224 



NATURE 



[February i6, 1922 



Societies and Academies. 



London. 

 Royal Society, February 9. — Sir Charles Sherrington, 

 president, in the chair. — Sir J. Alfred Ewing : The 

 atomic process in ferromagnetic induction. In the old 

 model representing the process of ferromagnetic in- 

 duction, the Weber elements or ultimate magnetic 

 particles were represented by pivoted magnets the 

 alignment of which, in the absence of an impressed 

 field, was determined by the forces which they exerted 

 on one another. The model is unsatisfactory ; when 

 the range of stable deflection is sufficiently narrow 

 the stability becomes too great. In the new model 

 the idea of magnetic control is retained, with a Weber 

 element in each atom, but the controlling force is 

 supposed to be exerted between the electrons of the 

 atom itself, namely, between the shell, which is held 

 more or less fixed by its relation to neighbouring 

 atoms, and an inner electron system which con- 

 stitutes the Weber magnet. The control depends on 

 the difference between two nearly equal opposing 

 forces ; this characteristic permits the model to com- 

 bine a sufficiently weak control with a narrow range 

 of stable deflection. In one model considered the 

 structure is based on the grouping of electrons sug- 

 gested by Hull in connection with his X-ray analysis 

 of iron crystals ; in another the electron orbits are 

 assumed to have the nucleus of the atom at their 

 common focus. — J. W. Nicholson: Problems relating 

 to a thin plane annulus. Only first approximations 

 of solutions of problems relating to a thin plane 

 annulus appear to have been used hitherto. Higher 

 approximations have now been obtained, and the 

 actual difference of radii of the circles bounding the 

 annulus is of comparatively small significance in such 

 magnitudes as the electrical capacity of the annulus. 

 The whole investigation is carried to the second order 

 of significance by treating the annulus as a special 

 case of the elliptic anchor ring, but it can be extended. 

 The convergence of such approximate solutions 

 appears to be analogous to the degree of convergence 

 found by Lord Rayleigh in certain solutions of 

 problems of vibration of discs in which eccentricity 

 is taken into account.— T. H. Havelock : The effect of 

 shallow water on wave resistance. An analysis of 

 the wave resistance of a surface pressure symmetrical 

 round a point and moving over the surface of deep 

 water is, extended so as to include the effect of finite 

 depth of water. The wave resistance is given by a 

 definite integral which is evaluated by numerical and 

 graphical methods. The cases intermediate between 

 deep water and shallow water show the effect of 

 limited depth in lowering the principal wave-making 

 velocity and in increasing the effects near the velocity 

 of the wave of translation. — R. H. Fowler and 

 C. N. H. Lock : The aerodynamics of a spinning shell. 

 Pt. 2. Of the shells fired from two guns giving 

 different degrees of axial spin, those fired from the 

 gun giving the more rapid spin were all stable, most 

 of the others being unstable, as shown by the larger 

 yaw developed. For yaws up to 35° a solution of the 

 equations of motion can still be obtained in elliptic 

 functions which proves adequately general. — F. B. 

 Pidduck : The kinetic theory of a special type of rigid 

 molecule. The methods of Chapman and Enskog in 

 the kinetic theory of gases are applied, with modi- 

 fications, to a type of rigid molecule to discover how 

 viscosity is affected by energy of rotation, and the 

 relative transport of translational and rotational 

 energy In thermal conduction. The molecule model 

 Is considered as a sphere which grips at each collision 

 arid rebounds without dissipation of energy. The 

 results support Eucken's views on Chapman's con- 

 NO. 2729, VOL. 109] 



stant / for polyatomic gases. — J. E. Jones : The velo- 

 city distribution function and the stresses in a non- 

 uniform rarefied monatomic gas. From Boltzmann's 

 equation a symbolic solution of the velocity distribu- 

 tion function is obtained ; from the new equation, by 

 an analogous treatment, the exact nature of the func- 

 tion is deduced. The rate of change of molecular 

 properties by collision follows more directly from this 

 equation than from that used by Maxwell, To illus- 

 trate the present method, the results obtained by 

 Chapman and Enskog for a normal gas are cal- 

 culated anew. The treatment is extended to a rarefied 

 gas and expressions are obtained for stresses due to 

 non-uniformity of temperature. The special Maxwellian 

 model Is considered and Maxwell's result confirmed. 

 The molecular model of a gas consisting of rigid 

 elastic spheres is then considered in detail. The 

 numerical coefficient in this case differs by about 

 20 per cent, from that of the Maxwellian gas.— H. 

 Bateman : The numerical solution of integral equations. 

 An approximate solution of an Integral equation of 

 Fredholm's type is obtained by using an approximate 

 representation of the kernel by means of a double 

 series of known functions. One such series Is 

 written down immediately In the form of a deter- 

 minant, and the solution of the integral equation with 

 the approximate kernel is also written in the 

 form of a determinant. The kernel of the integral 

 equation can also be represented approximately by a 

 polynomial.— W. B. Hardy and I^a Doubleday : 

 Boundary lubrication : The paraffin series. The lubri- 

 cating properties of normal paraffins and their related 

 acids and alcohols have been studied under the condi- 

 tions of boundary frictlorl. Amon ton's law, that fric- 

 tion varies as the loads and is independent of the 

 areas, is rigorously true for the same bearing surfaces 

 and lubricants. The friction is independent of the 

 quantity of lubricant present. It is a linear function 

 of molecular weight, so that /^ = friction -f load = a- bM, 

 where M is molecular weight and 6 a pure function 

 of chemical constitution ; the slope of the curve is 

 greatest for acids, and sensibly the same for 

 paraffins and alcohols. Changing from one acid to 

 another shifts the curves parallel to themselves, so for 

 the same chemical series a Is a pure function of the 

 nature of the solid faces. Each solid face contributes 

 one-half of a, and each molecule of lubricant fur- 

 nishes a constant quantity to the total effect indepen- 

 dently of the total number of molecules present. 



Aristotelian Society, January 16. — Dr. F. C. S. 



Schiller, president, In the chair.— H. J. Paton : Plato's 

 theory of flKaaia. In Plato's account of the Line and 

 the Cave in the " Republic " he distinguishes two sub- 

 divisions of opinion {fiKaaia, or intuition, and Triaris, or 

 belief) and two sub-divisions of knowledge (diavoia, or 

 mathematical reasoning, and voriais, or philosophical 

 reasoning). This must be understood as Implying a 

 difference of objects In each of the four sub-divisions, 

 just as the objects of opinion and knowledge are 

 different — the changing individuals as opposed to the 

 unchanging universals. The parallelism or analogy 

 between the objects of the two main divisions and 

 those of the sub-divisions is meant to be taken 

 seriously throughout. In particular, the objects of 

 the eiKaa-ia, or intuition, are the many appearances 

 whether given in what we call sense or memory or 

 Imagination, from which we pass to the objects of 

 nioTis, or belief— the solid bodies of the ordinary con- 

 sciousness and of science, things relatively permanent 

 and relatively intelligible In comparison with their many 

 appearances, although changing and unintelligible in 

 comparison with the really permanent and really intel- 

 ligible ftSjj, or universals.' It is a complete error to 



