And astonishing as this statement may be, we have still to add that, in face of the actual facts, it may be regarded as even a moderate estimate of the abundance of spirals in the universe. We must remember that a spiral nebula is a flat object with long arms extending from it which lie nearly in the same plane. If we are actually to see that such an object is spiral, it is necessary for it to be turned squarely towards the earth. If the object be too much foreshortened, it is quite plain that we can hardly expect to detect its spiral character. It is also obvious if the spiral happens to be turned edgeways towards us, that then its spiral form cannot be seen; it would merely appear as what astronomers often call a ray. In the enumeration of the spirals it is therefore only possible for us to include those which happen to be so far squarely turned towards the earth as to make their spiral character unmistakable. We might, therefore, reasonably expect that the numbers of spiral nebulæ actually counted would fall short of the reality. We know that there are many nebulæ of a somewhat elliptical shape (Fig. 31). There are also many nebulæ that look like long rays (Fig. 30). Those who are familiar with the appearance of nebulæ in great telescopes will recall at once the numerous spindle-shaped objects of this class. It can hardly be doubted that many of the nebulæ, more or less oval in form, and also these rays or the spindle-shaped objects so frequently seen in good telescopes (Fig. 33) are in reality spiral nebulæ, which are turned not squarely towards us, but which we are merely looking at more or less edgewise, so that they have been foreshortened enough to hide their peculiar structure (Figs. 34, 35). Taking these considerations into account, it becomes obvious that the estimate of Professor Keeler as to the number of spiral nebulæ in the heavens, vast as that estimate seems, may still fall short of the truth. Thus we are led to one of the most remarkable conclusions of modern astronomy, viz. that the spiral nebula, next to a star itself, is the most characteristic object in the sidereal heavens.