number of teeth the wheel is to contain, and the product will be the circumference of the wheel: thus However, by inspecting the column marked Circumference, I find the nearest number to this is 19 feet 4 inches, which is the eighth of an inch less than the true circumference; but if this were divided into sixty equal parts, it would not make the difference of a single hair's-breadth in the size of each tooth; so that it is sufficiently near for any practical purpose. The diameter answering to this circumference is 6 feet 2 inches; consequently, with one half of this number as a radius, the circumference of the wheel will be described. The manner in which the foregoing Table of Circumferences is found is as follows: Taking the diameter at unity, we have by decimal proportion In. In. As 13-1416: : 1.: 3·1416, and the decimal 1416 multiplied by 8, gives the circumference for 1 inch of diameter 3 inches. In these Tables the number 3.1416 is divided by 8, which gives 3927. This decimal proportion has been used as a constant, and the sum multiplied by 8 gives the excess above the decimal value in eighths of an inch. Note. The nearest eighth of an inch is only given, as I thought it quite unnecessary to add the first decimal figure in this Table. J. F. |