§ 3. A Definition is necessary (if possible) for every scientific name. To define a name is to give a precise statement of its meaning or connotation. The name to be defined is the subject of a proposition, whose predicate is a list of the fundamental qualities common to the things or processes which the subject denotes, and on account of possessing which qualities this name is given to them. Thus, a curve is a line of which no part is straight. The momentum of a moving body is the product of its mass and its velocity (these being expressed in numbers of certain units). Nitrogen is a transparent colourless gas, atomic weight 14, specific gravity .9713, not readily combining, etc. A lion is a monodelphian mammal, predatory, walking on its toes, of nocturnal habits, with a short rounded head and muzzle; dental formula: Incisors (3-3)/(3-3), canines (1-1)/(1/1), præmolars (3-3)/(2-2), molars (1-1)/(1-1) = 30; four toes on the hind and five on the fore foot, retractile claws, prickly tongue, light and muscular in build, about 9-1/2 feet from muzzle to tip of tail, tawny in colour, the males maned, with a tufted tail. If anything answers to this description, it is called a lion; if not, not: for this is the meaning of the name. For ordinary purposes, it may suffice to give an Incomplete Definition; that is, a list of qualities not exhaustive, but containing enough to identify the things denoted by the given name; as if we say that a lion is 'a large tawny beast of prey with a tufted tail.' Such purposes may also be served by a Description; which is technically, a proposition mentioning properties sufficient to distinguish the things denoted, but not the properties that enter into the definition; as if nitrogen be indicated as the gas that constitutes 4/5 of the atmosphere. § 4. The rules for testing a Definition are: I.--As to its Contents-- (1) It must state the whole connotation of the name to be defined. (2) It must not include any quality derivative from the connotation. Such a quality is called a Proprium. A breach of this rule can do no positive harm, but it is a departure from scientific economy. There is no need to state in the definition what can be derived from it; and whatever can be derived by causation, or by mathematical demonstration, should be exhibited in that manner.