1893 - 94 .] Prof. Cayley on Coordinates versus Quaternions. 275 
viation, it would be allowable to write A, = (ABC) to denote the 
determinant formed by the coordinates of the three points. 
In conclusion, I would say that while coordinates are applicable 
to the whole science of geometry, and are the natural and appro- 
priate basis and method in the science, quaternions seem to me a 
particular and very artificial method for treating such parts of the 
science of three-dimensional geometry as are most naturally dis- 
cussed by means of the rectangular coordinates x, y, z. 
