Thus, a plane surface is a number of straight lines, in contact, in the direction called a plane. It is of greater or less extent, according as these lines are longer or shorter from a central point; it is of one shape or another shape, according as the lines are of the same length, or of different lengths. When they are all of one length, the surface is called a circle. As they may be of different lengths in endless variety, the surface may have an endless variety of shapes, of which only a few have received names. The square is one of these names, the triangle another, the parallelogram another, and so on.
Bulk, which is the other great modification of extension, is lines from a central point in every direction. This bulk is greater or less, according as these lines are longer or shorter. The figure or shape of this 50 bulk is different, according as the lines are of the same or different lengths. If they are of the same length, the bulk is called round, or, in one word, a sphere; sphere meaning exactly round bulk. As the lines, when they differ in length, may differ in endless ways; figures, or the shapes of bulk, are also endless, as our senses abundantly testify. Of these but a small number have received names. In this number are the cube, the cylinder, the cone. We name some shapes by referring to known objects; thus we speak of the shape of an egg, the shape of a pear, and so on.
It seems that nothing, therefore, is now wanting, to shew in what manner the relative terms, expressive of Quantity, are applied to all the modifications of extension.
After what has been said, it will not be difficult to ascertain the sensations on account of which we apply the same relative terms to cases of Weight.
Weight is the name of a particular species of pressure; pressure towards the centre of the earth. Pressure, as we have already fully seen, is the name we apply, when we have certain sensations in the muscles, just as green is the name we apply when we have a certain sensation in the eye. As green is the name of the sensation in the eye, pressure is the name of the sensation in the muscles. Pressure upwards, is one thing; pressure downwards, is another; pressure of a body, when that body is urged by another body, is one thing; pressure of a body, when it is not urged by another body, is a different thing: pressure of a body in altering the position of its parts is one thing; pressure, when there is no alteration of the position of its parts, is another thing. Of this last sort is weight, 51 the pressure downwards, or towards the centre of the earth, of a body not urged by another body, and not altering the position of its parts.
In supporting in my hand a stone, I resist a certain pressure; in other words, have certain muscular feelings, on account of which I call the stone heavy. I support other stones, and in doing so have muscular feelings, in one case similar, in another dissimilar. In the case of similarity, I call two stones equal, meaning in weight; in the case of dissimilarity, unequal; and so I apply all the other relative terms by which quantity is expressed.
It seems unnecessary to carry this analysis into further detail. The words equal, unequal: greater, less; applied to Motion, to Heat, and other modifications of sensation, have a meaning, which in following the course so fully exemplified it cannot be difficult to ascertain.
It seems still necessary that I should say something of the word Quantus, from which the word Quantity is derived. Quantus is the correlate of Tantus. Tantus, Quantus, are relative terms, applicable to all the objects to which we apply the terms, Great, or Little; they are applicable, therefore, to all the modifications of extension, of weight, of heat; in short, to all modifications which we can mark as degrees.
Of two lines, we call the one tantus, the other quantus. The occasions on which we do so are, when the one is as long as the other. Tantus, and Quantus, then, in this case, mean the same thing as equal, equal. They will be found to have the same import as equal, equal, when applied also to surface, and bulk; and so in all other compatible cases.
52 What then, it may be asked, is the use of them? If it should appear that they were of no use, it would not be very surprising; considering by whom languages have been made; and that redundancy is frequent in them as well as defect. In the present case, however, a use is not wanting.