565 
1907-8.] Algebra after Hamilton, or Multenions, § 11. 
The generalisation of the pure mathematical properties of (j, “ fluxes ” 
and “ intensities ” as presented in “ The Mathematical Theory of Electro- 
magnetism” [Phil. Trans. A, 1893, pp. 685 et seq.'] to Multenions is now so 
much a mere matter of easy detail that to save space I will leave it alone. 
It will be time to record the formulae and ideas when useful applications 
happen to present themselves. [At this date I would re-name the “ fluxes ” 
and “ intensities ” perductors, and tractors. I would call Maxwell’s 
B, D, E, H, the magnetoductor, electroductor (or electrostatic perductor), 
electrotractor, magnetotractor ; the corresponding integrals would be 
magnetoduction, electroduction, electrotraction, magnetotraction; the path 
of a line integral might be called its track, the surface (or sometimes the 
ring boundary thereof) of a surface integral might be called its perduit (cf. 
circuit, conduit) ; I would banish for ever the word force or the indefinite 
“ intensity ” from such connections as electromotive force, magnetic force ; 
I would distinguish always in language between a vector and its line or 
surface integral, reserving the termination -tor for the former, and the 
termination -tion for the latter.] 
If we put o- above = yv where v is a given scalar function of p, du/dp 
becomes what we may call the Hessian colinity, namely 
)iv.W (21) 
dp dp 
and taking discriminants we have the Hessian determinant 
[^'] = (»!) _1 vir’lvS.“’» (22) 
11. Miscellaneous concluding remarks. — The ambiguity of sign 
of l 2 is an inconvenience, though not so serious as might have been 
anticipated. I have experimented with various possible systems of 
fictits, such as 
In correcting proofs (April 1908) I have left the next four paragraphs 
as they were despatched in 1906, because some important questions are 
here raised, but they do not correctly express my present views. The 
latter are given at the end of the Supplement below. 
Quaternions is undoubtedly the simplest three-dimensional geometrical 
method akin to our present algebra. Equally certain is it that for general 
algebraic purposes it is more convenient to suppose that d — l than that 
