It also sometimes happens that staminate and pistillate flowers are also naked, so that in such cases the flower is represented by stamens alone, or even by a single stamen, or by carpels alone, or by a single carpel. It would be hard to imagine a more simple flower than one composed of a single stamen or a single carpel. Such flowers may be found in the willows.

In this study of the lily it should be observed that the number three runs through all the parts of the flower. The flower formula may be expressed as follows: sepals 3, petals 3, stamens 3 plus 3, carpels 3. This number is established in many families related to the lilies, and is one of their characteristic features.

In other groups of flowering plants a different number is established, the number five being the most common. For example, in the common wild geranium the flower formula is as follows: sepals 5, petals 5, stamens 5 plus 5, carpels 5. In still other flowers the number four is established.

In many common flowers it will be noticed that no definite number is established, or that it is not completely established. For example, in the common wild rose there are 5 sepals and 5 petals, but an indefinite number of stamens and carpels; while in the water lily there is no definite number established, the sepals being usually 4, and the other parts indefinitely repeated.

In those flowers in which some number is definitely established, it often happens that one set may be reduced in number, and this is usually the carpel set. In the families of highest rank among flowering plants, such as the figworts, mints, and composites (sunflowers, asters, dandelions, etc.) the flower formula is sepals 5, petals 5, stamens 5, and carpels 2.

Another fact shown by the lily flower is that the different sets alternate with each other in position. The three petals do not stand directly in front of the three sepals, but in front of the spaces between the sepals. In the same way the three outer stamens alternate with the petals; the inner stamens alternate with the outer ones; and the three carpels alternate with the inner set of stamens. It is very uncommon to find one set standing directly in front of the next outer set, and this position opposite the other set always needs some special explanation. As a rule, therefore, the flower sets alternate with one another, but in some cases a set may be opposite.

The history of a flower does not end with the opening of the blossom. If the stigma has succeeded in receiving some pollen, and the pollen has succeeded in doing its work, the ovules within the ovary become gradually transformed into seeds, and the ovary becomes transformed into the fruit, the outer sets of the flower usually disappearing. In the lily these fruits take the form of dry pods, some of which may be seen in the illustration. Such pods have various ways of opening to discharge their ripened seeds.

In many cases the commonly recognized fruit includes more than the ovary. For example, in the apple and pear the modified ovary is represented by what is called the "core," and the pulpy part outside, forming the edible part of the fruit, is the thickened calyx. In the strawberry the real fruits are the small, nut-like "pits" which are more or less imbedded in the surface, while the pulpy part is the very much enlarged and fleshy tip of the stem which bore the numerous carpels. In the pineapple the change involves a whole flower cluster, and a pineapple is a cluster of flowers which has formed a pulpy mass, flowers, leaves, stems, and all.

From what has been said it will be noticed that some fruits ripen dry, as in the case of the lily pod, bean pod, etc., and that others ripen fleshy, as in the case of apples, strawberries, etc. It must not be supposed that flesh can only be formed by parts outside of the ovary, for the peach is a modified ovary, whose wall has separated into two layers, the outer of which forms the pulp, and the inner the "stone," the kernel within the stone being the real seed.

Whatever form or structure the fruit may take, everything is with reference to the dispersal of the seeds, which must be carried to places suitable for their germination. How seeds are carried about is a long story, which must be deferred to some later time, but it belongs to the general subject of flowers.