424 Prof. J. R. Young on a Theorem of Euler in reference 



from the material employed in goblets, as may be seen from 

 the following comparison with the results of the chemists 

 formerly named : — 



Bertliier, Dumas. Civas. Peligot. 



Silicic acid . . . 717 69-4 7l'6 76 



Lime 10'3 9-2 lO'O 8 



Alumina .... 0-4 9-6 2-2 1 



Sesquioxide of iron . 0*3 ... 3*9 



Oxide of manganese 0*2 ... 0*2 



Magnesia ... 2*3 



Soda 2-5 



Potassa .... 12-7 11- 8 lJ/0 J^ 

 98-1 100-0 101-2 100 

 In one of the last numbers of Dr. Otto's German trans- 

 lation of Professor Graham's Elements of Chemistry, re- 

 cently published, I find the analysis of a combustion-tube 

 enumerated, performed in the laboratory of Dr. Otto, which 

 has not yet been published in the Journals. He obtained 

 the following results : — 



Silicic acid .... 74*0 



Lime 7-2 



Alumina . . . 



Sesquioxide of iron 



Potassa 18*5 



lOO'O 

 The oxygen in the bases of this glass stands to the oxygen 

 in the silicic acid likewise as 1 : 6. Soda is entirely absent, 

 and completely replaced by potassa. The presence however 

 of a small amount of soda does not seem to be injurious to 

 the glass. 



LXV. On a Generalization of a Theorem of Euler in refer- 

 ence to the Products of the Sums of Squares. By J. R.Young, 

 Professor of Mathematics in Belfast College^. 



THE recent researches of Sir W. R. Hamilton, of Profes- 

 sors Graves and De Morgan, and of Messrs. J. T. Graves 

 and Cayley, in reference to the new analytical theory of ima- 

 ginary quantities, have revived attention to Eider's theorem, 

 that the sum of four scjuares. multipHed by the sum of lour 

 squares produces tlie sum of four squares ; to which theorem 

 an extension was given by Lagrange, by the introduction of 

 coefficients into the component squares. 



These recent researches have suggested the inquiry as to 



* Communicated by the Author, 



:}o. 



