card houses: the laws of nature and the reason of man are alike against it, in arts, as in politics. There is but one thoroughly ugly tower in Italy that I know of, and that is so because it is divided into vertical equal parts: the tower of Pisa.[12] XXIX. One more principle of Proportion I have to name, equally simple, equally neglected. Proportion is between three terms at _least_. Hence, as the pinnacles are not enough without the spire, so neither the spire without the pinnacles. All men feel this and usually express their feeling by saying that the pinnacles conceal the junction of the spire and tower. This is one reason; but a more influential one is, that the pinnacles furnish the third term to the spire and tower. So that it is not enough, in order to secure proportion, to divide a building unequally; it must be divided into at least three parts; it may be into more (and in details with advantage), but on a large scale I find three is about the best number of parts in elevation, and five in horizontal extent, with freedom of increase to five in the one case and seven in the other; but not to more without confusion (in architecture, that is to say; for in organic structure the numbers cannot be limited). I purpose, in the course of works which are in preparation, to give copious illustrations of this subject, but I will take at present only one instance of vertical proportion, from the flower stem of the common water plantain, _Alisma Plantago_. Fig. 5, Plate XII. is a reduced profile of one side of a plant gathered at random; it is seen to have five masts, of which, however, the uppermost is a mere shoot, and we can consider only their relations up to the fourth. Their lengths are measured on the line A B, which is the actual length of the lowest mass _a b_, A C=_b c_, A D=_c d_, and A E=_d e_. If the reader will take the trouble to measure these lengths and compare them, he will find that, within half a line, the uppermost A E=5/7 of A D, A D=6/8 of A C, and A C=7/9 of A B; a most subtle diminishing proportion. From each of the joints spring three major and three minor branches, each between each; but the major branches, at any joint, are placed over the minor branches at the joint below, by the curious arrangement of the joint itself--the stem is bluntly triangular; fig. 6 shows the section of any joint. The outer darkened triangle is the section of the lower stem; the inner, left light, of the upper stem; and the three main branches spring from the ledges left by the recession. Thus the stems diminish in diameter just as they diminish in height. The main branches (falsely placed in the profile over each other to show their relations) have respectively seven, six, five, four, and three arm-bones, like the masts of the stem; these divisions being proportioned in the same subtle manner. From the joints of these, it seems to be the _plan_ of the plant that three major and three minor branches should again spring, bearing the flowers: