Convert from palmo [Texas] to gnat's eye

Unit Definition (palmo [Texas])
The palmo is a traditional unit of distance in Spain and Portugal. The traditional Spanish palmo equals 9 pulgadas or 1/4 vara. In Texas, 1/4 vara comes to 8 1/3 inches (21.17 centimeters). These units are based on the width of a person's outstretched hand, from the tip of the thumb to the tip of the little finger, a definition identical to that of the English span.

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).