborate system of rigid bodies that they would be compelled 



it conform to the theory of screws. Nay, soaring still further 



.\\io the empyrean, he showed that all the instantaneous motions 



every molecule in the universe were only a twist about one 



■raw-chain while all the forces of the universe were but a wrench 



; 3on another. 



Mr. One-to-One expounded the " Ausdehnungslehre," and 



lowed that the theory of screws was closely related to parts of 



rassman's great work ; while Mr. Anharmonic told how 



liicker, in his celebrated " Ncue Geometric des Raumes," had 



Ivanced some distance towards the theory of screws, but still 



id never touched it. 



The climax of mathematical eloquence was attained in the 



leech of Mr. Querulous, who, with new-born enthusiism, 



iunched into appalling speculations. He had evidently been 



ading his " Cayley," and had become conscious of the poverty 



metrical conception arising from our unfortunate residence 



ace of an arbitrary and unsymmetrical description. 



hree dimensions," he said, "may perhaps be enough for 



lligent geometer. He may get on fairly well without a 



i'.nensioned space, but he does most heartily remonstrate 



I a flat infinity. Think of infinity," he cries, "as it 

 i be, perhaps even as it is. Talk not of your scanty 

 it line at infinity and your miserable pair of circular points. 



. assert that infinity is an ample quadric, and not the mere 

 )f one; and then geometry will become what geometry 

 to be. Then will every twist resolve itself into a right 

 and a left vector, as the genius of Clifford proved. Then 

 iie 'theory of screws' shed away some few adhering 

 aities, and fully develop its shapely proportio is. Then 

 — " But here the chairman said he feared the dis- 



II was beginning to enter radier wide ground. For his 

 he was content with the results of the experiments, 

 though they had been conducted in the vapid old space of 



He reminded them that their labours were now com- I 

 !, for they had ascertained everything relating to the rigid 



body which had been committed 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." 



NOTES. 

 At a public meeting held on Tuesday in Newcastle, under the 

 presidency of the Mayor, Sir B. L. Brown, it was finally decided,, 

 on the motion of the Sheriff, Alderman W. H. Stephenson, 

 seconded by Prof. Phili'pson, head of the medical staff at the Royal 

 Infirmary, that a cordial invitation should be sent to the British 

 Association to hold their annual meeting in Newcastle in 1889. 

 It was stated that the necessary amount to cover expenses would 

 be ^^4000, and of this ^1700 had been already subscribed. 



The New York meeting of the American Association for the 

 Advancement of Science seems to have been very successful, 

 although the attendance was not so large as had been expected. 

 The next meeting will be held in Cleveland, O. An invitation 

 from Toronto came just too late. The following are the officers 

 for the next meeting : — President, J. W, Powell, of Washing- 

 ton ; Vice-Presidents, Ormond Stone, of the University of 

 Virginia, (Mathematics and Astronomy), A. A. Michelson, of 

 Cleveland, (Physics), C. E. Munroe, of Newport, (Chemistry), 

 Calvin M. Woodward, of St. Louis, (Mechanical Science), George 

 H. Cook, of New Brunswick, (Geology and Geography), C. V. 

 Riley, of Washington, (Biology), C. C. Abbot, of Trenton, (An- 

 thropology), C. W. Smiley, of Washington, (Economic Science 

 and Statistics) ; Permanent Secretary, F. W. Putnam, of Cam- 

 bridge, '(office, Salem, Mass.) ; General Secretary, J. C. Arthur, 

 of La Fayette; Secretary of the Council, C. Leo Mees, of Athens ; 

 Secretaries of the Sections, C. L. Doolittle, of Bethlehem, 

 (Mathematics and Astronomy), A. L. Kimball, of Baltimore, 

 (Physics), William L. Dudley, of Nashville, (Chemistry), Arthur 

 Beardsley, of Swarthmore, (Mechanical Science), George H. 

 Williams, of Baltimore, (Geology and Geography), N. L. Britton, 

 of New York, (Biology), Frank Baker, of Washington, (Anthro- 

 pology), Charles S. Hill, of Washington, (Economic Science and 

 Statistics). 



The twenty-fourth annual meeting of the British Pharma- 

 ceutical Conference was opened on Tuesday in the Chemical 

 Theatre of Owens College, Manchester. There was a large 

 attendance of members of the Association. Mr. S. R. Atkins, 

 of Salisbury, occupied the chair, and in his presidential address 

 invited the attention of the Conference to "a brief review of 

 the Victorian era as it more especially affected themselves as 

 pharmacists." 



The International Astronomical Congress met at Kiel on 

 Monday, in the large hall of the University, under the presidency 

 of Privy Councillor Dr. Auwers, of Berlin. There was a large 

 assembly of astronomers, including delegates from Austria, 

 France, Sweden and Norway, and America. The delegates 

 were received on behalf of the Government by Herr Steinmann, 

 Civil Governor of the province of Schleswig-Holstein, and on 

 the part of the University by the Rector, Prof. Harsen. Dr. 

 Auwers, in replying, thanked the Prussian Government for the 

 interest which it had manifested in the Congress. 



The Hygienic Congress, which will meet in Vienna next 

 month, will be attended by over 1400 delegates from all 

 countries. The programme includes excursions to the Kahlen- 

 berg, the Semmering, Buda-Pesth, and Abbazzia. 



The Academy of Aerostation of France has presented a 

 medal to M. Mendeleieff, in recognition of the pluck exhi- 

 bited by him at Klin on August 19, when he went up alone 



