Mr Bennett, A Double-Four Mechanism. 401 
each separate set of four being congruent and homothetic. Such 
a parallelogram link-work may be generalized, obviously, to include 
any number of pieces linked to any number of others. A lattice- 
work, if made of two separately equal sets of arbitrarily curved slats, 
would afford a representative example. 
The parallelogram case and the isogram case above examined 
stand somewhat as companions among the species of double-four. 
For all other species the angles of the plates are equal or supple- 
mentary at every pin; and of these the most interesting has been 
specially treated by Fontené (Nouvelles Annales de Math. 1903, 
pp. 529—549, 1904, pp. 8—29). 
VOL. XVII. PT. Y, 27 
