which naturalists choose to fix upon, and which it is not possible to define more exactly. This use of the term, then, has no connection whatever with the logical use, according to which any class of things whatever is a species, provided it is regarded as part of a wider class or genus.

The fourth of the Predicables is Property (Latin proprium, Greek idov, own), which it is hardly possible to define in a manner free from objection and difficulty, but which may perhaps be best described as any quality which is common to the whole of a class, but is not necessary to mark out that class from other classes. Thus it is a property of the genus "triangle" to have the three internal angles equal to two right angles; this is a very remarkable circumstance, which is always true of triangles, but it is not made a part of the genus, or is not employed in defining a triangle, because the possession of three straight sides is a sufficient mark. The properties of geometrical figures are very numerous; the Second Book of Euclid is occupied in proving a few properties of rectangles; the Third Book similarly of circles. As we commonly use the term property it may or may not belong to other objects as well as those in question; some of the properties of the circle may belong also to the ellipse; some of the properties of man, as for instance the power of memory, or of anger, may belong to other animals.

Logicians have invented various subtle divisions of properties, but it will be sufficient to say that a peculiar property is one which belongs to the whole of a class, and to that class only, as laughter is supposed to belong only to mankind; the property of containing the greatest space in a line of given length is peculiar to circles. When a property is not peculiar, it may belong to other classes of objects as well as that of which it is called the property. We may further distinguish the Generic Property, or that

which belongs to the whole of the genus, from the Specific Property, which belongs to the whole of a lowest species.

Lastly, an accident (Latin accidens, Greek ovμßeßŋKós) is any quality which may indifferently belong or not belong to a class, as the case may be, without affecting the other qualities of the class. The word means that which falls or happens by chance, and has no necessary connection with the nature of a thing. Thus the absolute size of a triangle is a pure accident as regards its geometrical properties; for whether the side of a triangle be of an inch or a million miles, whatever Euclid proves to be true of one is true of the other. The birthplace of a man is an accident concerning him, as are also the clothes in which he is dressed, the position in which he rests, and so on. Some writers distinguish separable and inseparable accidents. Thus the clothes in which a man is dressed is a separable accident, because they can be changed, as can also his position, and many other circumstances; but his birthplace, his height, his Christian name, &c., are inseparable accidents, because they can never be changed, although they have no necessary or important relation to his general character.

As an illustration of some part of the scheme of classification described under the name of Predicables, I may here give, as is usual in manuals of Logic, the Tree of Porphyry, a sort of example of classification invented by one of the earliest Greek logicians, named Porphyrius. I have simplified the common form in which it is given by translating the Latin names and omitting superfluous words.

In this Tree we observe a succession of genera and species-Substance, Body, Living Being, Animal and Man. Of these Substance is the summum genus, because it is not regarded as a species of any higher class; Man

is the infima species, because it is a class not divided into any lower class, but only into individuals, of whom it is

usual to specify Socrates and Plato. Body, Living Being, and Animal are called subaltern genera and species, because each is a species as regards the next higher genus, and a genus as regards the next lower species. The qualities implied in the adjectives Corporeal, Animate, Sensible (i.e. capable of feeling) and Rational are the successive differences which occasion a division of each genus into species. It will be evident that the negative parts of the genera, namely Incorporeal Substance, In

animate Body, &c., are capable of subdivision, which has not been carried out in order to avoid confusing the figure.

Logical division is the name of the process by which we distinguish the species of which a genus is composed. ‹ Thus we are said to divide the genus "book" when we consider it as made up of the groups folio, quarto, octavo, duodecimo books, &c., and the size of the books is in this case the ground, basis, or principle of division, commonly called the Fundamentum Divisionis. In order that a quality or circumstance may be taken as the basis of division, it must be present with some and absent with others, or must vary with the different species comprehended in the genus. A generic property of course, being present in the whole of the genus, cannot serve for the purpose of division. Three rules may be laid down to which a sound and useful division must conform :

2.

I. The constituent species must exclude each other. The constituent species must be equal when added together to the genus.

3. The division must be founded upon one principle or basis.

A

It would be obviously absurd to divide books into folio, quarto, French, German and dictionaries, because these species overlap each other, and there may be French or German dictionaries which happen to be quarto or folio and belong to three different species at once. division of this kind is said to be a Cross Division, because there is more than one principle of division, and the several species in consequence cross each other and produce confusion. If I were to divide rectilineal figures into triangles, parallelograms, rectangles and polygons of more than four sides, I should commit all the possible faults in one division. The species parallelogram and rectangle do not exclude each other, since all rectangles must be

parallelograms; the constituent species are not altogether equal to the genus rectilineal figure, since irregular foursided figures which are not parallelograms have been omitted; and there are three principles of division, namely the number of sides, the directions of those sides, and the angles contained. But when subdivision is employed, and each of the species is considered as a genus which may be subjected to a further separation, a new principle of division may and in fact must be employed each time. Thus I can divide rectilineal figures according to the three principles mentioned above:

Here the principles of division are the number of their sides, and in the case of four-sided figures their parallelism. Triangles do not admit of division in this second respect. We may make a new division of parallelograms, adopting the equality of sides and the size of the angles as the principles; thus:

The most perfect divisions in a logical point of view are produced by continually dividing each genus into two