1895 - 96 .] Prof. Tait on the Linear and Vector Function. 163 
These give at once 
P =Pi<hPiSpiP +1W2 S P2P + Pz<hP^P‘6P 
which is obviously self-conjugate. 
4. The results above have immediate application to fluid motion. 
For, when there is a velocity-potential, the motion is “differentially 
irrotational ” : — i.e., the instantaneous change of form of any fluid 
element is a pure strain ; a particular cubical element at each 
point becoming brick-shaped without change of direction of its 
edges. But if we think of the result of two successive instan- 
taneous changes of this character, we see that there is in general 
at every point a definite elementary parallelepiped, the lengths, 
only, of whose edges are changed by this complex strain. In 
special cases, only, is a similar result produced by three successive 
pure strains. 
In connection with this Abstract I have now printed a little 
paper (read to the Society some time ago along with a speculation 
as to the Antecedents of Clerk-Maxwell's Equations ), which deals 
with closely connected matters. It was again presented as illus- 
trating some portions of my reply to Professor Cayley’s paper on 
Coordinates versus Quaternions (Proc. R.S.E. , 2/7/94); but these 
portions were not printed at the time, because of a letter from 
Professor Cayley to the following effect : — 
“ I venture to suggest the omission of the passages relating to 
Heaviside — merely on the ground that it is making the question 
into a triangular duel. As far as I am concerned, it is certainly 
£ Quaternions,’ and not ‘ Anything else ’, v. Coordinates, which I 
was arguing about.” 
The passage of my reply, which was suppressed in consequence 
of this request (though it formed a by no means unimportant part 
of my case), followed the first paragraph on p. 284 of the Proc. 
R.S.E . for July 2, 1894, and ran thus : — 
“ But I may refer to the recorded experience of a prominent 
practical worker at electro-magnetic theory, Dr 0. Heaviside. His 
testimony is specially valuable in the present question because he 
is avowedly not a partizan of quaternions. His case may be 
described, in a modification of Prof. Cayley’s Title, as “ Anything 
