Most Learned and Distinguished Sir,--I have read the paper you
were kind enough to send me, and return
you many thanks for the communication. I regret that I
have not been able quite to follow your meaning, though you
explain it sufficiently clearly, whether you think that
there is any cause for making the apertures of the glasses
small, except that the rays coming from a single point
are not collected accurately at another single point, but in
a small area which we generally call the mechanical point,
and that this small area is greater or less in proportion to
the size of the aperture. Further, I ask whether the lenses
which you call "pandochae" correct this fault, so that the
mechanical point or small area, on which the rays coming
from a single point are after refraction collected, always
preserves the same proportional size, whether the aperture
be small or large. If so, one may enlarge the aperture as
much as one likes, and consequently these lenses will be
far superior to those of any other shape known to me; if not,
I hardly see why you praise them so greatly beyond
common lenses. For circular lenses have everywhere the same axis;
therefore, when we employ them, we must
regard all the points of an object as placed in the optic axis;
although all the points of the object be not at the same
distance, the difference arising thence will not be perceptible,
when the objects are very remote; because then the
rays coming from a single point would, as they enter the glass,
be regarded as parallel. I think your lenses might be
of service in obtaining a more distinct representation of all the
objects, when we wish to include several objects in
one view, as we do, when we employ very large convex circular lenses.
However, I would rather suspend my
judgment about all these details, till you have more clearly explained
your meaning, as I heartily beg you to do. I
have, as you requested, sent the other copy of your paper to
Mr. * * * *.
He answers, that he has at present no time
to study it, but he hopes to have leisure in a week or two.
I have not yet seen the "Prodromo" of Francis Lana, nor the
"Physico-Mechanical Reflections" of John Oltius. What I
more regret is, that your "Physical Hypothesis" has not yet
come to my hands, nor is there a copy for sale here at
the Hague. The gift, therefore, which you so liberally promise
me will be most acceptable to me; if I can be of use to
you in any other matter, you will always
find me most ready. I hope you will not think it too irksome
to reply to this short note.
B. de Spinoza.
The Hague, 9 Nov., 1671.
P.S. Mr. Diemerbroech does not live here. I am, therefore,
forced to entrust this to an ordinary letter-carrier. I doubt
not that you know someone at the Hague, who would take charge
of our letters; I should like to hear of such a
person, that our correspondence might be more conveniently and
securely taken care of. If the "Tractatus Theologico-Politicus"
has not yet come to your hands, I will, unless you
have any objection, send you a copy. Farewell.