Lenses and Waves

46 CHAPTER 2
were convinced that the new optical devices were useful. The telescopic sight
and the micrometer, together with the pendulum clock, brought about a
revolution in positional astronomy between 1665 and 1680. 137 In dioptrics it
raised the question of the exact properties of lenses anew.
Understanding the telescope
Apart from the practical problems of mounting and aligning, the theoretical
problem of the working of the telescope now became a matter of sustained
interest. As a result of his discussion with Hevelius over the reliability of
telescopic sights, Flamsteed realized that a theoretical justification of his
claims was also needed: “… to prove that optick glasses did not impose
upon or senses. then to shew that they might be applyed to instruments &
rectified as well as plaine sights.” 138 His chance to elaborate a dioptrical
account of the telescope came in the early 1680s, when, appointed Gresham
professor of Astronomy, he could deliver a series of lectures on astronomy.
In these lectures, he discussed instruments and their use at length and
included an account of dioptrics.
“Yet such has beene the fault of or time that hitherto very little materiall on this subject
has been published in or language. [Tho severall learned persons have done well
concerning opticks in ye latine Tongue. Yet how glasses may be applyed to instruments
& how the faults commonly committed in theire applycation might be amended or
rather shund & how all the difficultys suggested by ingenious persons who had not the
good to understand them aright might be avoyded the best authors of Dioptricks have
been hitherto silent. … I shall therefore make it my businesse in this & my following
lectures of this terme fully to explain the Nature of telescopes the reason of their
performances, how they may be applyed to Levells, Quadrants, & Sextants. & how the
instruments furnished with them may be so rectified & adjusted that they may be free
from all suspicion of errors]” 139
Flamsteed began with a discussion of the focal distances of convex lenses. It
has two notable features. First, he took the consequences of Newton’s
theory of colors into account by pointing out the chromatic aberration of
lenses. Second, the paucity of his demonstrations shows that he was not an
outstanding geometer. 140 By means of the sine law, he calculated the
refraction of single rays numerically and then compared the result with the
Keplerian rules for focal distances of a bundle of rays. By calculating
spherical aberration he discovered – as Huygens had done earlier – that the
aberration of a plano-convex lens varies considerably depending on which
side is turned towards the incident rays. He gave only a qualitative account of
chromatic abberation. On this basis he argued that only telescopes consisting
of two convex lenses are useful in astronomy, because these admit the
137
Van Helden, “Huygens and the astronomers”, 156-157; Van Helden, Measure, 127-129.
138
Flamsteed, Gresham lectures, 154.
139
Flamsteed, Gresham lectures, 119 & 132. Flamsteed later deleted the part between brackets.
140 Flamsteed, Gresham lectures, 120-127.