The dividing head in the figure has a 40 : 1 worm ratio and the index plates listed on the figure. (a) A spur gear of 52 teeth is to be cut by simple indexing: how many holes must the crank be advanced per tooth on the hole circle that has to be used (answer in holes)? (b) A 97-tooth gear is to be cut by differential indexing using an approximate number A' = 100. Using the 20-hole circle, how many holes must the crank be advanced per tooth (answer in holes)? (c) For the same 97-tooth job, find the gear ratio (driver on spindle / driven on index plate) of the differential change gears, taking ratio = 40(A' − N)/A' (answer as a ratio, dimensionless).