1892-93.] Prof. Knott on Innovations in Vector Theory. 237 
are non-associative, but in no sense more general than 
the corresponding but associative quaternion quantities, 
and whose V is not the real efficient Nahla of quaternions. 
(5.) The invention of new names and new notations has added 
nothing of importance to what we have already learned 
from quaternions. 
The true entrance into vector analysis is by quaternion gate. 
Some there be who have climbed over definition fences, or meandered 
in along ‘‘ pleasant green” lanes. But these are not the true pilgrim ; 
and their character will declare itself when a real and novel difficulty 
has to be surmounted. One indispensable accoutrement is the pure 
V, and that is out and out quaternionic. 
But from the attacks of these innovators, Hamilton, one of the 
greatest analysts of any age, scarce needs defender. He is “ the 
strong man fully armed.” “ When a stronger than he, coming upon 
him, shall overcome him ” then — but when shall that be 1 There 
is, as yet, no sign of him ! 
