Turning the comb over, we see that the cells on this side also have pyramidal bottoms. If the depth of a cell on one side of the comb be taken, and added to the depth of a cell on the other side, and then the width of the whole comb be measured, it will be found that the combined depth of the two cells perceptibly exceeds the width of the whole comb. At first glance this seems like a case of the less including the greater, which is a manifest impossibility. But, holding the comb up to the light, a further discovery is made, and the seeming paradox is eliminated. The bottoms of the cells are so thin as to be almost transparent, and it is at once seen that the cells are not built end to end, in line, but that each cell-base on one side of the comb covers part of three cell-bases on the other. If the three diamonds, composing between them the triangular base of a single cell, be perforated with a needle, and the comb turned over, it will be found that the three perforations come each in a separate cell. Thus the saving in the total width of the comb is effected by allowing the pyramidal bases on each side to engage alternately like the teeth of a trap; instead of meeting point-blank, they overlap each other, and the faces of the pyramids are so contrived that each of them helps to close two cells. There is another advantage in this arrangement which will be immediately obvious. The apex and three ribs of each pyramidal cell-base form foundation-lines for the cell-walls on the other side of the comb. This means that not only do all cell-walls abut on an arch, but that every cell-base is strengthened throughout by a triple girdering. The result is that the amount of wax required in the construction of the comb can be everywhere reduced to an absolute minimum. It becomes merely a question of what thickness of wax will retain the honey; and this experience proves to be no more than 1/180 part of an inch. The whole thing, indeed, might very well be taken as an ideal exemplar of the triumph of mind over matter.