INFINITE LINKS. 295
connected to the lever c. We may therefore allow it to take the place of the latter : we shall find further on that kinematically the two are identical. The new arrangement may be written, beginning with a,
C+ ... || ... Ct C- ... || ... C- C+ ... || ... At A- ... || ... C,
for we have already chosen ( 57) the symbol A for a circular sector. The contracted formula is (CIA"). This shows even more distinctly than in the former case that the links must be so proportioned that c slides backwards and forwards in its curved path ; for otherwise the pair At A" would be insufficient.
We can now, without introducing any constructive difficulties,
FIG. 214.
make the radius of A of any required magnitude ; the only alteration will be that the slot and the slider become flatter than before. Let us therefore make this radius infinite. With this the distance of the centre 4 from the point 1, that is the length of the link d, must also become infinite. In other words the links c and d, or the distances 3.4 and 1.4, are made infinite simultaneously ; so that
c = d = co .
Our last formula will then require alteration, for the arc A becomes a prism P, and the pair AtA~ is replaced by the prism- pair PtP~. It follows from the equality of c and d that the line in which 3 moves relatively to d passes through the point 1, and is perpendicular to both the axes 3 and 1. The new chain, there- fore, which is shown in the following figure, and which is already known to us, must be written
C+ . ,. CtC- .,. || ., C- C+ . , JL - PtP~ . -JL ... C-
