Maxwell's equations In Jaynes' Probability Theory, he states:

There are many more analogies. In physics we are accustomed to finding that any advance in knowledge leads to consequences of great practical value, but of an unpredictable nature. Röntgen’s discovery of X-rays led to important new possibilities of medical diagnosis; Maxwell’s discovery of one more term in the equation for curl H led to practically instantaneous communication all over the Earth.

Does anyone know what is being referred to here? I think it is related to fibre optics but am not sure. More generally resources for understanding Maxwell's equations would be great.
 A: Only Jaynes knows exactly what he meant, but my guess is that he's referring to the second term in:
$$ \nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0\frac{\partial\mathbf{E}}{\partial t} \right) $$
Long before Maxwell's time people realised that a current $\mathbf{J}$ produced a magnetic field. The second term $\partial\mathbf{E}/\partial t$ means a magnetic field can be generated by a time dependent electric field even when the current is zero. This leads directly to the existance of a propagating electromagnetic wave i.e. radio waves. It also tells us that the constant $\mu_0\varepsilon_0 = 1/c^2$ and this is the bud from which special relativity sprouted.
Learning about Maxwell's Equations requires a reasonably sophisticated grasp of calculus, but they are more straightforward than the (sometimes frightening) notation might have you think. I found A Student's Guide to Maxwell's Equations by Dan Fleisch to be a good introduction.
A: This link gives a brief history of how Maxwell combined laws individually established into an electromagnetic theory.



Maxwell's great contribution, in reformulating Faraday's law was to tie the laws into one theory unifying electric and magnetic fields and in predicting electromagnetic waves, which is what is implied in the statement you question.
