The difficulty of expressing the complex reactions of puering numerically is, we have seen, very great, for, as Minot[71] says, “with human minds constituted as they actually are, we cannot anticipate that there will ever be a mathematical expression for any organ or even a simple cell, although formulæ will continue to be useful for dealing now and then with isolated details. Nevertheless, the value of graphic methods to every student of science has been immense.” [71] Minot, Address to Amer. Assoc. for Advancement of Science, Minneapolis, Dec. 29, 1910. Nature, 1911, p. 96. It has long been my endeavour to express quantitatively the degree to which a skin has fallen. My friend Dr. Sand has suggested that this may be done by subjecting a piece of the skin successively to increasing and then decreasing pressures, and measuring the thickness under each load. Experiments carried out with the apparatus described below show that a limed skin treated in this way is first compressed, and then on releasing the pressure recovers more or less of its former thickness, according to the amount of plumping it has received, i.e. it shows a certain amount of resilience. A well-puered sheep-skin, on the other hand, shows no resilience at all, i.e. on releasing the pressure the whole of the compression persists. In the case of an ox-hide subjected to a bate of hen-dung, a slight recovery takes place on releasing the pressure. This accords with the fact that it will never be possible to puer a thick ox-hide so effectively as a thin sheep-skin. A piece of india-rubber, on the other hand, is completely resilient, i.e. it wholly recovers its thickness on releasing the pressure. The relative thickness of the same skin in the limed and puered conditions under varying loads is also of interest. The process of puering may, as a rule, be taken to reduce a limed skin to between two-thirds and one-half of its thickness in the swollen condition. If both limed and puered skin be then subjected to the same load, the puered skin will at first be compressed very much more than the limed one. This is probably due to the expulsion from it of water, held simply by capillary attraction. On further increasing the load, however, the compression decreases greatly in the case of the puered skin; with both limed and puered skin increase of compression ultimately becomes practically proportional to increase of pressure, and is slightly greater with the former than with the latter. The table gives representative results obtained on the same sheep-skin (roan) in the limed and in the puered condition. These results are expressed graphically in Fig. 12.