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(4.) Magnitude.—Every body occupies space, that is, it has magnitude. This is a property observable by the senses in all bodies which are not so minute as to elude them, and which the understanding can trace to the smallest particle of matter. It is impossible, by any stretch of imagination, even to conceive a portion of matter so minute as to have no magnitude.

The quantity of space which a body occupies is sometimes called its magnitude. In colloquial phraseology, the word size is used to express this notion; but the most correct term, and that which we shall generally adopt is volume. Thus we say, the volume of the earth is so many cubic miles, the volume of this room is so many cubic feet.

The external limits of the magnitude of a body are lines and surfaces, lines being the limits which separate the several surfaces of the same body. The linear limits of a body are also called edges. Thus the line which separates the top of a chest from one of its sides is called an edge.

The quantity of a surface is called its area, and the quantity of a line is called its length. Thus we say, the area of a field is so many acres, the length of a rope is so many yards. The word “magnitude” is, however, often used indifferently for volume, area, and length. If the objects of investigation were of a more complex and subtle character, as in metaphysics, this unsteady application of terms might be productive of confusion, and even of error; but in this science the meaning of the term is evident, from the way in which it is applied, and no inconvenience is found to arise.