62 



NA TV RE 



\_Nov. 1 8, iSSo 



regards the accuracy of the construction of these chrono- 

 graphs, the best criterion is to be found in the force tliat 

 is required to work them. We find that 7 foot-pounds 

 per hour drives the clock-work and pendulum; 7 foot- 

 pounds more drives the carriage as well ; and only 3 foot- 

 pounds more is wanted for the cylinder — 17 foot-pounds 

 per hour for the whole instrument. Considering the 

 resistance of the carriage, the resistance of the glycerine, 

 and the weight of the cylinder, we think the result as 

 surprising as it is satisfactory. 



THE BELGIAN ENTOMOLOGICAL SOCIETY 



IN April, 1855, a circular with ten signatures was ad- 

 dressed to entomologists residing in Belgium, pro- 

 posuig the formation of a National Entomological Society, 

 the students of Insecta and allies having at that time no 

 organisation, no central meeting-place for interchange of 

 ideas, no special medium in which to publish the results 

 of their researches. The proposal was met by cordial 

 approval, and the first volume of the A/males of the 

 newly-formed Society, published in 1S57, indicated a 

 strength of forty-seven effective and four honorary mem- 

 bers, w-ith Baron de Selys-Longchamps as president. At 

 first its publications were occupied almost entirely by sub- 

 jects concerning the Belgian fauna, the volumes were thin, 

 and each represented the work of more than one year. 

 The Society was however well grounded, and notwithstand- 

 ing occasional short periods of depression, it gradually in- 

 creased in the number of its members, in the wideness of 

 the scope of the papers read at its meetings, and in repu- 

 tation as one of the leading entomological societies. 

 Naturally the size of the volumes of the Annales, and the 

 frequency of their appearance, also increased, and now 

 the Society produces a volume each year that no similar 

 society need be ashamed of The twenty-second volume 

 appeared in 1879, showing that the weakness inherent on 

 infancy was soon overcome. The list in this volume 

 shows a total of 171 effective ISIembers (including many 

 foreigners, of whom, however, only six are our own 

 countrymen), twelve Honorary Members (including Messrs. 

 Stainton and Westwood), with the addition of Corre- 

 sponding and Associate INIcmbers. It had also at that 

 time acquired the distinction of being recognised by the 

 State and of receiving a certain amount of State aid. 



On October 18, iSSo, the Society celebrated its twenty- 

 fifth anniversary, rejoicing in the attainment of more than 

 its majority, on which occasion the present President 

 (M. Weinmann) read a short congratulatory address, and 

 the indefatigable secretary (M. Preudhomme de Borre, to 

 whom the Society owes much of its recent success) gave 

 an instructive sketch of the history and progress of the 

 Society. On that occasion an especial honour was be- 

 stowed upon its first president. Baron de Selys-Long- 

 champs (recently elected President of the Belgian Senate\ 

 by conferring upon him (in spite of his protestations) the 

 title of Honorary President, a graceful tribute to one who 

 for so long had continually used his energies, his social 

 and scientific position, and his purse in furthering its 

 interests. 



Even apart from purely scientific considerations, the 

 history of Belgium is so indissolubly mixed up with our 

 own, and the feeling of fraternity so close, that all students 

 of entomology in this country cannot but reciprocate the 

 mutual congratulations that passed on this occasion 

 between the native members ; and the hearty and un- 

 affected demonstrations of friendship accorded to our 

 own entomologists who have attended the ineetings of 

 the Society show how warmly they welcome those of the 

 foreign members who occasionally visit Brussels. The 

 ineetings are held in a room in the Royal Natural History 

 Museum, in which is the library, and in connection with 

 the entomological collection of the Museum. The annual 

 subscription is small, and entitles the members to receive 



all the publications, including elaborate separate reports 

 of the proceedings at the monthly meetings. We hope 

 soon to see Englishmen figuring far more numerously in 

 the lists of members. R. McL. 



A GENERAL THEOREM IN KINEMATICS 

 'T'HE following theorem with regard to the motion of a 

 -*■ rigid body will doubtless be interesting to mathe- 

 matical physicists : — 



In all cases of the motion, parallel to one plane, of a 

 rigid body there is at every instant a point, /, of no 

 acceleration, in the plane of motion ; the acceleration of 

 every point, P, in the plane is in magnitude directly pro- 

 portional to the distance, yP; and its direction makes 

 with J P a.n angle which, though varying with the time, 

 is at any instant the same for all points in the body. 



If u is the angular velocity of the body at any instant 

 and to the angular acceleration, the angle between y/" and 

 the direction of acceleration of P is 



We have therefore in all cases of uniplanar motion of 

 a solid body an instatitatieoiis acceleration ceiiirc, which 

 is analogous to the ordinary instantaneous [velocity] 

 centre. 



Of course the ordinary equation 

 /cl = Z, 

 which holds for motion round an axis fixed in space and 

 in the body, and which expresses that the moment of the 

 external forces about the axis is equal to the moment of 

 the forces of inertia, holds also for the instantaneous 

 acceleration centre. 



As a particular case, whenever a solid moves with 

 constant angular velocity, the accelerations are all directed 

 towards the same point at any instant, and it follows that 

 the resultant stress e.xerted over the surface of any little 

 lutnp of the matter is a force directed to this point, if no 

 continuous forces act. 



This centre can be in any case geometrically constructed 

 by a rule analogous to that for the ordinary instantaneous 

 centre. 



When I had hit upon this theorem I mentioned it to 

 Prof. Wolstenholme, who at once looked out for its 

 extension to three dimensional motion. The result is 

 very simple. 



In all cases of the motion of a solid body there is at 

 every instant a point, /, of no acceleration ; and if at / 

 there be drawn two axes, J A and J B, which are those 

 respectively round which the resultant angular velocity, 

 10, and the resultant angular acceleration, a>, take place, 

 the acceleration of any point, P, is compounded of two — 

 one along the perpendicular, /, from P on J A, and the 

 other perpendicular to / B and to the perpendicular, q, 

 from P onJB, these two components being, respectively, 

 aflp and wg. 

 It seems surprising that such a simple and general 

 property of the motion of a rigid body should not have 

 been well known long ago. George M. Minchin 



Royal Indian Engineering College, 

 Cooper's Hill, November 6 



NOTES 



The awards of medals for the present year made by the 

 President and Council of the Royal Society are as follows :— The 

 Copl y Medal to Prof. James Joseph Sylvester, F.K.S., for his 

 long-continued investigations and discoveries in mathematics ; a 

 Royal Medal to Prof. Joseph Lister, F.R.S., for his contribu- 

 tions on various physiological and biological subjects published 

 in the Philosophical Tratisaclioits and Fivcccdiiigs of the Royal 



