PROCEEDINGS 



OF 



THE ROYAL IRISH ACADEMY. 



1844-45. No. 50. 



January 27, 1845. 



SIR Wm. R. HAMILTON, LL.D., President, in the 

 Chair. 



The Correspondence (see Appendix, No. I.) was read 

 from the Minutes of Council. 



The Rev. Charles Graves read the continuation of his 

 paper on Algebraic Triplets. 



The triplet x •\- ly -{■ i^z, or (x, y, z), being employed to 

 represent the right line drawn from the origin to the point 

 whose rectangular coordinates in space are x, y, and z, it be- 

 comes a matter of interest to determine the position of the 

 right line which represents the product of two such triplets. 

 For this purpose it will be convenient to lay down some defi- 

 nitions. 



1. The symmetric axis is the right line drawn from the 

 origin, so as to make equal angles with the three positive por- 

 tions of the axes of coordinates. 



2. The symmetric plane is a plane passing through the 

 origin, and perpendicular to the symmetric axis. 



3. The modular plane is the plane containing the axis of 

 X and the symmetric axis. 



4. The radius, r, of the triplet {x, y, z) is the right line 

 drawn from the origin to the point x, y, z. 



VOL. III. F 



