422 Dr. H. Herwig on the Expansion 



XXV. ; and with this my earlier experiments are in accord : it 

 must be remembered that the variations of vapour- density there 

 found are, in their significance, inversely proportional to the 

 variations of <f> which we have now obtained. 



Tt results further from the present observations (which often 

 extended over a wide interval) that this slight variation of $ is 

 by no means confined to the first two degrees of superheating 

 above the point of saturation, but is, on the average, uniformly 

 distributed over the entire interval. Of course this is to be 

 understood thus — that the gradual transition of <f> to its constant 

 maximum value, the occurrence of which when the heating is 

 continued within a constant space has just been made certain 

 by our present experiments, only ensues very slowly. It is true 



that the positive value of -~ will diminish and finally become 



nil, but the latter only with a very extreme degree of super- 

 heating. 



The lower limit to which the superheating must certainly be 

 carried, in order to arrive at constant values of $, can be ap- 

 proximately fixed. For example, for a temperature of saturation 

 of 90°, according to my previous formula the purely saturated 

 vapour would have a density equal to 0'0595 4/273-f 90 or 1*13 

 the constant density finally attained in the gaseous state. It 

 is true that, for sulphide of carbon and chloroform, this formula 

 was not pursued quite up to that temperature ; but at 50° the 

 ratio 1*07 was directly found; so that, according to all the ex- 

 perience then acquired, the above number for 90° is certainly 

 not far from correct. Accordingly, for purely saturated vapour, 

 the value of the function <£ would be less than the constant value 

 to which (j> continually more and more approaches, in the ratio 

 of 1 : 1*13. If now such vapour is heated in a constant volume, 

 for every 10 degrees of superheating <p increases at the com- 

 mencement, according to Tables XX. and XXV., to about 1*004 of 



its value. And since the value of ~j, in accordance with what 



has been observed, must subsequently become smaller, we may 



therefore say that, in order to attain the final constant value of 



130 

 (f>, a superheating of more than —j- . 10 degrees, or more than 



325°, is here required. 



In like manner for an extreme temperature of 50°, at which 

 the total deviation of cf> amounts to 1*07 its final value, Ta- 

 bles XX. and XXV. indicate on the average an initial increase of 



-r£ to 1*002 for 10° superheating. In this case, therefore, for 



LaZ 



