Substitution Groups whose Order is Four, 43l 



The tube was heated in an air-bath and illuminated by a 

 beam from an arc light, so that the faintest crystal film could 

 be easily observed, and the amount of alcohol necessary to 

 completely dissolve the salt in the gaseous state very 

 accurately determined. 



Half of the contents was then removed, the tube resealed 

 and heated. A thick film appeared on the wall, which 

 corresponds exactly to the reappearance of the lines in the 

 spectrum, in the experiments with iodine and bromine. 

 More alcohol was added until the vapour had the density 

 requisite for the solution of this amount of salt. 



The following values were reckoned for 1 gram of solvent 

 at different densities : — 



1 Gram Ether. 





1 Gram Alcohol. 



8 (H0 2 =1). 



X (Hgl 2 in 



grs.). 



5(H 2 0=1). 



x (KI in grs.). 



•020 



•0010 





•084 



•00083 



•053 



•0016 





•147 



•00106 



•080 



•0024 





•195 



•00195 



•114 



•0050 





•231 



•00270 



•133 



•0068 





•273 



•00450 



The curves plotted from these values (fig. 6) are quite 

 similar to the curves for iodine and bromine as determined by 

 the spectroscope, which is not unfavorable to the supposition 

 that the halogen vapour is in part dissolved in the vapour of 

 the bisulphide of carbon. If the dissolved substance is 

 volatile at the temperature used, as is the case with iodine 

 and bromine, the undissolved portion is in the state of a free 

 gas ; if non-volatile, as in the case of Hgl 2 and KI, it is 

 precipitated as a crystalline film on the wall. 



In conclusion I wish to thank Prof. Warburg for the means 

 of carrying on the investigations which he has placed at my 

 disposal and for the interest that he has taken in the work. 



Berlin, Physikalische Institut. 



XLV. The Substitution Groups whose Order is Four, 

 By G. A. Miller, Ph.D* 



IT seems proper to say that Professor Cayley began the 

 enumeration of all the regular substitution groups of a 

 given order since he determined these groups for the first 

 order that presents any difficulties, viz., for the order 8f« 



* Communicated by the Author. 



t Phil. Mag. vii. (1854) pp. 40-47 and 408-409; xviii. (1859) 

 pp. 34-37. 



