The Moorsom System is a method created in the United Kingdom of calculating the tonnage or cargo capacity of sailing ships as a basis for assessing harbour and other vessel fees. It was put into use starting in 1849 and became British law in 1854.

Previous methods
Previous methods of calculating tonnage, such as Builder's Old Measurement, were not consistently applied. Additionally, the methods designed for sailing ships could not be applied appropriately or fairly to steamships. Substantial portions of a steamship were required for boilers, machinery and coal, thus limiting the proportion of the ship's space available for cargo.

Moorsom commission
In 1849, the United Kingdom appointed a Commission with Admiral George Moorsom as secretary to resolve these problems. The Commission determined that fees should be proportional to the earning capacity of the ship, whether for cargo or passengers. 

The result was called The Moorsom System, which set forth the rules for the measurement of the internal volume of entire ship.
 The total internal volume in cubic feet (0.028 m3) was divided by 100 to produce the gross register tonnage.
 Net register tonnage was the volume remaining after subtracting the volume of the space used for machinery and other non-revenue producing functions.

The Commission sought to avoid a significant change in the fees charged to an existing vessel when the new system was implemented.

George Moorsom ordered the entire fleet of British merchant ships to be measured according to the new System and then divided the total gross tonnage by the total registered tonnage.

The result was  per gross ton, which was rounded to  per ton.

International Convention

While the rules for measuring ships changed over the years, the standard of  per ton remained in effect until a new system was established by The International Convention on the Tonnage Measurement of Ships, effective for new ships in July 1982.

References

Admiralty law
Nautical terminology
Ship measurements