( 2iO ) 



liquety iigain witliout division and witliout iiijnrin<>- the glass tlie 

 last resistance consists of a series of u-shaped glass capillaries tilled 

 with mercury arranged in a cii-cle and connected bv expansion 

 i-eservoii'S ; there are foui- j)latinuni leads for conj>ling it to the 

 measurinu- instruments. 



states to metals, which has been done repeatedly shice, and to regard the melting 

 point as a corresponding temperature. I also thought that when it was a question 

 of concluding from elastic phenomena, the principle of mechanical similarity could 

 well he apphed, as 1 had already tlone in explaining the extended validity of 

 VAN DER VVaals's law of corresponding slates. 



Metals, the-efore, in corresponding states are regarded as mechanically similar 

 systems the various properties of which, expressed in units depending upon length, 

 mass and time, are, when in corresponding states, given hy the same numerical 

 values by using units which are ot)tained for each metal from its own hmda- 

 mental units [L\, [M], [T]. The natural units of mass and volume are the atomic 

 weight M and the atomic volume, so that [i] = i(f' /s p - Vs where p is the density. 

 The particular unit of lime for each metal is the reciprocal of the frequency here 

 required, i. e. the period of the resistance vibrators. According to the dimensions 

 [L'-MT--] of kinetic energy which determines temperature, we get from llie cor- 

 responding melting point temperatures fl*- and S'^ and the expression for f. 



[T[ : [T] = LLJJ/V.<9,-V. : [L']il/'".^',-'. = 



from which it would follow lliat taking the Irequency for lead such that a — 54 

 the frequency for mercury should be such that ö = 37. As comparison with 

 platinum would give a value 47, we can regard the results of this method as 

 only a rough approximation, and a further reduction to 30 which promised to 

 give better agreement seemed quite permissible. 



I have more recently seen a formula for the frequency deduced by Lindemann 

 as far back as lUlO (Physik. Zeitschr.) from more specialized assumptions, from 

 which the expression just given follows at once; this is not surprising since the 

 principle of similarity may be applied to his assumptions. While I wish to take 

 this opportunity — as 1 should have done in my first paper on the subject — of referring 

 to these important calculations of Lindemann it is perhaps fortunate that 1 had 

 not seen them sooner, for they give a^ 46 for mercury, while it was just from 

 the estimate a = 30 that I was able to forecast that at some of the helium tem- 

 peratures the resistance of mercury could be measured and at lower temperatures 

 it would disappear, and it was this forecast that made experiments with mercury 

 so particularly inviting joined with the prospect of working with a pure metal. 



