n analyzing the process by which a machine was designed, Willis
observed: "When the mind of a mechanician is occupied with the
contrivance of a machine, he must wait until, in the midst of his
meditations, some happy combination presents itself to his mind which
may answer his purpose." He ventured the opinion that at this stage of
the design process "the motions of the machine are the principal subject
of contemplation, rather than the forces applied to it, or the work it
has to do." Therefore he was prepared to adopt without reservation
Ampere's view of kinematics, and, if possible, to make the science
useful to engineers by stating principles that could be applied without
having to fit the problem at hand into the framework of the systems of
classification and description that had gone before. He appraised the
"celebrated system" of Lanz and Betancourt as "a merely popular
arrangement, notwithstanding the apparently scientific simplicity of the
scheme." He rejected this scheme because "no attempt is made to subject
the motions to calculation, or to reduce these laws to general formulas,
for which indeed the system is totally unfitted."

Borgnis had done a better job, Willis thought, in actually describing
machinery, with his "orders" based upon the functions of machine
elements or mechanisms within the machine, but again there was no means
suggested by which the kinematics of mechanisms could be systematically
investigated.

Although Willis commenced his treatise with yet another "synoptical
table of the elementary combinations of pure mechanism," his view
shifted quickly from description to analysis. He was consistent in his
pursuit of analytical methods for "pure mechanism," eschewing any
excursions into the realm of forces and absolute velocities. He grasped
the important concept of relative displacements of machine elements, and
based his treatment upon "the proportions and relations between the
velocities and directions of the pieces, and not upon their actual and
separate motions."[72]

[Footnote 72: _Ibid._, pp. iv, x-xii, xxi, 15.]

That he did not succeed in developing the "formulas" that would enable
the student to determine "all the forms and arrangements that are
applicable to the desired purpose"--that he did not present a rational
approach to synthesis--is not to be wondered at. Well over a century
later we still are nibbling at the fringes of the problem. Willis did,
nonetheless, give the thoughtfu