July 22, 1892,] 



SCIENCE. 



51 



complicated phenomenon than that of rigidity. Rigidity is sim- 

 ply a function of tVie coliesive force. The tensile strength of a 

 substance depends not only on the cohesive force of the metal, 

 but also on its ability to resist flow. If a metal did not flow before 

 being pulled apart, there is no doubt but that its tensile strength 

 would be proportional to the i-power of the atomic volume. As, 

 however, it does flow, and the amount of flow is not simply pro- 

 portional to the diminishing of the cohesive force, we have to 

 make a fresh allowance for it. In all the metals the melting-point 

 is reached when the linear expansion has amounted to about 2 per 

 cent. So when the cohesion has diminished about 4 per cent the 

 atoms no longer hold the same relative positions, but one can slip 

 in and take the place of another. So at equal distances from their 

 melting-points only can the tensile strength be proportional to 

 the i-power of the atomic volume. Consequently this ratio can 

 only hold good with substances which have approximately the 

 same melting-point. On examining the table, it will be seen that 

 as copper, gold, and silver have approximately the same melting- 

 point, the ratio does hold good with them. The same with 

 tin and lead. Aluminium and zinc, which should be, the one 

 slightly weaker, the other slightly stronger, than silver, have a 

 melting-point about one-half that of gold and silver, and they 

 have about half the strength at the temperature of comparison 

 which they should have. The melting-point of iron and platinum 

 is higher than that of gold or silver, and consequently their tensile 

 strength is greater. The flow of a metal depends on two things, 

 the cohesive force and the kinetic energy of the atoms. What 

 function the flow is of the temperature, as reckoned in fractions 

 of the temperature at which the substance melts, it is hardly 

 worth while to go into now. If we suppose it directly propor- 

 tional (though we may feel fairly certain it is not as simple a 

 function) so that, at the same temperature, a metal melting at half 

 the temperature that another does flows twice as easily, we get 

 the following table, where Col. I. contains the observed tensile 

 strengths, and Col. II. the calculated ones: — 



Metal. I. 



Iron 65 



Copper 41 



Platinum 35 



Silver 39.6 



Gold 28.5 



Aluminium 18 



Zinc 15.7 



Tin 3.4 



Lead 3.36 



I have not been able to find any data on the tensile strength of 

 magnesium. Theory gives about 9 kilograms for a wire 1 milli- 

 meter in diameter. It would be interesting to find if experiment 

 confirms this. 



If, when we have met with a new phenomenon in a substance, 

 and are able to show that a certain property already known to 

 exist in the substance is capable of producing effects of the mag- 

 nitude observed, and that the phenomenon obeys the same laws 

 as it would if it were caused by the already known physical prop- 

 erty, we are to a certain extent justified in supposmg that this 

 property is really the cause of the phenomenon in question, and 

 in applying our knowledge still further, we have seen that the 

 charges which we know the atoms have on them are able to give 

 effects of the same size as those observed in experiments on ten- 

 sile strength, and that the various moduli follow the same laws as 

 they would if cohesion were an electrostatic effect, and we may 

 now apply our formula to other and less-known phenomena. 

 The velocity of sound in a wire is given by the formula : — 

 / Elasticity \ + 

 \ Density / 



Elasticity here means Young's modulus, the formula for which, 

 as we have seen, was constant -h- (atomic volume)^, and atomic 

 volume is atomic weight -i- density, so we have velocity of sound 



/ constant \* , 



m wire = I 1 I 



\atomic weight X atomic volume/ ' 



IL 



74 

 48 

 48 

 29 

 29 

 18 

 16 

 5 

 4 



Velocity 



ties of sound in wires. of a number of metals which have been 

 tested, and in C'ol. II. the calculated velocities for these and for 

 other metals which have not yet been tested. 



I. II. III. 



Col. III. gives the electrical resistance, silver being taken as 

 100, and it may be noticed that in any one group of metals the 

 conductivity varies directly as the velocity of sound, and in pass- 

 ing from one group to another, by multiplying the conductivity 

 by the valency we get proportionate values for all the metals. 

 The same holds good for the heat conductivity. No close agree- 

 ment can be expected here, for there rfre too many things to be 

 taken into account. It is merely mentioned here because the 

 fact of there being a relation between the velocity of sound and 

 the conductivity for heat and electricity throws a light on the 

 nature of these phenomena. This will form the subject of a sepa- 

 rate paper. It may be asked hoio an electrostatic force can pro- 

 duce such effects. If the atoms are all similarly charged either 

 4- or — they would repel each other and not attract. The expla- 

 nation is probably this: The atoms, if we may call them so, of 

 electricity are not infinitely smaller than the atoms of matter. 

 When an atom is neutral it does not mean that it has no charge 

 but that it has equal quantities of both kinds of electricity. The 

 resultant effect of these charges on a body at a distance is zero, it 

 behaves as if it had no charge, as shown below, in A. 



If the atoms be brought close together there is a state of un- 

 stable equilibrium, and the effect is that either the charges move 

 on the surface of the atoms or the atoms themselves move so that 

 the atoms attract each other, as in B. Consequently all atoms 



neutrally charged attract each other. If nothing further happens 

 the attraction is simply cohesion. If, however, any third sub- 

 stance connects the two outside parts of the atoms and so enables 

 these parts to neutralize each other we have chemical combination, 

 and the two atoms when separated show opposite charges, as 

 in C. 



the constant be- 



>vatomic weight X atomic volume> 

 ing 78 X 10'-. The following table gives in Col. I. the veloci- 



Whether we accept the electrostatic theory of cohesion or not. 

 from the above tables of moduli, the following laws are evident. 



I In any two metals the force of cohesion varies inversely as 

 the square of the distance between the centres of their atoms. 



