As the want of agreement between calculation and observation must be caused in part by the paucity of observations, it is worth while to make a larger group, by throwing the six series together, as in Table XXXIII., making a grand total of 965 observations. Their value is not so great as if they were observations taken from that number of different persons, still they are equivalent to a large increase of those already discussed. The six series of observed values were made comparable on equal terms by first reducing them to a uniform PE and then by assigning to M, the point of departure, the value of 0. The results are given in the last column but one, where the orderly run of the observed data is much more conspicuous than it was before. Though there is an obvious want of exact symmetry in the observed values, their general accord with those of the calculated values is very fair. It is quite close enough to establish the general proposition, that we are justified in the conception of a typical form of loop, different for the two thumbs; the departure from the typical form being usually small, sometimes rather greater, and rarely greater still. I do not see my way to discuss the variations of the arches, because they possess no distinct points of reference. But their general appearance does not give the impression of clustering around a typical centre. They suggest the idea of a fountain-head, whose stream begins to broaden out from the first. As regards other patterns, I have made many measurements altogether, but the specimens of each sort were comparatively few, except in whorled patterns. In all cases where I was able to form a well-founded opinion, the existence of a typical centre was indicated. It would be tedious to enumerate the many different trials made for my own satisfaction, to gain assurance that the variability of the several patterns is really of the quasi-normal kind just described. In the first trial I measured in various ways the dimensions of about 500 enlarged photographs of loops, and about as many of other patterns, and found that the measurements in each and every case formed a quasi-normal series. I do not care to submit these results, because they necessitate more explanation and analysis than the interest of the corrected results would perhaps justify, to eliminate from them the effect of variety of size of thumb, and some other uncertainties. Those measurements referred to some children, a few women, many youths, and a fair number of adults; and allowance has to be made for variability in stature in each of these classes.