(2) μ_2 = a^2(1 + 6x + 15x^2 + 2κ^2) 2κ^2(2κ^2 + Q)^2 (3) β = —————————————————————— (2κ^2 + R)^3 4κ^4 + 4κ^2S + T (4) ϵ = —————————————————————— (2κ^2 + R)^2 where the symbols, S, R, Q and T are defined as follows: S = 1 + 18λ + 90λ^2, R = 1 + 6λ + 15λ^2, Q = 1.5 + 18λ + 135/2λ^2, T = 2λ + 36λ^2 + 270λ^3 + 810λ^4. Obviously no algebraic solution can be obtained from equations (3) and (4) for κ and λ in terms of the computed values β and ϵ, and hence a resort to tables is necessary. The values of β and ϵ for values of κ from 0 to 0.0335 and of λ from -0.040 to +0.100 have been computed.[10] The process of determining the constants of the translated normal curve consists first in computing β and ϵ from the given data, and then in entering the table and interpolating for the corresponding values of κ and λ.[11] On substituting these values in (2) the value of a can be found and thence on multiplying a by κ the position of the median of the distribution is obtained. The sign of κ is determined by the sign of the third moment about the mean μ_3, that is, by the direction of the skewness or asymmetry. For positive skewness the mean must lie to the right of the median and hence μ_1´, the first moment about the mean, must be positive which necessitates a positive sign for κ. Therefore, the sign of κ is the same as that of the skewness. To fit a curve to the given data, after the constants have been determined it is necessary to find, by solving a cubic equation for each value, the values of t corresponding to the x’s of the respective classes. The cubic is aλt^3 + aκt^2 + at - x = 0. Any of the various methods of approximating to the solution of a cubic may be used in solving these equations. The area of each class can now be obtained by computing the corresponding areas under the standard normal curve from a table of the probability integral. =The Method of Interpolation.= The actual fitting of the curve can now be readily accomplished.[12] The distinctively geometrical operation is the interpolation for the values of λ and κ for a given pair of values of β and ϵ. Within the limits of the table[13] the curves resulting from the assignment of a constant value to β are practically straight lines, β = 0 is the λ-axis; β = 1 is a line parallel to the λ-axis. Hence we may safely assume that the variation from one column to the next and from one line to the next is linear for values of β. That is, ordinary first difference interpolation methods are applicable. As regards the system of ϵ curves we have for instance ϵ = .128 at (λ = .050, κ = 0); again, at approximately (.045, .060) and (.40, .085). We are therefore warranted in assuming the applicability of first difference methods to interpolation between the ϵ curves.