Mr Bennett, A Double-Four Mechanism. 395 
four points A, B, C, D on one side of #, and A’, B’, C’, D’ their 
images in #, on the other. The figure contains six isograms, such 
as ABA’B’. Hach gives a ratio, such as AB/AB’ (less than unity), 
for the lengths of the pairs of equal sides. The figure depends 
for its shape on only six parameters, so that, if the six ratios are 
kept constant, normal expectation indicates an invariable form for 
the figure, its size alone remaining variable. A porism, however, 
Fig. 2. 
upsets this presumption. The six ratios are subject to a relation 
which may be found thus :— 
Taking any point P it is possible (owing to the collinearity 
of the middle points of 4A’, BB’, CC’, DD’) to find constant 
multipliers a, b, c,d such that the equation 
a(PA?+ PA”) + b(PB? + PB”) +¢(PC? + PC”) 
see a hee Een IO) ere: (i) 
