Wheel-diameter calculation and a recipe for making indigo
Rule-of-three sizing of a wheel and its gear teeth, with a colour recipe
The upper fragment (sheet 570a) explains how to find a wheel's diameter from its circumference by the rule of three, using the ratio 22 to 7, and gives a rule for matching the teeth of a smaller wheel to those of a larger one so they engage properly; a small toothed wheel and columns of figures accompany the text. The lower fragment (sheet 570b) is a recipe 'to make indigo' from woad flowers and starch kneaded with urine and vinegar, dried in the sun and adjusted for depth of colour. The two are unrelated notes mounted on one sheet.
On this page
Sizing a wheel and its gear teeth
To find the diameter of any wheel from its circumference, apply the rule of three to the ratio 22 (circumference) to 7 (diameter); for a circumference of 36 this yields about 11 and 5/11 as the wheel's height, when the hub is 1/3 thick. A further rule removes from the smaller wheel a portion whose arc matches the height of its teeth, so its teeth stay engaged with those of the larger wheel along that arc.
Columns of calculation
Beside the wheel note stand worked figures — 36, 22, 7 and repeated multiplications and divisions such as 252, 11, 24 and 312 — carrying out the rule-of-three computation described in the text.
Recipe to make indigo
Take woad flowers and starch in equal parts, knead them together with urine and vinegar, form a cake and dry it in the sun; if it comes out pale, add more woad flowers and re-knead until the colour is as dark as you wish.