Three empirical relationships have been derived between reciprocals of pairs of partial dispersions of the ordinary optical glasses. The relationships are of the form X = a+b Y+c Y2 where X and Y are variable and a, b, and c the empirical constants. a, b, and c were determined by least squares making use of the data on sixteen optical glasses manufactured by The Bausch and Lomb Optical Company. The fit obtained appears to hold within the 5th place experimental error of the index determinations. Determination of ND and Nh, and the use of the three empirical relationships quoted above allows calculation of NF, NC, NG′, and V in a simple manner. These relationships, however, do not apply to the barium glasses.
D. H. RANK, "Empirical Relationships between the Partial Dispersions of the Ordinary Types of Optical Glasses," J. Opt. Soc. Am. 38, 885-885 (1948)