| 1854 | Trinity College, Cambridge - 2nd Wrangler and First Smith's Prize |
| 1856 | Fellow of the Royal Society of Edinburgh |
| 1857 | Adams Prize |
| 1860 | Rumford Medal of Royal Society |
| 1861 | FRS |
| 1870 | LL.D. University of Edinburgh Keith Prize, Royal Society of Edinburgh |
| 1871 | Honorary Fellow of Trinity College, Cambridge University |
| 1874 | Foreign Honorary Member of American Academy of Arts and Sciences in Boston Member of American Philosophical Society of Philadelphia |
| 1875 | Corresponding Member of Royal Society of Sciences of Göttingen |
| 1876 | DCL, Oxford University Hon. Member, New York Academy of Science |
| 1877 | Member of Royal Academy of Science of Amsterdam Foreign Corresponding Member in the Mathematico-Natural-Science Class of the Imperial Academy of Sciences of Vienna |
| 1878-65 | Volta Medal, Doctor of Physical Science, honoris causa, in University of Padua |
Last modified 24 March 2006