Avšak analytické společnosti nebyly přežít na velmi dlouho. Herschel absolvoval v roce 1813 při první místo v závěrečné zkoušce.
Herschel did not offer these three approaches with equal recommendation for he believed that the algebraic approach of Lagrange was the right one. However the Analytical Society did not survive for very long. Herschel graduated in 1813 taking first place in the final examination.