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), praemolars (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.

Sec. 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.

(3) It must not mention any circumstance that is not a part of the connotation, even though it be universally found in the things denoted.  Such a circumstance, if not derivable from the connotation, is called an Accident.  That, for example, the lion at present only inhabits the Old World, is an accident:  if a species otherwise like a lion were found in Brazil, it would not be refused the name of lion on the score of locality.  Whilst, however, the rules of Logic have forbidden the inclusion of proprium or accident in a definition, in fact the definitions of Natural History often mention such attributes when characteristic.  Indeed, definitions of superordinate classes—­Families and Orders—­not infrequently give qualities as generally found in the subordinate classes, and at the same time mention exceptional cases in which they do not occur.

II.—­As to its Expression—­

(4) A Definition must not include the very term to be defined, nor any cognate.  In defining ‘lion’ we must not repeat ‘lion,’ nor use ‘leonine’; it would elucidate nothing.