Convert from gill [UK] to gallon [US, dry]

Unit Definition (gill [UK])
The gill [UK] is a traditional unit of volume for liquids, especially wine and other alcoholic beverages. The gill is 1/4 pint. In the British Imperial system, the gill equals 5 fluid ounces, 8.670 cubic inches, or about 137.7 milliliters. The unit is pronounced "jill", with a soft "g" sound. Its name comes a Latin word gillo for a small wine vessel.

Unit Definition (gallon [US, dry])
The gallon [US, dry] is a historic British unit of dry volume still used implicitly in the U.S. In the U.S., the term "gallon" is not used in dry measure, but if it were it would be equal to 1/2 peck, or 4 dry quarts, or 268.8025 cubic inches, or approximately 4.404 884 liters. This unit is the English corn or grain gallon, standardized during the reign of Elizabeth I in the sixteenth century. The earliest official definition of a dry gallon in Britain is a 1303 proclamation of Edward I, where the gallon is defined as the volume of 8 pounds of wheat; the current U.S. "gallon" contains about 7.5 pounds of wheat. Grain gallons have tended to be larger than liquid gallons throughout the history of British units, apparently because they were based on heaped rather than "struck" (leveled) containers. A container in which grain has been heaped above the top will hold as much as 25% more grain, and the traditional corn gallon is in fact 16.4% larger than the wine gallon.