Lenses and Waves

1655-1672 - DE ABERRATIONE 61
well how to grind lenses to suitable proportions and
configure appropriately. The nature of this knowledge
and to what extent they understood the dioptrical
properties of lenses will be discussed now. Note that
this is a discussion of very limited scope, determined
by the considerations and activities of Huygens, that
passes over the a wealth of historical knowledge that
can be, and has been, gathered regarding the telescope
making trade. 35
A booklet on spectacles written in 1623 gives an
indication of the understanding their manufacturers
had of glasses. Uso de los antojos was written by the
Andalusian licentiate Daza de Valdez. It explained
how to choose glasses of appropriate strength for a
patient. Daza described a procedure to determine the
‘grado’ of a given lens (Figure 23). 36 He drew two solid
circles X and Q of unequal diameter on a sheet of
paper as well as a specific scale at one of the circles. A
glass was then positioned on the scale in such a way
that both circles were seen equally large. The position
of the lens on the scale gave its ‘grado’. 37 Daza did not
explain the method, he only described how it was
employed. It was a practical procedure that did not require any
understanding of its effect on rays.
A manuscript written around 1670 in Rome by a certain Giovanni
Bolantio contains a similar kind of procedural knowledge. It discussed the
manufacture of telescopes and probably recorded the daily routine in some
workshop. 38 It contains two tables listing the ocular and objective lenses
needed to make a telescope of a specific strength, characterized by its length.
The lenses are characterized by the doubled radius of the pattern in which
they were ground. 39 Figure 23 Daza’s scale
With these tables at hand, the workman could choose the
patterns needed to make a telescope on order. Bolantio did not explain
whether he had constructed the tables himself nor how they were made.
Some dioptrical rules are implicit in them. For example, the length of a
35
See for example the recent, formidable study on Wiesel by Inge Keill which may serve as a guide to
themes and literature: Keil, Augustanus Opticus.
36
Daza, Uso de los antojos, 137-140. It appears that this classification in terms of ‘degrees’ was, at that time,
replacing an older one in terms of the common age of someone bearing spectacles of a particular
strength. The ‘grados’ Daza employs seem to be identical with the ‘punti’ Garzoni mentions in his
discussion of the craft in La piazza universale (1585). See also: Pflugk, “Beiträge”, 50-55.
37
Daza did not explain how the scale on the paper was established. Von Rohr has given an alluring
suggestion as to how such a scale might be construed. Spectacle makers knew that multiple lenses of a
given strength could be substituted by a stronger one to reach the same effect. Thus the first position on
the scale was determined by a weak lens and the other positions determined by the amount of equal lenses
which had to be put in those positions. Von Rohr, “Versuch”, 4.
38
Bedini & Bennet, “Treatise”.
39
Bedini & Bennet, “Treatise”, 120-121.