What was the energy of light thought to be before Einstein I'm studying the photoelectric effect where it turned out that the kinetic energy of the emitted electron was dependent on the frequency of the u.v. light and not its intensity. It was previously predicted that the kinetic energy of the electron would be dependent on the intensity of the light but not its frequency. This got me thinking, before Einsteins $E_{p h o t o n}=h \nu $ was lights energy not thought of being dependent on its frequency? And what formula was there to determine its energy?
 A: To determine the energy of light we can consider what classical electrodynamics has to say about the energy of any electromagnetic (EM) field.
The energy density stored in EM fields is
$$u = \frac{1}{2}\left(\epsilon_0 E^2 + \frac{1}{\mu_0}B^2\right). $$
This comes from Poynting's Theorem.
To calculate the energy of an EM wave we need use the $\vec{E}$ and $\vec{B}$ for the wave.  For a monochromatic plane wave, the magnitude of $E$ and $B$ are related
$$B^2 = \frac{1}{c^2} E^2$$
so
$$u = \epsilon E^2$$
A more useful measure is the power per unit area transported by an EM wave.  We get this by averaging the energy density over one cycle of the wave and integrating how much energy passes through the unit area surface.  This is the intensity of the wave, and it ends up being
$$ I = c \left<u\right>,$$
where $\left<u\right>$ is the time average of the wave's energy density.
The intensity is directly connected to the energy carried by a classical wave.
A: Here is what seems plausible to me:  
I take it that before Einstein 1905 energy was attributed to light in a way that was analogous to attributing energy to other types of transversal waves, such as seismic waves and waves of strings, or the standing waves of chladni plates
A chladni plate in a particular vibration pattern has a corresponding energy. The vibration of the chladni plate is a behavior of the plate as a whole. The total energy of a vibrating chladni plate will be proportional to the frequency, the amplitude, and the total surface area.
I suppose a measure of chladni vibrational energy that strives to be independent of the size of the plate will express an energy density; an amount of energy per area unit.
I assume the energy of electromagnetic waves was thought of that in analogous ways, but in the case of electromagnetic radiation the energy occupies volume.
A: In classical physics, before Einstein and before Planck, energy of light was thought to be exchangeable with energy of matter, in a continuous manner. One could have arbitrarily small energy exchange, for any kind of light. When EM wave interacts with matter in macroscopic physics, total energy exchanged usually is function of intensity of light and time of interaction; the shorter the interaction, the less energy gets exchanged. Frequency of light did play a role, because the rate of energy exchange depends in a complicated way on it and this dependence is a characteristic of the kind material body. But other than that, there were no quanta of energy associated with light frequency, and no other simple rule involving frequency.
Then Planck introduced the idea that EM radiation exchanges energy with matter particles in a novel way, where at any time (or most of times) either whole multiple of energy $h\nu$ is transferred, or no energy is transferred. He did not provide any mechanism, so the exchange of energy became an obscure process - something unknown makes sure energy changes only by finite steps $h\nu$. For Planck, this was just one possible way to derive the EM radiation spectrum of black body, he also developed other models.
Einstein later developed Planck's idea into a picture where the EM radiation consists of quanta carrying energy $h\nu$. He used it (and the idea of discrete energy levels of molecules) to formulate kinetic model for a molecule interacting with thermal radiation and with this he rederived Planck's blackbody spectrum.
