Holding the endpoint signals fixed while distance changes exposes the gradient ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Three metres gives four per metre
Hold endpoint signals at 6 and 18. Separation 3 m gives gradient 4 per metre.
12/3=4
Four metres gives three per metre
The signal difference stays 12. With separation 4 m, the gradient is 3 per metre.
12/4=3
Six metres gives two per metre
At separation 6 m, the same endpoint difference gives gradient 2 per metre. The rows show inverse distance directly.