334 
contains further researches in regard to the curves in the case 
of the particular theorem, or say, as to the rhezic curves 
P=0, Q=0. 
A communication was also read by Professor Cayley 
(2) On Peaucillier’s Parallel Motion. 
(3) On some models of Peaucillier’s and other Parallel 
Motions. By Mr Ennis. 
DK isa fixed guide upon which A slides. ABC is a rod 
moveable round a pin at A and bisected in B. BD is a rod 
whose length is }4C and moveable round pins at B and D. 
It is manifest that C will trace out a straight line CDC’ per- 
pendicular to KD. Supposing CAD (=C’AD) when greatest 
to equal 45°, the space described by C to space described by 
A ::2: /2—l,oras5 : 1 nearly. This method may therefore 
often be employed with advantage to reduce friction instead of 
employing a guide for C. The friction may be again reduced 
almost to any extent by the following arrangement. 
The point A instead of sliding is attached by a pin to the 
