together. This invention is in universal use.
In 1841 he published his ‘Principles of Mechanism.’ In this work he reduced the study of what he called pure mechanism to a system. It is the earliest attempt to develop, with anything like completeness, the science of machines considered from the kinematic point of view, without reference to the forces which are at work or to the energy which is transmitted. A machine, according to him, is a contrivance for producing a specific relation between the motions of one of its parts and another. To express this relation completely the two elements velocity-ratio and directional relation are required. Accordingly he groups machines in three general classes: (1) those in which both of these elements are constant; (2) those in which one (a) is constant and the other (b) is variable; (3) those in which this variability is reversed. In each class there are divisions depending on the mode in which motion is communicated, whether by rolling contact, sliding contact, link-work, and so forth. The first part of the book expounds this system of classification as applied to elementary combinations of moving pieces; the second part deals with what he calls aggregate combinations, in which two or more elementary combinations co-operate in producing a relation of motion between the driving and following parts of the machine. A second edition of this work appeared in 1870.
In 1849 Willis was a member of a royal commission appointed to inquire into the application of iron to railway structures, and contributed to the report of the commissioners Appendix B, ‘On the effects produced by causing weights to travel over elastic bars,’ reprinted in Barlow's ‘Treatise on the Strength of Timber.’
In 1851 he was one of the jurors of the Great Exhibition. In that capacity he drew up the report for the class of manufacturing machines and tools, and contributed a lecture to the series on the results of the exhibition, organised by the Society of Arts in 1852. He was also a vice-president at the Paris Exhibition of 1855, and reporter of the class for the machinery of textile fabrics. In connection with this office he published in 1857 a report on machinery for woven fabrics, for which he received the cross of the Legion of Honour. When the government school of mines was established in Jermyn Street in 1853, Willis was engaged as lecturer on applied mechanics. In 1862 he was president of the British Association, which that year met at Cambridge; and in the following year at Newcastle he presided over the mechanical section.
During all these years Willis was studying architecture and archæology with the same energy as mechanism, and perhaps with even greater originality. In 1835, after a rapid tour through a part of France, Germany, and Italy, he published ‘Remarks on the Architecture of the Middle Ages, especially of Italy,’ a work which first called serious attention to the Gothic style, and which in many ways is still without a rival. He treated a building as he treated a machine: he took it to pieces; he pointed out what was structural and what was decorative, what was imitated and what was original; and how the most complex forms of mediæval invention might be reduced to simple elements. This publication was the starting-point of that portion of his career which was devoted to studies combining practical architecture with historical and antiquarian research. For these he was singularly well fitted. He had no sentiment and no preconceived theory. His mechanical knowledge enabled him to understand construction, and his power of observation was so keen that he never failed to seize the meaning of the faintest indication that fell in his way. The industry that he brought to bear on these pursuits was amazing. He learnt to decipher mediæval handwriting with rapidity and accuracy, and devoted much time to the study of manuscript authorities; he mastered not only the whole literature of the subject, but that of the history that bore upon it; and, as the mass of notes bequeathed by him to the present writer shows, he tabulated the information thus gained with infinite care, so as to have it always ready to his hand when wanted.
The ‘Remarks’ were succeeded by an elaborate paper ‘On the Construction of the Vaults of the Middle Ages’ (Trans. Inst. Brit. Arch. 1841), an essay as remarkable for thoroughness of treatment as for the beauty of the illustrations, all drawn by himself. By this time his reputation for architectural knowledge was established, for in this year the dean and chapter of Hereford consulted him respecting the condition of their cathedral. He published the result of his investigations in a ‘Report of a Survey of the Dilapidated Portions of Hereford Cathedral in the year 1841’ (Hereford, 1842, 8vo; and London, 1842, 4to, with plates). In this same year he invented and described the ‘Cymagraph for copying mouldings’ (Engineers' Journ. July 1842), a contrivance which he himself used exten-
