304 Proceedings of the Royal Society 
In 1856 he first projected a treatise on shipbuilding, which he 
ultimately finished in 1866, and published in conjunction with J. 
R. Napier and others. Of this treatise it may be said it is unique 
of its kind. It has recently been published in G-erman. 
In the autumn of 1857 he contrived a theory of skin resistance 
of ships, based on experiments furnished by J. R. Napier, and in 
the next year applied it with complete success to the steam-ship 
“Admiral,” verifying his theory. 
The work on shipbuilding occupied much of his spare time. He 
records at several intervals, from 1863 to 1866, brief notes, such as 
“Working hard at Treatise on Shipbuiling,” “Researches on 
Neoids,” “ Stream lines.” In 1866 the folio treatise was pub- 
lished. Rankine wrote the greater portion of it, and was the editor. 
The preparation of this treatise led to a series of researches on 
fluid motion, which are acknowledged to be of the highest import- 
ance, and they certainly belong to the most abstruse parts of 
mathematical science. Rankine’s genius overcame all difficulties, 
and the “Theory of the Propagation of Waves,” the “Theory of 
Waves near the Surface of Deep Water,” and his investigations on 
plane water lines in two dimensions, i.e., of the lines of motion 
of water flowing past a ship, advanced, in his hands, the appli- 
cation of science to naval architecture as much as his discovery of 
the second law of thermodynamics did that of the theory of the 
steam-engine and other heat engines. For, the practical use of his 
theory of oogenous water-lines reproduces known good forms of 
water-line, and even reproduces their numerous varieties , which 
differ very much from each other. In fact, there is no form of 
water-line that has been found to answer in practice which cannot 
be imitated by means of oogenous neoids — that is, ship-shape 
curves generated from an oval. 
Besides Mr J. R. Napier, the late John Elder was the intimate 
friend of Rankine, and the bold improvements introduced by 
that distinguished engineer in marine steam machinery were con- 
stantly discussed with Rankine, whose scientific aid in insuring 
success was gracefully and munificently acknowledged by Elder’s 
widow, by the gift of a large endowment to increase the emolu- 
ments of the chair of Civil Engineering and Mechanics. 
Rankine’s professional business was that of a consulting engi- 
