56 M i c r o s c o p i c a l E s s a y s .
three inches long, on the board D ; draw three lines with ink on
this piece of piper, fo as to divide it into four equal parts, taking
care that the middle of the paper correfponds with the center o f
the-iens. There is alfo a Hiding eye-piece, which is reprefented
at e.
Take this apparatus into the darkeft part o f the room, but op-
polite to the window; direfit the glafs towards any remarkable
and diftant objefit which is out of doors, and move the Hiding
piece B, until the image o f the objeff on the papër is fharp and
clear. The diftance between the face of the paper and the lens,
(which is fliewn on the fide o f the rule by the divilions thereon)
is the focus o f the glafs ; now fet the eye-piece e E to thé; fame
diftance on the other fide of the glafs, then with one eye clofe to
the fight at e, look at the magnified image 'o f the lines, and
with the other eye at the lines themfelves : the image, feen by
means o f the glafs, and exprefled in the figure by the dotted
lines, will be double the breadth of the fame objeff feen by the
natural eye. This will be found to be true, whatfoever is the focus
o f the lens with which the experiment is made.
This experiment is rendered more fimple to thofe who are not
accuflomed to obferve with both eyes at the fame time, by
making ufe o f half a lens, and placing thediameter perpendicular
to the rule, as they may then readily view the magnified image
and real objeff with the fame glance of the eye, and thus compare
them together with eafe and accuracy.
Let the angle A F B, Fig. 3, Plate II. A , reprefent that which is.
formed at the naked eye, by the rays o f light which pafs from theextremities
extremities o f the object, and unite at the eye in the point F.
The angle D F E is formed o f the two rays, which at firfi proceeded
parallel to each -other from the extremities o f the objeff, but that
were afterwards fo refracted, or bent, by patfing through the
glafs, as to unite at it’s focal point F. C O is equal to the focal
diftance o f the lens on the fide next the objefit, C F equal thereto
on the fide next the eye, F O the diflanee o f the eye.
From the -allowed principles of optics, it is evident, that the.
objeff would appear double the fize to the eye at c, that it would
to the eye when placed at F ; becaufe the diftance F O is double
the diftance CO . We have only to prove then, that the angle
A C B is equal to the angle I F K, in order to eftablifh the
propofition.
The optical axis is perpendicular to the glafs and the furface o f
the objeff. The rays A I, B K, which flow from the points A B,
are parallel to each other, and perpendicular to the glafs, till
they arrive at i t ; they are then refraffed, and proceed to F,
where they form the triangle IF K , refting on the bafe I K : now
as C F is equal to C O, and I K is equal to A B, the two triangles
A C B IF K are fimilar, and confequently the angle
at C is equal to the angle F. I f the vifual rays are continued to
the furface of the objeff, they will form the triangle D F E,
equiangled to the triangle A B C ; and therefore, as C O is to A B,
fo is F ’D to D E ; and confequently, the apparent diameter of
the objeff feen through the lens, is double the fize that it is w hen
viewed by the naked eye. No notice is here taken o f die double
refraffion o f the rays, as it does not affeff the demonftration.
H If