An often used definition of "Faraday's Law of Induction" goes something like this (found in Wikipedia)
The electromotive force around a closed path is equal to the negative of the time rate of change of the magnetic flux enclosed by the path.
This law is often attributed to Faraday's 1832 Report to the Royal Society published under the name "Experimental Researches in Electricity"
However, in that document, I was unable to find any reference to an equality between a quantified electromotive force with a rate of change of a quantified magnetic flux. Rather, in section 42 of that document, he refers to
a law hereafter to be described (114)
and in section 114, describes a qualitative, but not quantitative law which he refers to as
The relation which holds between the magnetic pole, the moving wire or metal, and the direction of the current evolved
I will not repeat everything Faraday wrote about this relation. Suffice it to say, that the explication of this law turns out to be a far cry from a quantitative law equating the e.m.f. and the rate of change of magnetic flux.
Now, there is another published work by Faraday with the same name i.e. "Experimental Researches in Electricity", published in three volumes from 1839 to 1855. The first part of volume 1 of this larger work appears to be identical to that published in 1832. I did not read it all. However, a search of the words "flux" and "electromotive" shows they only appear 3 times each in the first volume, and none in conjunction with each other.
So, my question is, when was Faraday's Law of Induction, in the form of a quantitative equality, first expressed. And was it even first expressed by Faraday? Was it by Maxwell? Heaviside? Or did it come earlier than those two scientists? Is there something that Faraday wrote that entails a mathematical equality, even though it may have been expressed with words other than "flux" or "electromotive force"?