284 SCIENCE PROGRESS. 



as much as 4 per cent, between o° and ioo°. Strecker, on 

 the other hand, found no certain change for the halogens 

 and their hydracids up to 400°. From the arrangement of 

 Wiillner's apparatus it is difficult to believe that the gases 

 really had as high a temperature as he attributed to them, 

 and the result needs confirmation. 



Neither Strecker nor Wiillner took account of the 

 deviation of the gases from Boyle's law, but this would not 

 account for anything like so great a change as Wiillner 

 found, and in any case hydriodic acid, which showed no 

 change, deviates far more widely than carbon monoxide, 

 which changed considerably. 



A repetition of the experiments on carbon dioxide, for 

 instance, would be of value. The observations should not 

 be made merely at 0° and 100°, but at intervals over as 

 long a range as possible, in order to see whether the value 

 of y approaches asymptotically to an intelligible limit. If 

 Wiillner's results prove to be substantially correct, the 

 question arises why some gases vary with the temperature 

 and others do not, and opens up a large field for research. 



Any discussion of the ratio of the specific heats would 

 be incomplete without reference to a theorem that has at- 

 tracted considerable attention lately — Boltzmann's theorem 

 on the partition of energy in a dynamical system. We 

 shall consider here only the physical side of the theorem, 

 as the mathematical arguments for and against it have 

 already been discussed in this journal by Mr. H. S. Bur- 

 bury ; but before stating the theorem it will be necessary, 

 for the benefit of non-mathematical readers, to explain 

 briefly what is meant by "degrees of freedom," a term 

 that will be frequently used. 



By the number of degrees of freedom of a system is 

 meant the minimum number of co-ordinates — lengths, 

 angles, etc. — necessary to specify completely the position 

 and configuration of the system. 



As an illustration take the case of a ship at sea. The 

 locality of the ship cannot be fixed by less than two co- 

 ordinates ; its latitude and longitude are the two usually 

 chosen, though other pairs would do equally well. Next 



