Repeating the process with a much larger square of paper, say of twelve ridge-intervals in the side, the improbability of correctly reconstructing the masked portion will have immensely increased. The number of ridges that enter the square on any one side will perhaps, as often as not, differ from the number which emerge from the opposite side; and when they are the same, it does not at all follow that they would be continuous each to each, for in so large a space forks and junctions are sure to occur between some, and it is impossible to know which, of the ridges. Consequently, there must exist a certain size of square with more than one and less than twelve ridge-intervals in the side, which will mask so much of the print, that it will be an even chance whether the hidden portion can, on the average, be rightly reconstructed or not. The size of that square must now be considered. If the reader will refer to Plate 14, in which there are eight much enlarged photographs of portions of different finger prints, he will observe that the length of each of the portions exceeds the breadth in the proportion of 3 to 2. Consequently, by drawing one line down the middle and two lines across, each portion may be divided into six squares. Moreover, it will be noticed that the side of each of these squares has a length of about six ridge-intervals. I cut out squares of paper of this size, and throwing one of them at random on any one of the eight portions, succeeded almost as frequently as not in drawing lines on its back which comparison afterwards showed to have followed the true course of the ridges. The provisional estimate that a length of six ridge-intervals approximated to but exceeded that of the side of the desired square, proved to be correct by the following more exact observations, and by three different methods.