57

Optics.

it would represent theMagnified, and more

Obiect erect, equallydistinct and bright J

v *

last Article we substitute its V alue -—, it gives the

•p 2a

equation above in this. _ . .

9- Hence also it follows, that the Ei ror K F is al-

as the Sagitta or versed Sine G B, or the S.quare

ot *e Semichord N G. „ . . ,

. 1 °. If the Ray A N K be given in Position, and a n

L) any other parallel Ray nearer to the Axis, and on

* he oth «r Side j os which let n k be the refracted Part

' utt *ng the Axis in k, and the refracted Ray N K in Q*

from Q draw O a perpendicular to the Axis : Then

* l11 the Line K 0 become greatest of all, or a Man-

“ m -> when the Ray a n is about half the Distance of

e Ray A N from the Axis. ,

ror, draw n g; perpendicular to the Axis, an pnn ^ - v . _ r ~ f and KF=ii and since,

v x? . i F. or f :

_ __ . n g perpciiw.^-.. ...

C7 !,) G K ~f, and K F — £ ; and since,

rt ’ 9s we have N G 1 : n» ! :: K F : IF, or / : ■

w : f, . v 2 h

h tzr2

byy.

aave - vt-h-

. T r TP __ ZZ K, A --

kF, therefore K b

hw

n. Moreover, G K : G N :: K e : Qj > whereforeAlsogn : GK ( = g i nearly)::

y s ,

therefore ^ o -p K o ^ ~ T *

v v

; and dividing by v y, and reducing the

ctuation, we have i — - ^

13. Now to determine r a Maximum, we must make

. hi 1 — %bv<u _ n .

-hw

Fluxion = 0, that is, § —whence we get b i y — ■y.b'vv

. y_h F y

yy ,

e t that is, by~* h *’