Dec. 9, 1886] 



NA TURE 



143 



each to Mel.istomacece and Composita;. Of well-known Cape 

 types, Pc!arg,mium, Stocbe, Cineraria, and Bdinoitia are now 

 for the first time added to the Madagascar flora. The faint 

 affinity of the flora of Madagascar to that of India and Malaya 

 is strengthened by the di-covery of the genu; Cycica, and of new 

 species of Aly.xia, Didymocarptis, and Strjbilanthcs. Of types 

 of economic interest there are new species of Dalbergia, Macar- 

 an«a, Slrychiios, Balsainodendron, and Gctrciiiia. It seems that 

 during the last ten years between iioo and 1200 new plants from 

 Madagascar (29 of which are new genera) h.we been described 

 in the jfouriial of the l.innean Society and Journal of Botany, 

 nearly all of them collected by our own countrymen. 



Chemical Society, November iS. — W. Crookes, F.R.S., 

 Vice-President, in the chair.— The following papers were read ; 

 — Researches on the relation between the molecular structure of 

 carbon compounds and their absorption-spectra ; part 8, a study 

 of coloured substances and dyes, by \V. N. Hartley, F.R.S. — 

 Spectroscopic notes on the carbohydrates and albumenoids from 

 grain, by \V. N. Hartley, F.R.S. — Preliminary note on the 

 electrolysis of amnionic sulphate, by Herbert McLeod, F.R.S. 

 — The preparation and hydrolysis of hydrocvanides of the di- 

 ketones, by Francis R. Japp, F.R.S., and N. H.J. Miller, Ph.D. 

 — The action of salicylic aldehyde on sodium succinate in pre- 

 sence of acetic anhydride, by Gibson Dyson. — The reduction of 

 nitrites to hydroxylamine by hydrogen sulphide, by E. Divers, 

 F.R.S., and T. Haga. — Note on some double thiosulphates, by 

 J. li. Cohen, Ph.D. — Preliminary note on the action of triphenyl- 

 nielhyl bromide on ethyl sodio-malonate, by George G. Hender- 

 son, M.A., B. Sc, — Action of silicon tetrachloride on aromatic 

 amido-compounds, by Arthur Harden, B.Sc. 



Physical Society, November 27. — Prof. W. G. Adams in 

 the chair. — The following papers were read : — On a method of 

 measuring the coefficient of mutual induction of two coils, by 

 Prof. G. Carey Foster, F.R.S. The two coils are for conve- 

 nience designated by P and S (primary and secondary). The 

 method as originally devised consists of two parts : (l) observing 

 the swing of the needle of a galvanometer placed in series 

 with the secondaiy coil when a current of strength 7 is started 

 in the primary ; (2) placing the galvanometer and a condenser 

 of known capacity, <-, as a shunt between two points, A and B, 

 of the primary circuit, such that the first swing of the galvano- 

 meter needle on completing the primary is the same as in (i). 

 It is easily seen that under these conditions M = cn\, where J\l 

 is the coefficient to be determined, r = resistance between the 

 points A and B, and r^ = resistance of galvanometer and 

 secondary coil. The method requires the value of 7 to be the 

 saine in the two experiments, and facilities for varying r with- 

 out altering 7. To overcome these difficulties the arrangement 

 has been modified so as to make it a null method. The con- 

 nections remain the same as in (2), excepting that the ends of 

 the secondary coil are connected to the terminals of the galvano- 

 meter through a variable resistance with no self-induction. If 

 f be the resistance of the secondary coil and variable resistance 

 when adjusted, so that, on completing the primary circuit, the 

 integral current through the galvanometer is zero, it is shown 

 that .1/ = (-//-, where and ;• have the same meaning as before. 

 For let A and E be the potentials of the galvanometer terminals 

 at any time, /, i/ the resistance of galvanometer, y the current 

 through it, and TV^and Z the coefficients of self-induction of the 

 galvanometer and secondary coil re-pectively. Then consider- 

 ing the path from A to £ through the secondary coil we have — 



a'x dy 



A - E-px + L III—. 



dl St 



For path through galvanometer — 



dv 

 A - E =^ qy + N—. 

 dl 

 Equating these, and integrating from / = o to / = 00 , we get — 

 / / xdl - My = o. 



Since / xdt = charge of condenser, 

 J 



= <■>'•, 

 we see that M — cpr. 



It is easily shown that i( L = M then .-^ - .£ = o for all values 

 of /. Hence the galvanometer might in this case be replaced by 



a telephone. By inversion, the method could be used for de- 

 termining the capacity of condensers in absolute measure if M 

 be known. The author thinks the method will be useful for 

 dynamo-machines, and gave a series of numbers obtained by 

 experiments on different coils, showing that it gives consistent 

 results. Mr. C. V. Boys suggested that, by arranging a switch 

 to change the connections from (i) to {2) in rapid succession, a 

 steady deflection might be obtained, and thought that this would 

 enable very small coefficients to be determined. Remarks by 

 Prof. Forbes, Prof. Adams, and Prof. Perry were answered by 

 Prof. Foster and Dr. Fison. — On the critical mean curvature of 

 liquid surfaces of revolution, by Prof. A. W. Riicker, M.A., 

 F.R.S. The paper is chiefly mathematical, and deals with 

 liquid surfaces of revolution attached to two circular rings, the 

 planes of which are at right angles to the line joining their 

 centres. By '• mean curvature " the author designates half the 

 sum of the reciprocals of the two principal radii of cui-oature of 

 the surfaces. Maxwell has shown in his article on " Capillary 

 Action "(" Encycloptedia Britannica "), that, if the film be a 

 cylinder, a slight bulge will cause an increase or decrease in the 



mean curvature according as the length is < or > - times the 



diameter. If / = - d, then a small change in the volume of the 



surface will modify its form, but will not alter the mean curvature. 

 Thus the mean curvature of such a cylinder is evidently a maximum 

 or minimum with respect to that of other surfaces of constant 

 mean curvature, which pass through the same two rings at the 

 same distance apart, and which differ but little from the cylin- 

 drical form. Hence the cylinder may be said to have a critical 



mean cur 



vature when the distance between the rings is - times 



their diameter. If the distance between the rings is altered, a 

 similar property is possessed by some other surface. The 

 author's paper investigates the general relation between the 

 magnitude and distance apart of the rings, and the form of the 

 surfaces of critical curvature. If x is the axi- of revolution, 

 then the equation to a liquid surface of revolution is given by the 

 expressions — 



X = aE -^ &F, y" = a- coi-(p + ffhin'tp, 



where E and E ifre elliptic integrals of the first and .second 

 kinds respectively, of which the ampl itude i s 9, and the 

 modulus A" = ^/«- - $'-la as usual, A = ^ 1 - A'- sin- (f>, whence 

 )' = aA, and if A' = sin fl, then = a cos 6, and since a>B, 

 a and /3 are the maximum and minimum ordmates. The re-ults 

 show that as B increa-es from 0° to 90°, the surface of critical 

 mean curvature is an unduloid with limits of cylinder and ^phere, 

 when 9 = 0°, and e = 90° respectively. When 9 passes from 90° to 

 iSo", the surface is a nodoid with limits of sphere and a circle 

 whose plane is perpendicular to the surface of revolution. In 

 the third quadrant the surface is still a nodoid the limits of which 

 are a circle and the catenoid. Finally, in the fuurth quadrant 

 the surface is an undidoid, the limits being the catenoid and 

 cylinder. Experiments were shown proving that with cylindrical 



films, where /< - d, increase of internal pressure produced a 



bulging, whereas if / > - n', a bulging was produced by decrease 



2 

 of pressure. From this it is evident that if the interiors of two 



IT 



cylindrical films, whose /< -(/.be connected, stable equilibrium 

 2 



will result, whereas if / > - d, there will be unstable equilibiium. 



2 

 These facts were illustrated experimentally with great success. 

 After some remarks by Mr. C. V. Boys, the proceedings 

 terminated. 



Anthropological Institute, November 23. — Francis Gal'o % 

 F.R.S., President, in the chair. — The election of Mr. C. W. 

 Rosset as a Corresponding Member was announced. — Prof. A. 

 H. Keane read a paper, by Con ul Donald A. Cameron, on the 

 tribes of the Eastern Soudan. — The Assistant Secretary ex- 



