To the naked eye this hymenium appears simply as a very thin smooth membrane, but when a small portion of it is viewed through a microscope with high powers its complex structure is readily observed and can be carefully studied. The _Sporidiferous_ fungi are represented by the families Physomycetes and Ascomycetes. The first of these consists wholly of microscopic fungi. _Ascomycetes._--In the plants of this family the spores are not supported upon basidia, but instead are enclosed in minute sacs or asci formed from the fertile cells of a hymenium. In this connection it would be well to state that Saccardo does not recognize the divisions _Sporifera_ and _Sporidifera_ by those names. They are nearly the equivalent of Basidiomycetes and Ascomycetes. What Cooke names Physomycetes, Saccardo calls Phycomyceteae, introducing it in his work between Gasteromyceteae and Myxomyceteae, which some mycologists consider somewhat out of place. Saccardo calls its asci (sacs which contain the spores) sporangia. He does not regard them as genuine asci, but as corresponding more to the peridium of the _Gasteromyceteae_ and _Myxomyceteae._ Peck says that this group seems to present characters of both Hyphomycetes and Ascomycetes, with a preponderance towards Hyphomycetes. It is a small group, however, and since it consists wholly of microscopic fungi, need not be farther considered in this work. In the Ascomycetes are included the sub-families Discomycetes, Pyrenomycetes, and Tuberacei. Of these the Discomycetes and the Tuberacei are the only groups which contain any of the mushrooms, and but few of these are large enough or sufficiently tender to possess value as esculents. A good example of the first (Discomycetes) is found in the Morel, and of the second (Tuberacei) in the Truffle. In the Discomycetes or "disk fungi," the spores are produced in minute membraneous sacs, each sac usually containing eight spores. These spore sacs are imbedded in the flesh of the exterior and upper surface of the mushroom cap. In the four classes, Hymenomycetes, Gasteromycetes, Discomycetes, and Tuberacei, therefore, are included all of the plants which are here designated under the generic term of "mushrooms." Some idea of the relative numerical value of these classes may be obtained from the following figures given by the distinguished British mycologist, M. C. Cooke: "Hymenomyceteae--total number of described species 9,600 Gasteromycetae-- " " " " " 650 Discomyceteae-- " " " known " 3,500" (The Tuberacei comprise a very small group of subterranean fungi, and comparatively few of the species are described.) Saccardo in his Sylloge gives a total of 42,000 described species of fungi of all classes, including the most minute. Of these the Hymenomycetes include by far the largest number of edible mushrooms.