Table of the Radii of Wheels, from Ten to Three Hundred Teeth, the Pitch* being Two Inches. By Mr.B. DONKIN, Millwright, Dartford, Kent. * By the Pitch is understood the distance between the centres of two contiguous teeth; and by the radius is understood the distance between the centre of the wheel and the centre of each tooth. For any other pitch, say, as two inches is to the radius in the table, so is the given pitch to the radius required. APPENDIX, No. II. TO ESSAY ON TEETH OF WHEELS. ON THE USE OF CHARTS, AND SOME FURTHER EXPLANATION OF THE CONSTRUCTION OF THE TABLES OF PITCHES OF WHEEL-WORK. 1. WHEN quantities of any kind, such as time, space, money, &c. expressed in numbers, are mentioned, it often requires a painful exertion of the mind to recollect and compare them. Hence the utility of bringing them into one view in Tables. But there is another mode of comparing quantities not so generally practised, though, in many cases, much more easy and satisfactory to the mind. I allude to charts, in which, instead of using figures, as in tables, the quantities are geometrically represented. This is done by dividing the sides of a square or rectangle into equal parts, and drawing parallel lines at right angles from the divisions. The quantities are pointed off at certain intersections of these scales. 2. When the quantities increase or decrease in arithmetical proportion, as 1,2,3,4, &c. that Y proportion will be represented by a straight line, which will pass through these points. 3. But supposing the quantities to increase in geometrical proportion, as 1,4,9,16, &c. the line passing through the points of intersection will form a curve. These two cases will be best explained by examples. 4. First, Suppose the value of any thing to increase as its weight,-the scale on the one side of the square will then represent the value, and that on another the weight. Let A C Fig. 1st, represent weight (say ounces), and A D value (say shillings). Now, suppose we mark the price of four ounces, it is done by placing a dot opposite to four, on the line of value, and opposite to four on the line of weight, at the intersections of the perpendiculars from these points, which intersection is marked by b d on the figure. In the same manner, we may mark the value of 1, ,2,3,5,6 ounces. These points are marked abcef, and the straight line A B passes through them all, and shews the regular progress of the proportion. It is of no consequence whether the divi sions on the line A C be greater or less than |