certain Specific Heats at High Temperatures. 299 



at 0° given by these formula? have naturally discredited Hirn's 

 results, seeing that Regnault's values at 0° are certainly nearly 

 correct. In the case of CS 2 and CC1 4 Hirn's results are in 

 much better agreement with Regnault's ; but the above dis- 

 crepancies, as they condemned Hirn's method, condemned 

 therefore the whole of his results. 



But by recalculating the specific heats from Hirn's experi- 

 mental data I have been able to bring his results at high 

 temperatures into good agreement with Regnault's at low, and 

 so to obtain expressions for the specific heats of ether, alcohol, 

 OS* and 001^ from 0° up to 140°. 



Hirn (Ann. de Chim. et de Phys. ser. 4, x.) adopted the 

 method of cooling, but on so large a scale that he was able to 

 avoid the difficulties usually inherent in that method. The 

 vessel in which the liquids were heated was of about 8 litres 

 capacity, and might be regarded as the bulb of a huge thermo- 

 meter, the stem of which was 11 metres long and was filled 

 with mercury ; the pressure of the mercury-column per- 

 mitted the temperature of the volatile liquids to be raised to 

 160°. The size of this apparatus allowed of the introduction 

 of an efficient stirring mechanism to keep the whole mass of 

 liquid uniform in temperature ; thus the radical difficulty of 

 the method of cooling when used on a small scale was avoided. 



When the liquid in the bulb was heated, the overflow of 

 mercury at the top of the stem enabled Hirn to measure very 

 accurately the expansion of the liquid up to high temperatures, 

 and gave him a connexion between the volume and tempera- 

 ture of the liquid at any moment in the process of cooling. 

 h\ this way he succeeded in measuring the rate of cooling at 

 temperatures ranging from 160° to 40°. 



Unfortunately he adopted a cumbersome and inaccurate 

 method of treating his experimental numbers in order to obtain 

 from them the specific heats. Instead of estimating the rate 

 of cooling direct from the experimental numbers, he found an 

 empirical formula connecting the observed times and tempe- 

 ratures, and then from this, by differentiation, got the rate of 

 change of temperature. But it is obvious that this method 

 becomes dangerous at low temperatures ; for then the rate of 

 change becomes slow, and inaccuracy in the formula which 

 may not appear of appreciable importance in affecting the 

 absolute value of the temperature at a given time, may 

 seriously affect the value of the rate of change. In other 

 words, if the ordinate of a curve is approaching a stationary 

 value, a formula may represent the absolute values of the 

 ordinate^ fairly well and yet give large errors in the values of 

 the small slope of the' tangent. 



