312 



'SCIENCE. 



[N. S. Vol. XXII. No. 558. 



elongation, torsion. Eind the law of force 

 and displacement, stress and strain. 



ProMem. — iind mathematical expressions 

 for the motion of a free particle under such 

 a law of force. 



Take ee' as the path, with center c. Let 

 h equal the acceleration at unit distance from 

 c; and let the acceleration at any point in the 

 path be directed toward c and vary as the dis- 

 tance from c. 



ce = a, amplitude. 



eJc = a.h 



cp^x, a variable, displacement. 



then 



2a.rt./i = work from e to c. 



ia;— fl./t = work from p to c. 

 a 



'— = work irom e to p. 



2 



=^ 14 V^, velocity squared, if work was 



done on unit mass.^ 



To construct this geomerically and deter- 

 mine the constant a\/h. 



For any point, p, with cq = a, construct 

 pcq, by bringing q into the perpendicular 

 from p. 



Take gr perpendicular to cq, = a\/h on 

 some scale (which need not be known). 



On qr make the right triangle qsr, r^=6- 



Then qs =^ a\/h sin 6 = velocity at p in 

 the simple harmonic motion. 



Let T = the period, the time of a complete 

 vibration, from e to e' and back to e; and let 

 t = any portion of time. 



If cq is given a uniform angular velocity 

 '^itt/T, that is, B is made to vary uniformly 

 with time, the component of g's motion par- 

 allel to p's path will at every instant equal 

 the motion of p. The linear velocity of q, 

 '2nra/T, is equal to the constant a\/}i. is at 



^ Unit mass was taken to simplify work in 

 getting the form of the equations. The relation 

 of mass to simple harmonic motion should be 

 determined and put in the formulae. Though 

 only two or three of the text-books under consider- 

 ation make any allusion, even, to mass. 



any instant (reckoning time from leaving e) 

 equal to 2Trt/T. 



Hence, for velocity at point, p, in simple 

 harmonic motion. 



27ra . 2TTt 



—=r sm —=- . 



T T 



From this the equation for acceleration can 

 be obtained. Phase and epoch can be defined 

 and introduced into the equations. 



I. Thornton Osmond. 



THE BRITISH. ASSOGIATIOW AND AFFILI- 

 ATED AND OORRESPONDING SOCIETIES. 



The report of the council of the British 

 Association presented at the South African 

 meeting the following resolution, from the 

 conference of delegates, was referred to the 

 council by the general committee for con- 

 sideration and action, if desirable : 



(i.) That a committee be appointed, consisting 

 of members of the council of the association, to- 

 gether with representatives of the corresponding 

 societies, to consider the present relation between 

 the British Association and local scientific so- 

 cieties. 



(ii.) That the committee be empowered to make 

 suggestions to the council with a view to the 

 greater utilization of the connection between the 

 association and the affiliated societies, and the ex- 

 tension of affiliation to other societies who are at 

 present excluded under regulation 1. 



This resolution, having been referred to a 

 committee, consisting of Dr. E. H. Griffiths, 

 Sir Norman Lockyer, Professor Meldola, M.v. 

 F. W. Kudler, Mr, W. Whitaker and the gen- 

 eral ofiicers, to consider and report thereon to 

 the council, the committee made the following 

 recommendations : 



I. ( i ) " That any society which undertakes local 

 scientific investigation and publishes the results 

 may become a society affiliated to the British 

 Association. 



(ii.) "That the delegates of such societies shall 

 be members of the general committee. 



(iii.) "That any society formed for the purpose 

 of encouraging the study of science, which has 

 existed for three years and numbers not fewer 

 that fifty members, may become a society asso- 

 ciated with the British Association. 



