Mr. A. Cayley's Note on a System of Imaginaries. 25*7 



would amount to 5"896 grains. In some other specimens of 

 urine which I examined there was however no apjoroach to 

 this quantity of phosphorus in an unoxidized slate, and as 

 the mode of analysis employed in these preliminary experi- 

 ments was not the most accurate, I intend to make the deter- 

 mination of the quantity of phosphorus the subject of further 

 experiments. 



The only opportunity I have had of examining urine in a 

 diseased state, was a portion obtained from a patient suffering 

 from diabetes mellitus. As might have been anticipated from 

 the character of this disease, the amount of sulphur which the 

 urine contained in an unoxidized state, was considerably 

 greater (by one-fourth) than in healthy urine. 



The diabetic urine had a specific gravity of 1046. 



Of this urine 1046 grains, precipitated with nitrate of ba- 

 rytes, gave— 



4*308 grains sulphate of barytes= 1'479 grain SO3 =0'592 

 grain S. 



After the precipitation of the sulphuric acid by baryta, the 

 urine was evaporated down with nitric acid, mixed with nitre 

 and deflagrated. An excess of nitrate of barytes having been 

 used to precipitate the sulphuric acid, there remained on 

 treating the fused mass with thlute nitric acid, an insoluble 

 residue of sulphate of barytes, the sulphuric acid of which had 

 been derived from the oxidation of the sulphur by the nitre; 

 the sulphate of barytes amounted to 



1'837 grain =0-629 grain sulphuric acid =0'25I grain sul- 

 phur, or 0'024 per cent., 



whilst in healthy urine the sulphur in this state never exceeded 

 0*018 per cent. 



XLII. Note 071 a System of Imaginaries. By A. Cayley*. 



THE octuple system of imaginary quantities, ?\, i^, i^, i^, ?'<;, 

 ^6» hi which I mentioned in a former paper, (and the con- 

 ditions for the combination of which are contained in the 

 symbols 



123, 246, 374, 145, 275, 365, 167, 



i. e. in the formulas 



with corresponding formuhe for the other triplets i^ i^, i^ &c.,) 

 possesses tlie following property ; namely, if ?^, «^, i be any 



• Communicated by the Author. 

 Phil. Mag. S. 3. Vol. 30. No, 20 1 . April 1847. T 



