Lenses and Waves

THE 'PROJET' OF 1672 137
consisted of six generally accepted principles required to elaborate
mathematical theory. In a way reminiscent of the ‘Projet’, Barrow said that
these hypotheses, as he called them, were empirically founded but also
needed some sort of explanation:
“The hypotheses agree with observation, but we must also fortify them with some
support of reason, by treading on the foundations and suppositions laid down.” 105
In his first lecture Barrow discussed these foundations and suppositions,
although he mainly defined terms like ‘light’ (in relation to illumination,
images, ‘phasmata’ and the like), ‘refraction’ and ‘opaque’. He then proposed
a theory of light that is a hybrid of viewing light as a pulse and as a pressure
propagated simultaneously in the first and second matter of the Cartesian
scheme. 106 Whatever he meant precisely, Barrow did not lend much weight to
this theory.
“Still, since it is desirable for me to lay some preliminary foundations about the nature of
light, to agree with my explanation of hypotheses which I shall later offer, I conceive
the facts to be these, or something like them: …” 107
These preliminary foundations merely needed to be consistent with the
ensuing explanations of the laws of optics and Barrow expressly did not
claim any authority in these matters. 108 In what followed, Barrow’s theory of
light came down to considering a ray to be the path traced out by a pulse-like
entity, “… two-dimensional and like a sort of rectangular parallelogram lying
in a plane at right angles to the surface of the inflecting medium, …” 109 This
conception of a physical ray traced out by a line of light emitted by a shining
object went back to Hobbes’ theory of light. Barrow’s derivation of the law
of sines can likewise be traced back to Hobbes. 110 With this definition of a
ray, Barrow now could make ‘some attempt to explain’ the laws of optics,
stressing once more that they were empirically founded:
“… I need practically nothing else to explain the hypotheses which all opticians in
common with each other assume and which must necessarily be laid down as a
foundation for building up this science. I shall make no effort to prove what I have
said, since … it seems clearer than light itself that such proofs cannot be given,
although a number of experiments show that they are given in actuality.” 111
Besides accounting for the rectilinearity of light rays, he discussed some basic
assumptions of geometrical optics, like the fact that ‘inflections’ take place in
a plane perpendicular to the surface of the ‘inflecting’ medium. Then, in the
second lecture, he moved on to these ‘inflections’ proper, reflection and
105
Barrow, Lectiones, [26].
106
Barrow, Lectiones, [15-16].
107
Barrow, Lectiones, [15]; (emphasis in original).
108
Barrow, Lectiones, [8, 15].
109
Barrow, Lectiones, [26].
110
Shapiro, “Kinematic optics”, 177-181. Hobbes’ optics is discussed in the next chapter, section 5.2.1.
111 Barrow, Lectiones, [17]