He served three terms as president of this Society, first from 1873 to 1878, for the second time from 1886 to 1890, and for the third time from 1895 until his death in 1907. Thomson served as president of yet a third society when he was elected as president of the British Association for the Advancement of Science in 1871.
Siya nagsilbi ng tatlong termino bilang pangulo ng Kapisanan na ito, unang 1873-1878, para sa ikalawang oras mula sa 1886 na 1890, at para sa ikatlong oras mula 1895 hanggang sa kanyang kamatayan sa 1907. Thomson nagsilbi bilang pangulo ng pa ng isang ikatlong lipunan kapag siya ay elected bilang pangulo ng British Association para sa pagpapalaganap ng Science sa 1871.