I did some more digging on Ohm's law. Doug's suggestion that maybe
Kirchoff was the person who started referring to this relation as "Ohm's
law" seems to be right. In 1849 Kirchoff published a paper : Ueber eine
Ableitung der Ohm'schen Gesetze, welche sich an die Theorie der
Elektrostatik anschliesst (Poggendorf's Annalen,78,506,1849) -which
freely translated reads: About the derivation of Ohm's law consistent
with the theory of electrostatics. So the expression "Ohm's law" clearly
appears in the title of that paper. I do not have the original at my
disposal, but in a French handbook (P. Duhem, Leçons sur l'electricite
et le magnetisme, Paris 1891, p409) I find: Kirchhoff remarked in his
1849 paper that the condition for electric equilibrium in the interior
of a homogeneous conductor, expressed by Ohm by stating that the
electroscopic force must be constant, is equivalent to the statement by
Poisson that the potential function should be constant. This remark lead
him (i.e. Kirchhoff) to admit that the electroscopic force must be
proportional to the potential function, and to formulate the following
hypothesis, from then on called "Ohm's law". Ohm's law, as formulated in
his 1849 paper is almost unrecognizable as such, I'll try to render
Kirchhoff wording as accurately as possible, (but remember I do not have
the original, I'm translating form Duhem's French version) "In a point
of a homogeneous conductor through which permanent currents flow, the
electromotive force is identical in both amplitude and direction to the
electrostatic force as given by Coulomb's law". Duhem continues : Ohm's
law can be enounced in a far more convenient form. After almost three
pages of reasoning he obtains the familiar equation: I = (Delta V)/R
(Duhem uses different symbols, e.g. k for resistance, but he truly
arrives at the equation as we usually known as "Ohm's law".
Now to Brian's question: how "recognizable" is Ohm's law if we look at
his original paper?.
Kirchhoff's statement of 1849 would certainly fool any physics student.
Again, instead of Ohm's original paper I only have a French excerpt (E.
Hoppe, Histoire de la Physique, Paris 1928). To understand it, I have to
go through a description of the experimental setup. Ohm used a Voltaic
pile, the two poles of it connected to the flasks A and B, filled with
mercury. From A a short piece of wire ran to the galvanometer, and
further on to a connector C. The conductor to be studied was placed
between B and C. To begin with, Ohm placed a very thick copper wire of
approximate one third of a foot between B and C, and called the
corresponding reading of the galvanometer the "normal force". Then he
measured the loss of the "mean force" v for different lengths of wire.
Ohm thought his results could be best expressed by the formula: v = m
log(1 +x/a), where m is a function of the "normal force", of the cross
section of the conductor and of the "electric tension", a is the length
of the fixed conductor and x is the length of the variable conductor. An
extensive account of these experiments appeared in the Schweigg.
Journal, 44,110,1825. I believe few people reading this today would
immediately recognize "Ohm's law". In his 1927 publication the
mathematical formula reads: e = k q dU/dN. dU/dN is the newly introduced
"potential drop", q is the cross section of the wires, k is called
"reduced length" by Ohm, it is the inverse of the resistance for a wire
of length 1 and cross section 1, and e would in modern times be called
the current. Ohm obviously did not have a word for "resistance", he
invented the expression "reduced length" to indicate the resistivity of
his wires. This is the formula I referred to as "more or less
recognizable" in my previous message.
As to Brian's remark about the restricted range of applicability, I'm
not sure I'm getting his point. Indeed, Ohm only investigated metal
wires, but surely it was an enormous feat to find "Ohm's law" at a time
where the concept of "resistance" was completely unknown, when no words
yet existed for what is now called "electric current" , "voltage" or
"potential difference". Linearity, as far as Ohm's original experiments
is concerned means that the resistance of his metallic wires was indeed
proportional to their length, cross sections being equal. From remarks
in different 19th century books it seems to me that any deviation from
linear behavior was due to the non- homogeneity of the composition of
the wires. Deviations from linearity due to temperature effects were
recognized early on, among others by Ohm himself. The 1895 edition of
the "Handbuch der Physik", states that for metallic wires Ohm's law is
accurate to within one billionth if very large and very small currents
are compared, provided "all necessary precautions are taken". The
"Handbuch" discusses for three pages the limits of applicability of
Ohm's law, and mentions among others that iron wires exhibit non linear
behavior with respect to both intensity and direction of the current.
Many results obtained for non metallic materials - among others selenium
and sulfur - were in the 1880's apparently still very controversial.