638 
Proceedings of the Royal Society 
In 1869 we had “ The Practical Application of Eeciprocal Figures 
to the Calculation of Strains on Framework,” in which he ex- 
emplified in a very clear manner the mode of applying to important 
statical questions a beautiful principle, due in part to Eankine hut 
mainly to Clerk-Maxwell. 
The paper for which the award of the Keith Prize is now made 
is more thoroughly original, and may he roughly described as an 
extension of Maxwell’s principle to the kinetics of machinery, where 
all parts move in one plane. It is entitled “ The Application 
of Graphic Methods to the Determination of the Efficiency of 
Machinery.” The first part was read to the Society in 1877, and 
the second in the following year. All three of these papers are in 
our Transactions. 
Among his other contributions may he mentioned his application 
(in conjunction with Professor Ewing) of the Phonograph records 
to the “ Harmonic Analysis of certain Vowel Sounds.” This is an 
ingenious and elaborate piece of work, and shows us (among other 
things) within what wide limits the components of a sound may 
vary while it is still recognised by the ear as having a definite vowel 
quality. 
Professor Jenkin, in handing you this medal I express, I am sure, 
the feelings of all the Fellows of the Society, when I say that we 
thank you heartily for the valuable contributions you have already 
sent to our Transactions, and that we look with confidence for an 
additional series. 
Professor Jenkin then took the Chair. 
The following communications were read : — 
1. Non-Euclidean Geometry. By Professor Chrystal. 
(Plate XX.) 
When I had the honour of being asked by the Council of the Eoyal 
Society to give the following address, I chose the subject partly because 
it had been brought under the notice of the fellows by my predecessor, 
Professor Kelland. His memoir was written comparatively early in 
the history of the subject; and he seems to have been but little 
acquainted with what others had done even up to the time at which 
