1892-93.] Prof. Knofct on Innovations in Vector Theory. 233 
111 quaternions 
— Si7/o V .0) = dii) 
Yet lie recognises that Vw has a possible significance other than an 
operator when he writes {Vcoj^ and {Vw}x as equivalent expressions 
for V.w and V x to. These suffixes are simply another way of 
selecting convenient bits of a thing complete in itself. They are 
more troublesome to write, distinctly more cumbrous in appearance, 
and less amenable to analytical transformations than are Hamilton’s 
time-honoured forms. Besides, in quaternions, the treatment is uni- 
form throughout. 
(10.) There is something almost naive in the way in which 
Heaviside, in § 192 of “ Electromagnetic Theory” {The Electrician, 
Xovember 18, 1892), introduces the dyadic as if nothing like it was 
to be found in either Hamilton or Tait. The truth is, it is all 
there. The “dyadic” of Heaviside’s equations (137) and (138) is 
stated to be “ of a very peculiar kind, inasmuch as its resultant effect 
on any vector is to reproduce that vector.” It is what Gibbs calls an 
idemfactor. But it amounts to nothing more than equating a 
vector to the sum of its components along three given directions. 
The equations are simply Hamilton’s ancient 
pSajSy = aS/Syp + /3Syap 4- ySa/3, 
expressed in the abridged form 
p = aSa^p + ^S/3jp + ySy^p 
This is an almost fundamental formula, and yet it is characterised 
as being “ very peculiar.” As Hamilton showed long ago, if 
<hp = aSAp -1- /3Sftp -}- ySvp 
then 
(fi~^p = AjSttjp + p-jS^jp + v^Sy^^p, 
where a-^Sa/Sy = ~V ^y, &c., &c., 
and &c., &c., 
and then that “ very peculiar ” dyadic is seen to be = 1. Now 
Heaviside fusses greatly over this method of inverting cf > ; and any 
reader of § 172 would infer that the inventor of the name dyadic 
was the first to give this demonstration which Hamilton and Tait 
had somehow missed in their development of “ the very clumsy 
way” of expressing ^“^p in terms of p, cj>p, and <^^p. But the whole 
