Encyclopaedia Britannica > Volume 15, NIC-PAR

Theory. OPT
Law of transparent substance, Sir Isaac Newton enjoins us to
Refraction, employ a ray of light falling on the surface quam obli-
‘ quissime. But Mr Beguelin found, that when the obli¬
quity of incidence in glass was about 89° 50', no light
was refracted, but that it was wholly reflected. Pie al¬
so observed, that when he gradually increased the obli¬
quity of incidence on the superior surface of the glass,
the light which emerged last of all did not skim a-
long the surface, making an angle of 90° with the per¬
pendicular, as it should do by the Newtonian theory,
but made an angle of more than ten minutes with the
posterior surface. Also, when he began with very great
obliquities, so that all the light was reflected back into
the glass, and gradually diminished the obliquity of in¬
cidence, the first ray ol light which emerged did not
skim along the surface, but was raised about 10 or 15
122 minutes.
be the ne- .a^ ^iese phenomena are necessary consequences of
cessarycon-our principles, combined with what observation teaches
lequencc us concerning the forces which bodies exert on the rays
ot that of light. It is evident, from the experiments of Gri-
ofcourse a maldi and Nevvton> that light is both attracted and re-
oonfirraa- Pehed by solid bodies. NewTton’s sagacious analysis of
tionofit. these experiments discovered several alternations of ac¬
tual inflection and deflection j and he gives us the pre¬
cise distance from the body when some of these attrac¬
tions end and repulsion commences j and the most re¬
mote action to be observed in bis experiments is repul¬
sion. Pet us suppose this to be the case, although it be
Plate not absolutely necessary. Let us suppose that the forces
ccclxxvii. are represented by the ordinates of a curve a b n p c
7- which crosses the abscissa in b. Draw b 0 parallel to
the refracting surface. When the obliquity of incidence
of the ray AB has become so great, that its path in the
glass, or in the refracting stratum, does not cut, but on¬
ly touches the line 0 b, it can penetrate no further, but
is totally reflected j and this must happen in all greater
obliquities. On the other hand, when the ray LE,
moving within the glass, has but a very small perpendi¬
cular velocity, it will penetrate the refracting stratum
no further than till this perpendicular velocity is extin¬
guished, and its path becomes parallel to the surface,
and it will be reflected back. As the perpendicular
velocity increases by diminishing the obliquity of inci¬
dence, it will penetrate farther; and the last reflection
will happen when it penetrates so far that itspath touches
the line 0 b. Now diminish the obliquity by a single
second •, the light will get over the line 0 b, ivill de¬
scribe an arch 0 cl H concave upwards, and will emerge
in a direction BA, which does not skim the surface, but
is sensibly raised above it. And thus the facts observed
by M. Beguelin, instead of being an objection against
this theory, afford an argument in its favour.
Euler’s Cor. 6. Those philosophers who maintain the theory
tlieory of of undulation, are under the necessity of connecting the
undulation dispersive powers of bodies with their mean refractive
^aryt(J powers. M. Euler has attempted to deduce a necessary
difference in the velocity of the rays of different colours
from the different frequency of the undalations, which
he assigns as the cause of their different colorific powers.
His reasoning on this subject is of the most delicate na¬
ture, and unintelligible to such as are not completely
master of the infinitesimal calculus of partial differences,
and is unsatisfactory to such as are able to go through
its intricacies. It is contradicted by fact. He says,
A ^ Q. 2][1
that musical sounds which differ greatly in acuteness are Law of
propagated through the air with different velocities : but Refraction.
one of the smallest bells in the chimes of St Giles’s '
church m Edinburgh was struck against the rim of the
very deep-toned bell on which the hours are struck.
W hen the sound was listened to by a nice observer at
the distance of more than two miles, no interval what¬
ever could be observed. A similar experiment was ex¬
hibited to M. Euler himself, by means of a curious in¬
strument used at St Petersburg, and which mav be
heard at three or four miles distance. But the experi¬
ment with the bells is unexceptionable, as the two sounds
were produced in the very same instant. This connec¬
tion between the refrangibility in general and the velo¬
city must be admitted, in its full extent, in every at¬
tempt to explain refraction by undulation ; and Euler
was forced by it to adopt a certain consequence which
made a necessary connection between the mean refrac¬
tion and the dispersion of heterogeneous rays. Confident
of his analysis, he gave a deaf ear to all that was told
him of Mr Dollond’s improvements on telescopes, and
asserted, that they could not be such as were related ;
for an increase of mean refraction must always be ac¬
companied with a determined increase of dispersion.
Newton had said the same thing, being misled by a li¬
mited view of his own principles ; but the dispersion as¬
signed by him was different from that assigned by Eu¬
ler. The dispute between Euler and Doilond was con¬
fined to the decision of this question only ; and when
some glasses made by a German chemist at Petersburg
convinced Euler that his determination was erroneous,
he did not give up the principle which had forced him
to this determination of the dispersion, but immediately
introduced a new theory of the achromatic telescopes of
Doilond ; a theory which took the artists out of the
track marked out by mathematicians, and in which
they had made considerable advances, and led them in¬
to another path, proposing maxims of construction hi¬
therto untried, and inconsistent with real improvements
which they had already made. The leading principle in an£}
this theory is to arrange the different ultimate images of leads art-
a point which arise either from the errors of a spherical‘sts-.
figure or different refrangibility, in a straight line pas¬
sing through the centre of the eye. The theory itself
is specious ; and it requires great mathematical skill to
accomplish this point, and hardly less to decide on the
propriety of the construction which it recommends. It
is therefore but little known. But that it is a false
theory, is evident from one simple consideration. In
the most indistinct vision arising from the worst con¬
struction, this rectilineal arrangement of the images ob¬
tains completely in that pencil which is situated in the
axis, and yet the vision is indistinct. But, what is to
our present purpose, this new7 theory is purely mathema¬
tical, suiting any observed dispersive power, and has no
connection with the physical theory of undulations, or
indeed with any mechanical principles whatever. But,
by admitting any dispersive power, whatever may be
the mean refraction, all the physical doctrines in his
Nova Theoria Lucis et Colorum are overlooked, and
therefore never once mentioned, although the effects of
M. Zeiher’s glass are taken notice of as inconsistent with
that mechanical proposition of Newton’s which occa¬
sioned the whole dispute between Euler and Doilond.
They are indeed inconsistent with the universality of
D d 2 that