The dispersion of the cocoon shape and its Mahalanobis's generalized-distance between races

In this report, we extracted a characteristic of the cocoon shape by the Fourier coefficient. It was known that the basic cocoon shape of the Dumbbell (Japanese race) type, the Oval (Chinese race) type, and the Hybrid (Hybridized race) type could be mainly defined by the Fourier coefficients asub(2), asub(4), and asub(6) of the cosine terms. The principal components were obtained by using these coefficients that were standardized as asub(0)/2=12 millimeters. The cocoon shapes of a Dumbbell (Japanese race) type, a Oval (Chinese race) type and the Hybrid (Hybridized race) type are distinguishable by Fourier coefficients. In addition, using these coefficients, the Mahalanobis's generalized-distance between arbitrarily chosen two silkworm races is obtained.