Here are a few examples of these inequalities. A glass tube with a diameter of 12 millimetres (.468 inch.--Translator's Note.), inside measurement, contains ten cells. The five lower ones, beginning with the bottom-most, have as the respective distances between their partitions, in millimetres: 11, 12, 16, 13, 11. (.429,.468,.624,.507,.429 inch.--Translator's Note.) The five upper ones measure between their partitions: 7, 7, 5, 6, 7. (.273,.273,.195,.234,.273 inch.--Translator's Note.) A reed-stump 11 millimetres (.429 inch.--Translator's Note.) across the inside contains fifteen cells; and the respective distances between the partitions of those cells, starting from the bottom, are: 13, 12, 12, 9, 9, 11, 8, 8, 7, 7, 7, 6, 6, 6, 7. (.507,.468,.468, .351,.351,.429,.312,.312,.273,.273,.273,.234,.234,.234, .273 inch.--Translator's Note.) When the diameter of the tunnel is less, the partitions can be still further apart, though they retain the general characteristic of being closer to one another the nearer they are to the orifice. A reed of five millimetres (.195 inch.--Translator's Note.) in diameter, gives me the following distances, always starting from the bottom: 22, 22, 20, 20, 12, 14. (.858,.858,.78,.78,.468,.546 inch.--Translator's Note.) Another, of 9 millimetres (.351 inch.--Translator's Note.), gives me: 15, 14, 11, 10, 10, 9, 10. (.585,.546,.429,.39,.39,.351,.39 inch.--Translator's Note.) A glass tube of 8 millimetres (.312 inch.--Translator's Note.) yields: 15, 14, 20, 10, 10, 10. (.585,.546,.78,.39,.39,.39 inch.--Translator's Note.). I could fill pages and pages with such figures, if I cared to print all my notes. Do they prove that the Osmia is a geometrician, employing a strict measure based on the length of her body? Certainly not, because many of those figures exceed the length of the insect; because sometimes a higher number follows suddenly upon a lower; because the same string contains a figure of one value and another figure of but half that value. They prove only one thing: the marked tendency of the insect to shorten the distance between the party-walls as the work proceeds. We shall see later that the large cells are destined for the females and the small ones for the males.