Page:Proceedings of the Royal Society of London Vol 60.djvu/249

228 The critical function 2/32—3/h—6 = —-0087561 is negative, and so the theoretical curve has a limited range. The calculated range was 7T313123 units, and the observed range 21 units; thus they differed very widely. The range on the positive side of the origin was 31*658658, and on the negative side 39*654465. As the frequency curve is very symmetrical, Professor Pearson’s generalised curve with limited range and symmetry was taken,

The distance of maximum ordinate from centroid vertical is 0*0596, and this could not be indicated on the scale of diagram. Both this and the normal curve are drawn over the curve of observation (fig. 3). The ‘generalised curve differs exceedingly little from the normal one, the areal deviations in the two cases being 7*7 and 7*5 per cent, respectively.

The flat top to the frequency curve made it at first seem probable that the curve was really the resultant of two normal ones. It was attempted to resolve it into its constituents by means of Professor Pearson’s equation of the ninth degree (‘Phil. Trans.,’ vol. 185). There were three real roots to the equation; two gave quite inappropriate solutions; the third gave a negative group of sixty crabs (with standard deviation = 1*450), having its maximum ordinate situated at —1*337 from the centroid, and a positive group of 1492 crabs (standard deviation = 3*012), with maximum ordinate at 0*0540. The selection of crabs so close to the mean would scarcely seem to correspond to any natural phenomenon, and the resultant curve, which was the difference of the two normal curves, fitted the curve of observation but very little better than the normal or skew curve in fig. 3, the areal deviation being 7*0 per cent.

L. Antero-lateral.—Here the range of the mean is somewhat larger than on the right side, being about 1^- units. The range of deviation in the whole series is 720—823 thousandths. A frequency curve was drawn (fig. 4) with groups 6—12, where the range was 724—819 thousandths, giving 24 units.

y = y0( l —*2/a2)m, where y0 = 186*357143. a = 35*656561. to = 66*048343. Centroid = 14*046787. = 9*127467. a = 3*021170. fi3 = -1*885642. /h - 263*267646. A = 0*004676. yS2 = 3*160072. r = 42*246651. Skewness = 0*031099.