408 Mr. Oliver Heaviside on the 
where the bracketed quantities are scalar products. Put in 
this form 
{(cpo)p—me}H=po(ouH),. . . . (89) 
{(aeo)e =np}H =co(ocH), . . 2 See) 
and perform on them the inverse operations to those contained 
in the {}’s, dividing also by the scalar products on the right 
sides. Then 
EK peo 
eS Sa a e e e e 37 
op (opo)u—me’ Ce 
ocH (cco )e— np - 
Operate by c on (37) and by mw on (38), and transfer all 
operators to the denominators on the right. Then 
cl o 
NE ee matte De IE ERE S £1 -tead 
op (opo)e1—mp7! Pree (39) 
poll tee o 
ocH (aco) u-!—ne™! 
=, say. «ee 
[It should be noted that, in thus transferring operators, care 
should be taken to do it properly, otherwise it had better not 
be done at all. Thus, we have by (37), 
po as 
lage cE or B,=c{(opuo)w—me}—"yo, 
and the left ¢ and the right p are to go inside the {}. Operate 
by c~? and then again by {}*?, thus cancelling the { }—, giving 
po = {(ouo)u—mce}c'6y. 
Here we can move c™' inside, giving 
po= {(opo)uc*—m} Ry 3 — 
and now operating by w—1, it may be moved inside, giving 
o= { (ope )c~'—mp-"} 6, 
as in (39). | 
We can now, by (389) and (40), get as many forms of the 
index equation as we please. We know that the displacement 
is perpendicular to the normal, and so is the induction. Hence 
of,=0, oy oy —i Uy ol bie Cas tore . (41) 
where ; and 8, are the above vectors, [(39) and (40) ], are 
two equivalent equations of the index surface. 
Also, operate on (39) by ouec7'!, and on (40) by acu, and 
