For instance, if a grain is specified at 300 SRM, what is the equation to convert that to Lovibond? What is the equation to convert it back?
First, a little history. Joseph Lovibond developed the Lovibond Scale in the 1860's, as a means of implementing quality control into beer production. The Lovibond Scale works by having the user visually compare the shade of a substance to the nearest shade of colored disks. Thus, determination of a color on the Lovibond Scale is a human estimation, rather than a scientific measurement.
SRM, or standard reference method, is a more recent method, which measures the absorption of a substance using a spectrophotometer. The SRM was developed as an answer to the inaccuracies found in implementation of the Lovibond Scale.
The variance in measuring the color in °L has led different beer experts to develop different methods for converting between the two. They are as follows:
SRM = 1.4922 * (W * L / V) ^ .6859
SRM = (.2 * W * L / V) + 8.4
SRM = (.3 * W * L / V) + 4.7
where W = weight of malt (in lbs.) L = color of malt (in °L) V = volume of wort (in gal.)
Morey's formula gives a better approximation than the others, since it is a nonlinear conversion. However, if you want simpler math, both Mosher and Daniels' methods are good approximations.
Beer color is usually measured in SRM. Malts are often given in °L. In practicality, the discrepancy makes sense. I've never seen the inner workings at a maltster, but I imagine color is determined by holding a sample of grain next to a color palette and estimating it's darkness by comparison. On the other hand, if someone wanted to know the darkness of beer, it wouldn't be difficult to run a specimen through a spectrophotometer, and measure it's absorbency at 430 nm. It wouldn't be possible to run the malts through a spectrophotometer to find the SRM value, so °L is given instead, and human error is deemed acceptable.
From what I understand, the formula is:
°L = (SRM + 0.6) / 1.35
However, for all values light enough to be visibly different to the human eye, L=SRM. They only start splitting when you get too dark to be visibly different without a spectrometer.
There is a one to one correspondence as the SRM is the absorption at 430 nm and one can calculate the density at 430 nm of a Lovibond series 52 glass. The series 52 glasses are 'made up' of Lovibond R and Y glasses and the only people who can tell you what the composition of a series 52 glass are the people at The Tintometer Ltd and they used to do this in a leaflet they included with their instruments but it was demonstrated years ago that what they publish and what they sell are different. Using the published data we can calculate the absorption of the 52 series glasses ant 430 nm and compare to the SRM. Notice that nothing has been said about path or viewing light color both of which are important in the use of a Lovinbond tintometer. We do know that Miller and Stone adjusted the SRM multiplier to get °L and SRM to agree for the light beers they studied. Doing this the formula for SRM in terms of °L is SRM = °L + 0.04662*(°L)^2 and, going in the other direction °L = 0.808*SRM - 0.0083*SRM^2.