December 23, 1920] 



NATURE 



535 



idea of the so-called mechanical properties of sub- 

 stances from an inspection of their more fundamental 

 physical constants. 



It seems highly probable that there is some simple 

 relation between the many physical constants of sub- 

 stances, and, indeed, many formulae connecting them 

 have been put forward, viz. : 



(i) Sutherland (Phil. Mag., 1890 and 1891) proposed 

 to find the characteristic frequency of the atoms of 

 elements bv the formula 



J 



V A 

 '" aT.V* ' 



where v is the characteristic frequency of the atoms, 

 T, the melting point on the Absolute scale, A atomic 

 weight, o mean coefficient of linear expansion between 

 0° .Abs. and T,° .'\bs., and V atomic volume = A/p, 

 where p is the density. 



(2) Einstein (Ann. d. Physik, 191 1) has proposed 



,=6 



V K.A' 



where v, V, and A have the same significance as 

 above, K is the bulk modulus of elasticity of the 

 body, and fe a constant which Einstein's theory 

 demands should have the value 2'8xio', but for 

 which the empirical value 33 x 10' seems to agree 

 much better with observation. 



(3) Debye (Phys. Zeits., vol. xviii., p. 276, 1917, 

 and Ann. d. Physik, vol. xiv., p. 789, 1912) asserted 

 that V is the .frequency of vibration of those elements 

 in a substance which determine the velocity of sound 

 in it, and he has therefore calculated v from E, and <r, 

 where E is the Young's modulus of elasticity of the 

 bodv and <r its Poisson's ratio. 



If, now, the v of Debye and that of Sutherland or 

 Einstein are identical in their physical significance, 

 we may write 



/f. 



where F(E.<r) is Debye's function for the deter- 

 mination of V in terms E and c. 



It is of interest to note that Debye's formula does 

 not involve an empirical constant, and that the con- 

 stant of proportionality in Sutherland's formula is 

 VP, where P is Dulong and Petit's constant, i.e. the 

 product of the specific heat and atomic weight of the 

 clement. 



Other formulae have been put forward by Planck, 

 l.indemann, and Griineisen, but it is not considered 

 necessary to add them here. 



For a discussion of the agreement of these formula 

 with experimental results the reader is referred to 

 Phil. Mag. for December, 1917, ".Atomic Freauency 

 and .Atomic Number, P'requency Formula ami Em- 

 pirical Constants," by Dr. H. S. -Allen. 



Perhaps these formulae are of the type of which Mr. 

 Innes is in quest. 



It will be obstrved that, in the foregoing, reference 

 to the " hardness " value has been omitted ; it is now 

 proposed to justify this omission. 



I'he moduli of elasticity-, the ultimate strength, and 

 the coefficients of expansion of a substance are, with- 

 out doubt, the mathematical expression of certain 

 body or bulk properties, and their magnitudes will 

 depend on the stale of equilibrium of the molecules 

 within and throughout the b<Kly, as well ns on those 

 on the surface. On the other hand, the hardness of a 

 substance was defined in Engineering for n ' r 12, 

 1919, as "the resistance of a surface ti' ion 



NO. 3669, VOL. 106] 



by mechanical means," and is, therefore, a surface 

 effect and not a bulk effect. If this is admitted, then 

 the hardness" number of a surface is probably closely 

 related to its surface energy, and is, perhaps, a 

 measure of a property analogous to the surface-tension 

 property of a liquid. In this connection proposals 

 put forward by Frenkel (Phil. Mag., .April, 1917) on 

 "The Surface Electric Double Layer of Solid and 

 Liquid Bodies " are of interest. In that paper it is 

 maintained that every free surface is a parallel plate 

 condenser the outer plate of which is negatively 

 charged, and consists of electrons in the outer half 

 of their orbits about their positive nuclei which form 

 the positive plate. The charge per unit-area of this 

 condenser is calculated from (i) the number of posi- 

 tive nuclei per unit of area of surface, (2) the number 

 of electrons moving in orbits about one nucleus, and 

 (3) the electronic charge. 



The distance between the plates is obtained from 

 the mean radius of orbit of the electrons of any one 

 atom. Thus the energy per unit-area of surface can 

 be calculated. Results obtained in this way were 

 shown to be in agreement with the known surface 

 enerffv and contact potential of the various elements 

 considered. 



It seems to the present writer that attempts to 

 obtain formulae connecting the mechanical constants 

 of elements with their fundamental physical constants 

 must be along this line if the hardness number is 

 the main object of the search. Many difficulties, 

 however, remain to be overcome, for it appears that 

 the plasticitv of a substance must have a much 

 greater effect in determining the " Brinell hardness " 

 than it d^es in determining the " Moh hardness " of 

 anv given substance. V. T. Saundbrs. 



Royal Naval Colletre, Dartmouth, 

 South Devon, November 29. 



Needs of Polish Universities. 



I AM travelling in East Galliia, and have only 

 just seen Mr. H. G. Wells's remarks on the need's 

 of scientific workers in Russia (see Nature of Novem- 

 ber I r, p. 352). Using Mr. Wells as a text and applying 

 it to Russia's neighbour, I should like to enter a plea 

 for the Polish Universities of Krakow, Lw6w (Lem- 

 berg), and Warsaw, which stand in the greatest pos- 

 sible need of .American, English, and French scientific 

 and technical literature. From the middle of 1914 

 to 1918 such literature was unobtainable, and since 

 1918 the rate of exchange — to-day 1500 Polish marks 

 to W. — has placed it bcvond the possibility of purchase 

 by the three impoverishcfl universities. For some 

 months the Friends' Relief Mission has been making 

 an effort at home to arouse practical interest in the 

 problem, and recently we received some volumes of 

 Nati-rk. These I took to the librarian of Warsaw 

 I'niversily, who showed me over the library. The 

 new English books could have been counted on the 

 fingers of the two hands, and in the periodical-room 

 not a single English periodical was being received, and 

 only two in Frencli. Similar conditions obtain in 

 Krakow and Lwow, capitals of West and East Galicin, 

 and two of the most important intdlcctual centres In 

 reunited Poland. 



Ci;tiihfrt F. .A. Clayton, 

 Sec. in the Field of the French Poland Unit. 



Nadworna, East Galicia, November 24. 



Wb believe that the Anglo-.American University 

 Library for Central Europe exists to supply the need 

 to which Mr. Clayton refers. The addn-ss of the 

 secretarv is London School of Economics (L'niversily 

 of London), Clare Market, W.C.a.— Ed. Nature. 



