48 J. 0. Thompson — Law of Elastic Lengthening. 



himself seems not to have made, for conclusion VII shows that 

 he did not look for any change in the modulus of elasticity 

 until the density of the body had been permanently altered. 

 Wertheim proved that the density of a wire before an experi- 

 ment differs very slightly from its density after it has been 

 broken by its load. He therefore concludes that in one and 

 the same wire, even when it is in different conditions of equi- 

 librium, the modulus of elasticity can vary only a very little. 



But it should be kept in mind that, although on account of 

 the contraction of cross-section the change in density is slight, 

 the mean molecular distance in the direction in which the 

 tension is exerted probably increases by a very considerable 

 'amount. And it is probable that the variability of the modu- 

 lus of elasticity should be attributed not so much to the altera- 

 tion in density of the body considered as a whole, as to this 

 change of mean molecular distance in the direction of the ten- 

 sion. According to Wertheim's own assumption we should 

 have in one and the same metal 



Mod. of elasticity X« 7 = constant, 



where a represents the mean molecular distance. According 

 to this any change in a would produce in the modulus a change 

 proportionally seven times as great, and this in the case of the 

 stretching of a wire can become very noticeable. According 

 to my own measurements to be sure a much higher power than 

 the seventh must be assumed in the formula. 



If it is universally true that an increase of the mean mole- 

 cular distance causes a diminution of the modulus of elasticity 

 according to a definite law, then in those metals which have 

 the largest coefficients of thermal expansion the decrease of 

 the modulus of elasticity with the temperature ought to be 

 most rapid. That this is actually the case has been already 

 mentioned by Miller* and Katzenelsohn.f A further deduc- 

 tion would be that since by higher temperatures the coefficient 

 of thermal expansion grows larger, the modulus should here 

 decrease more rapidly than by lower temperatures. That this 

 is also true has been proved by the measurements of Kohl- 

 rausch and Loomis^: and Pisati.§ 



Further if a substance like india rubber has a negative co- 

 efficient of thermal expansion, it would follow from our prin- 

 ciple that as the temperature increases the modulus should 

 increase too. Just such an increase in the modulus of elasticity 



* Miller, Wied. Beibl., si, p. 211, 1887. 



f Katzenelsohn, Wied. Beibl, xii, p. 307, 1888. 



\ F. Kohlrausch and Loomis, Pogg. Ann., cxli, p. 498, 1870. 



§ Pisati, Wied. Beibl., i, p. 305, 1877. 



