Routledge History of Philosophy Volume IV

RENAISSANCE AND SEVENTEENTH-CENTURY RATIONALISM 119
motion whose degree of speed was half of the last and highest degree of
speed of the former uniformly accelerated motion. 40
The medieval version of this theorem is now usually referred to as the Merton
rule, after its probable origins in Merton College, Oxford, in the first half of the
fourteenth century. There has been much discussion of the possibility of
medieval influence on Galileo in this regard, but it seems ill-advised to look for
anything more specific than the important step of (implicitly or explicitly)
representing the intensities of speeds by segments of straight lines.
The second theorem and its corollary descend from speeds, or their intensities,
to distances. The theorem shows that in a uniformly accelerated motion the
distances traversed are as the squares of the times, and the corollary that the
successive distances traversed in equal times, starting from rest, are as the
successive odd numbers 1, 3, 5, 7,…. We are now reaching directly measurable
quantities, and so the stage is set for Simplicio to ask for experimental evidence
to show whether this is in fact the mode of acceleration employed by nature in
the case of falling bodies. Salviati willingly complies.
As a true man of science [scienziato] you make a very reasonable demand,
and one that is customary and appropriate in the sciences which apply
mathematical demonstrations to physical conclusions, as is seen with
perspectivists, with astronomers, with mechanicians, with musicians, and
others who confirm with sensory experiences their principles, which are
the foundations of the whole succeeding structure. 41
The experiments involved rolling well-prepared bronze balls down different
lengths of an extremely smooth channel arranged at different inclinations to the
horizontal, and measuring the times of their descents by water running out of a
hole in a pail of water. One’s initial impression may be that the set-up smacks of
Heath Robinson (or Rube Goldberg), but repetitions of the experiments in recent
years have shown that they can be surprisingly accurate, and so we may say that
they did indeed give Galileo strong support for his ‘law’ of falling bodies.
The burden of the Fourth Day of the Discorsi is to combine the horizontal and
the vertical, and so produce a general description of the behaviour of unimpeded
‘natural’ motion. The result is the famous parabolic path for projectiles. This was
admirable mathematically but less satisfactory empirically for, as gunners and
others were quick to point out, the maximum horizontal trajectory was not to be
achieved by firing at an elevation of 45°, nor did actual cannon balls follow a
neat mathematical parabola. 42 All this goes to show the extent to which, despite
his practical rhetoric, such as that provided by setting the Discorsi in the Arsenal
at Venice, the success of Galileo’s mechanics depended on his focusing on ideal
situations and ignoring many of the messy complexities of the actual physical
world.