Organizing diggers to excavate a mile of ditch
Pyramidal gangs of workmen, and the reckoning of shovelfuls, years and ducats
This sheet is a study in organizing labour to excavate a great ditch or moat. Leonardo argues that a gang of diggers set across the trench must be ranged in a pyramidal (tapering) line so that earth passed hand to hand keeps the floor level, illustrating the idea with several plans of numbered workmen and relays. A long left-hand column and columns of arithmetic then reckon a mile of ditch at over 130 million shovelfuls, some 148 years for 14 men, and about 37,000 gold ducats. A marginal jotting names 'Ser Franco' and twice repeats that 'it was never done.'
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Diggers ranged across the ditch in a pyramidal line
Men set across the width of the ditch dig only as deep as one man can, the one farthest from the bank, and pass earth from hand to hand up onto the mound heaped above. Because each stage removes only what the man ahead can take, the excavation forms a pyramidal figure with its base at the first digger and its point at the foot of the earth-heap. When the workers are equal, the line a n stays straight and no mounds ever build up.
Passing earth hand to hand: the relays must be equal
If man b lifts the earth from a into c, and o adds his, then c holds three shovelfuls; the two men at d move these to v, where n adds one, and so on up the line. Each relay must carry more workers than the last so the flow stays even, which is why the diggers must be arranged in pyramidal number and position.
The cost of the ditch reckoned in gold ducats
A canna equals 11,520 shovelfuls, and 27,000 canne, one mile of ditch, come to over 130 million shovelfuls. At two days per square canna the work would take about 148 years for 14 men, or one year for 2,072 men. At 7 soldi a day the digging amounts to some 37,000 gold ducats, and every soldo added raises the total by 3,000 ducats.
Columns of calculation figuring days, men and money
Several columns of long multiplication and division work through the totals, handling 27,000 canne, 54,000 days, the 365-day year and figures running up to 130,400,000. They reduce the mile of ditch to the number of men, day-works and ducats required.