As I proceeded with the study of Faraday, I perceived that his
method of conceiving the phenomena was also a mathematical one,
though not exhibited in the conventional form of mathematical
symbols. I also found that these methods were capable of being
expressed in the ordinary mathematical forms, and thus compared
with those of the professed mathematicians.
For instance, Faraday, in his mind’s eye, saw lines of force
traversing all space where the mathematicians saw centres of
force attracting at a distance. Faraday saw a medium where
they saw nothing but distance. Faraday sought the seat of the
phenomena in real actions going on in the medium; they were
satisfied that they had found it in a power of action at a
distance impressed on electric fluids.
When I had translated what I considered to be Faraday’s ideas
into a mathematical form, I found that in general the results
of the two methods coincided, so that the same phenomena were
accounted for and the same laws of action deduced by both
methods, but that Faraday’s methods resembled those in which
we begin with the whole and arrive at the parts by analysis,
while the ordinary mathematical methods were founded on the
principle of beginning with the parts and building up the whole
by synthesis.
I found, also, that several of the most fertile methods of
research discovered by the mathematicians could be expressed
much better in terms of ideas derived from Faraday than in
their original form.
The whole theory, for instance, of potential, considered as
a quantity which satisfies a certain partial differential
equation, belongs essentially to the method which I have called
of Faraday....
If by anything I have here written I may assist any student
in understanding Faraday’s modes of thought and expression, I
shall regard it as the accomplishment of one of my principal
aims: to communicate to others the same delight which I have
found myself in reading Faraday’s “Researches.”
Clerk Maxwell may also be credited with the remark that Faraday’s work
had had the result of banishing the term “the electric fluid” into the
limbo of newspaper science.
[Sidenote: ELECTRIC LIGHT IN LIGHTHOUSES.]
Public-domain text, read in full here on John Shaqi.
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