In studying the law of variation two facts are especially evident. (1) The law applies only to a series of terms representing notions of the same family. The extension and intension of “text book,” for example, could not be compared with the extension and intension of “house” as they belong to a different class of words, the genus of _text book_ being _book_, while the genus of _house_ is _building_. To illustrate the law of variation, determine upon any class name, then think of its proximate genus (the next _higher-up_ class to which it belongs). Continue this till the series is sufficiently complete to illustrate the law. Or proceed in the opposite direction. That is, after selecting the class name think of the next lower term in the class and thus continue till series is complete. Illustration: The class name _man_ is determined upon; the proximate genus of man is _biped_, the proximate genus of biped is _animal_, and so on. Or thinking downward: a proximate species of man is _white man_, of white man. _European_, etc. Thus the series: animal biped _man_ white man European (2) As a second fact: the increase and decrease is not a mathematical one. That is, by doubling the extension the intension is not halved. Or if the intension is decreased by one quality the extension is not necessarily increased by one object. Thus “man” stands for one billion seven hundred million beings or objects. Decrease the intension of “man” by the one quality of rationality and the extension would include all bipeds――many billion objects. =6b. THE LAW OF VARIATION DIAGRAMMATICALLY ILLUSTRATED.= In a general way _lines_ may be used to represent the variation in extension and intension. For example: we may let a line an inch long represent the extension of _man_, one two inches long represent the extension of _biped_, three inches long represent the extension of _animal_, etc. While on the other hand, if a line an inch long represents the intension of _man_, a line one-half inch long may be used to represent the intension of _biped_, one a quarter of an inch long to represent the intension of _animal_, etc. The following illustrates this scheme in connection with another series of words: _Extension_ _Intension_ ―― barn ―――――――― ―――― building ―――――― ―――――― structure ―――― ―――――――― object ――