This section is from the book "Commercial Gardening Vol1", by John Weathers (the Editor). Also available from Amazon: Commercial Gardening, A Practical & Scientific Treatise For Market Gardeners.
Most true bulbous plants, like Tulips, Daffodils and Narcissi, Hyacinths, Liliums, Snowdrops, etc, produce offsets from the parent bulbs. When the offsets are detached and replanted they produce flowering plants the following season, or a season or two afterwards. If some bulbous plants - e.g. Daffodils and Snowdrops - are left undisturbed for years they increase rapidly and produce numerous bulbs. Nerines, Vallotas, Hippeastrums, Crinums, Pancratiums, etc, also develop numerous offsets from the base of the older bulbs.
Corms as produced by Gladioli, Montbretias, Crocuses, Colchicums, are known as "solid" bulbs - as they have no coats as in Tulips and Daffodils or thick scaly leaves as in Liliums. They produce numerous offsets, but the old corm always shrivels up or vanishes while the new ones are forming on top. In such corms as those of the florists' Gladioli (Brenchley-ensis, Childsi, Lemoinei, and Nanceianus) numerous seed-like outgrowths are also to be seen. These are known as "spawn" and will produce new plants in a year or two if sown like seeds in nice gritty soil.
In the case of tuberous plants like the Arum Lily, Jerusalem Artichoke, the Potato, the Dahlia, etc, large numbers of tubers or tuberous roots are produced, each one of which will give rise to one or more plants. The tubers of the Artichoke and Potato, for example, if cut into pieces each containing an "eye" or bud, will produce several plants. The tuberous roots of the Dahlia and the herbaceous Paeony, however, must have a piece of the old stem attached, as no shoots are produced by the roots themselves. The tubers of Begonias, Cyclamen, and Gloxinias may be cut into pieces each with an eye or sprout.
Underground stems or rhizomes, as met with in the German, Florentine, and other Irises, Solomon's Seal, Mint, etc, are utilized for increasing the stock, each portion having a bud being capable of forming a new plant.