Convert from gnat's eye to bee space

Unit Definition (gnat's eye)
The gnat's eye is an idiomatic "unit" of distance; it's common to hear that something is "as small as a gnat's eye". In fact, the eyes of typical gnats tend to have diameters similar in size to a hair's breadth: roughly 100-150 micrometers (0.10-0.15 millimeters).

Unit Definition (bee space)
The Bee Space is an informal unit of distance used in beekeeping. In a hive, bees seal up an opening smaller than a bee space, and they fill a larger opening with new honeycomb. If an opening is equal to a bee space, the bees leave it open as a passageway. A hive can be disassembled to remove the honey if the individual comb frames are carefully spaced one bee space apart. This discovery, made by the British beekeeper Lorenzo Longstroth in 1852, is crucial to modern beekeeping. The exact size of the bee space varies somewhat with the strain of bees being raised, but it is generally very close to 1/4 inch or 6.5 millimeters.