additions which proceed out to the number 250. It is a linear scale generated by the function , where n is an integer between 1 and 250, inclusive, and L is the length at mark 250. The geometric lines The next scales are called the geometric lines and are divided out to 50 in lengths which vary as the square root of the labeled values. If L represents the length at 50, then the generating function is , where n is a positive integer less than or equal to 50. The stereometric lines The stereometric lines are so called because their divisions are according to the ratios of solid bodies, out to 148. One of this scale's applications is to calculate, when given one edge of any solid body, the corresponding edge of a similar one that has a given volume ratio to the first. If L is the scale length at 148, then the scale-generating function is , where n is a positive integer less than or equal to 148. The metallic lines These lines have divisions on which appeared these symbols (Italian abbreviations): "or" (for , gold), "pi" (for , lead), "ar" (for , silver), "ra" (for , copper), "fe" (for , iron), "st" (for , tin), "mar" (for , marble), and "pie" (for , stone). These give the ratios and differences of specific weights of the materials. With the instrument set at any opening, the intervals between any correspondingly marked pair of points indicate the diameters of balls (or sides of other solid bodies) similar to one another and equal in weight. The polygraphic lines From the given information, the side length and the number of sides, the polygraphic lines yield the radius of the circle that will contain the required regular polygon. If the polygon required has n sides, then the central angle opposite one side will be 360/n. The tetragonic lines Tetragonic lines are so called from their principal use, which is to square all regular areas and the circle as well. The divisions of this scale use the function , between the values of 3 and 13. The added lines These added lines are marked with two series of numbers, of which the outer series begins near the outer end at a certain mark "D" (a semicircle symbol, not the capital letter D), which is followed (going inward) by the numbers 1, 2, 3,