I have heard it both ways. I will check.
Certainly, the telegraph equation is sufficent and Kelvin did get a knighthood
for this. And certainly, other professionals
( telegraph engineers who distrusted mathematicians and PDE)
missed the point. Also, certainly Heavyside was a genius, who did do some
brilliant work in the field.
The problem was more than the slowness, it was that the signal speed
depended seriously on frequency.
I will check to see Heavyside's exact contribution. I am also a fan of
Heavyside. The IEEE publishes a very inexpensive bio of Heavyside.
p.s. The current form of Maxwell's equations is really the work of Heavyside.
( But, his push for vector calculus instead of clifford algebra slowed physics
for a century).
Heavyside did very nice work in operational calculus, which was pioneered by
Euler and Laplace. He was the first to consider infinite structured networks of
elements ( now used as a basis for the electrodynamic modeling of materials).
Charles Proteus Steinmetz often gets credit for inventing "impedences" and
phasors--these were used by Heavyside first in electronics--but had been used
in mechanics by Laplace.
p.s. And the ionosphere used to be called the Heavyside-Ken layer.
in article [Only registered users see links. ], PSmith9626 at [Only registered users see links. ] wrote on 8/30/03 3:57 AM:
Kelvin certainly deserved a knighthood for making the cable work. It think
that it was LORD Kelvin not just Sir Kelvin.
Heavyside was most mistrustful of "Cambridge mathematicians," especially
Tate. Mathematicians were mistrustful of Heavyside because of his lack of
rigor. Nevertheless, the heavyside calculus was put on a firm mathematical
footing with the development of laplace transforms.
That is exactly the problem without additional inductance. That is what
turns propagation of the signal into a diffusion of the signal. Series
inductance evens out propagation speed as a function of frequency.
One of the other things that Heavyside observed experimentally was that the
a failing submarine cable, from water seepage shorting out the cable was
able to signal faster even as it was failing. The shunt conductivity
equalized propagation speed across the spectrum used.
Variations of these methods were later applied to telephony when Pupin used
loading coils to equalize frequency response.
I am not familiar with clifford algebra. Is that the same as the quaternions
Heavyside hated? Willard Gibbs made vector analysis into the form we like
today. Even today, we prefer using vectors to using Quaternions. Maybe using
relativistic 4-vectors and tensors may be a more mathematically satisfying
way to go, but I see no great rush to do so.
I few years ago, there was a paper in Proc. IEEE, about the first use of
impedance. There was a reprint of the paper. It was not Steinmetz. IIRC
Rayleigh developed the concept of impedance for mechanics if not for
Heavyside did have his blind spots. He called Einstein's theory limiting
mecahnical speeds to those below the speed of light obvious nonsense.
Laplace predated Heavyside in the use of his transform, in the use of the
"delta function" and in the use of operational calculus. But, Heavyside used it
Dirac gets credit for the delta these days.
Pupin get's credit for inventing the lumped parameter approach. He based the
electonic application on a paper of Lagrange.
Clifford Algebra is a general algebra that includes differential form algebra (
grassman algebra), spinors, quaternions,
and tensor analysis. There are some good websites and books.
....Into the form, we HATE today. Using differential forms one never has to
learn vector identities, everything works in all dimensions and looks exactly
the same, Green's/Gauss/Stokes theorems all look identical.
In lots of applications we use SU(2) which is essentially the same thing: Gauge
theories for example.
Right, but Laplace did it first.
p.s. Chem board--shouldn't we be discussing Dalton et al., instead of these
Kelvin also had his blind spots--he needed a mechanical analogy for things.