Cargill G. Knott and the abacus

 A Scottish scientist writes about soroban

Prof. Cargill G. Knott

Cargill Gilston Knott (30 June 1856 – 26 October 1922) was a Scottish physicist and mathematician who was a pioneer in seismological research. From 1883 to 1891 he was  Professor of Physics and Engineering at Tokyo Imperial University and on the conclusion of his stay in Japan in 1891, he was awarded the Order of the Rising Sun by Emperor Meiji. During this period he came into contact with the soroban abacus which he studied in depth and wrote a complete article on its history and methodology in 1885.

Almost 140 years after its publication, this article still deserves a reading by fans of abacus. Personally, I would highlight the clear vision he presents of the traditional division (kijoho 帰除法) and especially the analysis carried out on the traditional methods of extraction of square and cubic roots (hankukuho 半九九法 and sanbunkukuho 三分九九法), where he indicates the different philosophy followed in the methods used in paper and pencil calculations (preparation of the divisor) and the corresponding ones followed on the abacus (preparation of the dividend) for both types of roots. 

Although for cube roots I still prefer the (non-traditional) Newton's  method, I am indebted to Knott for changing my view of traditional  methods, and the discovery that a modest abacus with only 13 rods has enough space to process up to four digits of such a root if I follow the procedure explained by him, and up to eight figures if I complete the process with the corresponding abbreviated operation, but this is a very very long process ...

You can read his article: The Abacus, in its Historic and Scientific Aspects in archive.org.