CLAUSIUS «97 



in particular such as are directly suited to calculation; this 

 was done by Clausius. 



For this purpose he introduced a new quantity, the 'en- 

 tropy,' which he defined, but which we cannot here discuss 

 any further. We can only remark that the second law also 

 enables us to determine what fraction of the heat supplied 

 can be transformed into work in a heat engine of the best 

 possible description, that is to say, as Carnot showed, one 

 completely reversible. This fraction is given by the ratio 

 of the available range of temperature to the absolute tem- 

 perature, that is to say, the temperature of the body reckoned 

 from — 273° C, at which the heat to be transformed is taken. 

 This result was of great importance for all progress in the 

 construction of heat engines, from the steam engine to the 

 most recent type of internal combustion engine. 



Regarding other results of thermo-dynamics, we can 

 only mention the deduction of the relationship between 

 melting point and pressure, and the discovery of the peculiar 

 properties of saturated vapours. The former is of im- 

 portance in connection with our estimate of the state of the 

 earth's interior, and also our knowledge of glaciers, the latter 

 regarding the finer observation of the processes connected 

 with water vapour in the earth's atmosphere, and in the steam 

 engine. 



Before we go into further achievements of these two men of 

 science, we will shortly consider their lives. 



Clausius was born in Koslin in Pomerania, being the 

 sixth son among the eighteen children of a school inspector. 

 He attended the gymnasium in Stettin, studied in Berlin, 

 went early into teaching as a means of assisting the educa- 

 tion of his younger brothers and sisters, became a member of 

 the university of Berlin at twenty-eight, and five years later 

 was called to the technical university in Zurich, where he 

 remained for twelve years and founded a family. He then 

 became professor at Wiirzburg, and soon afterwards at 



