The lines _pa_, _pb_,
_pc_, and _pd_ are velocity vectors. This novel, original, and powerful
analytical method was not generally adopted in English or American
schools until nearly 50 years after its inception. From _Transactions of
the Royal Society of Edinburgh_ (1882-1885, vol. 32, pl. 82).]

By 1885 nearly all the tools for modern kinematic analysis had been
forged. Before discussing subsequent developments in analysis and
synthesis, however, it will be profitable to inquire what the
mechanician--designer and builder of machines--was doing while all of
this intellectual effort was being expended.

Mechanicians and Mechanisms

While the inductive process of recognizing and stating true principles
of the kinematics of mechanisms was proceeding through three generations
of French, English, and finally German scholars, the actual design of
mechanisms went ahead with scant regard for what the scholars were doing
and saying.

After the demonstration by Boulton and Watt that large mechanisms could
be wrought with sufficient precision to be useful, the English tool
builders Maudslay, Roberts, Clement, Nasmyth, and Whitworth developed
machine tools of increasing size and truth. The design of other
machinery kept pace with--sometimes just behind, sometimes just ahead
of--the capacity and capability of machine tools. In general, there was
an increasing sophistication of mechanisms that could only be accounted
for by an increase of information with which the individual designer
could start.

Reuleaux pointed out in 1875 that the "almost feverish progress made in
the regions of technical work" was "not a consequence of any increased
capacity for intellectual action in the race, but only the perfecting
and extending of the tools with which the intellect works." These tools,
he said, "have increased in number just like those in the modern
mechanical workshop--the men who work them remain the same." Reuleaux
went on to say that the theory and practice of machine-kinematics had
"carried on a separate existence side by side." The reason for this
failure to apply theory to practice, and vice versa, must be sought in
the defects of the theory, he thought, because "the mechanisms
themselves have been quietly developed in practical machine-design, by
invention and improvement, regardless of whether or not they were
accorded any direct and proper theoretical recognition." He pointed out
that the theories had thus far "furnished n